algebra.order.monoid.lemmas
⟷
Mathlib.Algebra.Order.Monoid.Lemmas
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
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Constantly extending monotone/antitone functions preserves their convexity.
@@ -244,6 +244,23 @@ variables [linear_order α] {a b c d : α} [covariant_class α α (*) (<)]
@[to_additive] lemma min_le_max_of_mul_le_mul (h : a * b ≤ c * d) : min a b ≤ max c d :=
by { simp_rw [min_le_iff, le_max_iff], contrapose! h, exact mul_lt_mul_of_lt_of_lt h.1.1 h.2.2 }
+end linear_order
+
+section linear_order
+variables [linear_order α] [covariant_class α α (*) (≤)] [covariant_class α α (swap (*)) (≤)]
+ {a b c d : α}
+
+@[to_additive max_add_add_le_max_add_max] lemma max_mul_mul_le_max_mul_max' :
+ max (a * b) (c * d) ≤ max a c * max b d :=
+max_le (mul_le_mul' (le_max_left _ _) $ le_max_left _ _) $
+ mul_le_mul' (le_max_right _ _) $ le_max_right _ _
+
+--TODO: Also missing `min_mul_min_le_min_mul_mul`
+@[to_additive min_add_min_le_min_add_add] lemma min_mul_min_le_min_mul_mul' :
+ min a c * min b d ≤ min (a * b) (c * d) :=
+le_min (mul_le_mul' (min_le_left _ _) $ min_le_left _ _) $
+ mul_le_mul' (min_le_right _ _) $ min_le_right _ _
+
end linear_order
end has_mul
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The existing strict_mono_pow
lemma is renamed to pow_strict_mono_right
to match the new pow_strict_mono_right'
.
From this zulip thread.
Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>
Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>
@@ -5,6 +5,7 @@ Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro, Johannes Hölzl, Dami
Yuyang Zhao
-/
import algebra.covariant_and_contravariant
+import order.min_max
/-!
# Ordered monoids
@@ -237,6 +238,14 @@ le_antisymm (le_of_mul_le_mul_right' h.le) (le_of_mul_le_mul_right' h.ge)
end partial_order
+section linear_order
+variables [linear_order α] {a b c d : α} [covariant_class α α (*) (<)]
+ [covariant_class α α (swap (*)) (<)]
+
+@[to_additive] lemma min_le_max_of_mul_le_mul (h : a * b ≤ c * d) : min a b ≤ max c d :=
+by { simp_rw [min_le_iff, le_max_iff], contrapose! h, exact mul_lt_mul_of_lt_of_lt h.1.1 h.2.2 }
+
+end linear_order
end has_mul
-- using one
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Define arithmetic operations on interval
/nonempty_interval
and prove their correctness.
@@ -797,6 +797,18 @@ iff.intro
and.intro ‹a = 1› ‹b = 1›)
(assume ⟨ha', hb'⟩, by rw [ha', hb', mul_one])
+@[to_additive] lemma mul_le_mul_iff_of_ge [covariant_class α α (*) (≤)]
+ [covariant_class α α (swap (*)) (≤)] [covariant_class α α (*) (<)]
+ [covariant_class α α (swap (*)) (<)] {a₁ a₂ b₁ b₂ : α} (ha : a₁ ≤ a₂) (hb : b₁ ≤ b₂) :
+ a₂ * b₂ ≤ a₁ * b₁ ↔ a₁ = a₂ ∧ b₁ = b₂ :=
+begin
+ refine ⟨λ h, _, by { rintro ⟨rfl, rfl⟩, refl }⟩,
+ simp only [eq_iff_le_not_lt, ha, hb, true_and],
+ refine ⟨λ ha, h.not_lt _, λ hb, h.not_lt _⟩,
+ { exact mul_lt_mul_of_lt_of_le ha hb },
+ { exact mul_lt_mul_of_le_of_lt ha hb }
+end
+
section left
variables [covariant_class α α (*) (≤)] {a b : α}
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(first ported)
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -1337,10 +1337,10 @@ theorem exists_square_le [CovariantClass α α (· * ·) (· < ·)] (a : α) :
by_cases h : a < 1
· use a
have : a * a < a * 1 := mul_lt_mul_left' h a
- rw [mul_one] at this
+ rw [mul_one] at this
exact le_of_lt this
· use 1
- push_neg at h
+ push_neg at h
rwa [mul_one]
#align exists_square_le exists_square_le
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -363,20 +363,24 @@ section LinearOrder
variable [LinearOrder α] [CovariantClass α α (· * ·) (· ≤ ·)]
[CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c d : α}
+#print max_mul_mul_le_max_mul_max' /-
@[to_additive max_add_add_le_max_add_max]
-theorem max_hMul_hMul_le_max_hMul_max' : max (a * b) (c * d) ≤ max a c * max b d :=
+theorem max_mul_mul_le_max_mul_max' : max (a * b) (c * d) ≤ max a c * max b d :=
max_le (mul_le_mul' (le_max_left _ _) <| le_max_left _ _) <|
mul_le_mul' (le_max_right _ _) <| le_max_right _ _
-#align max_mul_mul_le_max_mul_max' max_hMul_hMul_le_max_hMul_max'
+#align max_mul_mul_le_max_mul_max' max_mul_mul_le_max_mul_max'
#align max_add_add_le_max_add_max max_add_add_le_max_add_max
+-/
+#print min_mul_min_le_min_mul_mul' /-
--TODO: Also missing `min_mul_min_le_min_mul_mul`
@[to_additive min_add_min_le_min_add_add]
-theorem min_hMul_min_le_min_hMul_mul' : min a c * min b d ≤ min (a * b) (c * d) :=
+theorem min_mul_min_le_min_mul_mul' : min a c * min b d ≤ min (a * b) (c * d) :=
le_min (mul_le_mul' (min_le_left _ _) <| min_le_left _ _) <|
mul_le_mul' (min_le_right _ _) <| min_le_right _ _
-#align min_mul_min_le_min_mul_mul' min_hMul_min_le_min_hMul_mul'
+#align min_mul_min_le_min_mul_mul' min_mul_min_le_min_mul_mul'
#align min_add_min_le_min_add_add min_add_min_le_min_add_add
+-/
end LinearOrder
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -4,8 +4,8 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro, Johannes Hölzl, Damiano Testa,
Yuyang Zhao
-/
-import Mathbin.Algebra.CovariantAndContravariant
-import Mathbin.Order.MinMax
+import Algebra.CovariantAndContravariant
+import Order.MinMax
#align_import algebra.order.monoid.lemmas from "leanprover-community/mathlib"@"3ba15165bd6927679be7c22d6091a87337e3cd0c"
mathlib commit https://github.com/leanprover-community/mathlib/commit/001ffdc42920050657fd45bd2b8bfbec8eaaeb29
@@ -1263,7 +1263,6 @@ theorem mul_eq_one_iff' [CovariantClass α α (· * ·) (· ≤ ·)]
#align add_eq_zero_iff' add_eq_zero_iff'
-/
-#print mul_le_mul_iff_of_ge /-
@[to_additive]
theorem mul_le_mul_iff_of_ge [CovariantClass α α (· * ·) (· ≤ ·)]
[CovariantClass α α (swap (· * ·)) (· ≤ ·)] [CovariantClass α α (· * ·) (· < ·)]
@@ -1275,9 +1274,8 @@ theorem mul_le_mul_iff_of_ge [CovariantClass α α (· * ·) (· ≤ ·)]
refine' ⟨fun ha => h.not_lt _, fun hb => h.not_lt _⟩
· exact mul_lt_mul_of_lt_of_le ha hb
· exact mul_lt_mul_of_le_of_lt ha hb
-#align mul_le_mul_iff_of_ge mul_le_mul_iff_of_ge
-#align add_le_add_iff_of_ge add_le_add_iff_of_ge
--/
+#align mul_le_mul_iff_of_ge mul_le_mul_iff_of_geₓ
+#align add_le_add_iff_of_ge add_le_add_iff_of_geₓ
section Left
@@ -1383,9 +1381,8 @@ def Contravariant.toRightCancelSemigroup [ContravariantClass α α (swap (· *
#align contravariant.to_right_cancel_add_semigroup Contravariant.toAddRightCancelSemigroup
-/
-#print Left.mul_eq_mul_iff_eq_and_eq /-
@[to_additive]
-theorem Left.mul_eq_mul_iff_eq_and_eq [CovariantClass α α (· * ·) (· < ·)]
+theorem Left.hMul_eq_hMul_iff_eq_and_eq [CovariantClass α α (· * ·) (· < ·)]
[CovariantClass α α (swap (· * ·)) (· ≤ ·)] [ContravariantClass α α (· * ·) (· ≤ ·)]
[ContravariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c d : α} (hac : a ≤ c) (hbd : b ≤ d) :
a * b = c * d ↔ a = c ∧ b = d :=
@@ -1396,13 +1393,11 @@ theorem Left.mul_eq_mul_iff_eq_and_eq [CovariantClass α α (· * ·) (· < ·)]
rcases eq_or_lt_of_le hbd with (rfl | hbd)
· exact ⟨mul_right_cancel'' h, rfl⟩
exact ((Left.mul_lt_mul hac hbd).Ne h).elim
-#align left.mul_eq_mul_iff_eq_and_eq Left.mul_eq_mul_iff_eq_and_eq
+#align left.mul_eq_mul_iff_eq_and_eq Left.hMul_eq_hMul_iff_eq_and_eq
#align left.add_eq_add_iff_eq_and_eq Left.add_eq_add_iff_eq_and_eq
--/
-#print Right.mul_eq_mul_iff_eq_and_eq /-
@[to_additive]
-theorem Right.mul_eq_mul_iff_eq_and_eq [CovariantClass α α (· * ·) (· ≤ ·)]
+theorem Right.hMul_eq_hMul_iff_eq_and_eq [CovariantClass α α (· * ·) (· ≤ ·)]
[ContravariantClass α α (· * ·) (· ≤ ·)] [CovariantClass α α (swap (· * ·)) (· < ·)]
[ContravariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c d : α} (hac : a ≤ c) (hbd : b ≤ d) :
a * b = c * d ↔ a = c ∧ b = d :=
@@ -1413,12 +1408,11 @@ theorem Right.mul_eq_mul_iff_eq_and_eq [CovariantClass α α (· * ·) (· ≤
rcases eq_or_lt_of_le hbd with (rfl | hbd)
· exact ⟨mul_right_cancel'' h, rfl⟩
exact ((Right.mul_lt_mul hac hbd).Ne h).elim
-#align right.mul_eq_mul_iff_eq_and_eq Right.mul_eq_mul_iff_eq_and_eq
+#align right.mul_eq_mul_iff_eq_and_eq Right.hMul_eq_hMul_iff_eq_and_eq
#align right.add_eq_add_iff_eq_and_eq Right.add_eq_add_iff_eq_and_eq
--/
-alias mul_eq_mul_iff_eq_and_eq := Left.mul_eq_mul_iff_eq_and_eq
-#align mul_eq_mul_iff_eq_and_eq mul_eq_mul_iff_eq_and_eq
+alias mul_eq_mul_iff_eq_and_eq := Left.hMul_eq_hMul_iff_eq_and_eq
+#align mul_eq_mul_iff_eq_and_eq mul_eq_mul_iff_eq_and_eqₓ
attribute [to_additive] mul_eq_mul_iff_eq_and_eq
@@ -1813,23 +1807,19 @@ protected theorem inj [Mul α] [PartialOrder α] {a b c : α} (ha : MulLECancell
#align add_le_cancellable.inj AddLECancellable.inj
-/
-#print MulLECancellable.injective_left /-
@[to_additive]
protected theorem injective_left [CommSemigroup α] [PartialOrder α] {a : α}
(ha : MulLECancellable a) : Injective (· * a) := fun b c h =>
ha.Injective <| by rwa [mul_comm a, mul_comm a]
-#align mul_le_cancellable.injective_left MulLECancellable.injective_left
-#align add_le_cancellable.injective_left AddLECancellable.injective_left
--/
+#align mul_le_cancellable.injective_left MulLECancellable.injective_leftₓ
+#align add_le_cancellable.injective_left AddLECancellable.injective_leftₓ
-#print MulLECancellable.inj_left /-
@[to_additive]
protected theorem inj_left [CommSemigroup α] [PartialOrder α] {a b c : α}
(hc : MulLECancellable c) : a * c = b * c ↔ a = b :=
- hc.injective_left.eq_iff
-#align mul_le_cancellable.inj_left MulLECancellable.inj_left
-#align add_le_cancellable.inj_left AddLECancellable.inj_left
--/
+ hc.injective_leftₓ.eq_iff
+#align mul_le_cancellable.inj_left MulLECancellable.inj_leftₓ
+#align add_le_cancellable.inj_left AddLECancellable.inj_leftₓ
variable [LE α]
@@ -1842,14 +1832,12 @@ protected theorem mul_le_mul_iff_left [Mul α] [CovariantClass α α (· * ·) (
#align add_le_cancellable.add_le_add_iff_left AddLECancellable.add_le_add_iff_left
-/
-#print MulLECancellable.mul_le_mul_iff_right /-
@[to_additive]
protected theorem mul_le_mul_iff_right [CommSemigroup α] [CovariantClass α α (· * ·) (· ≤ ·)]
{a b c : α} (ha : MulLECancellable a) : b * a ≤ c * a ↔ b ≤ c := by
rw [mul_comm b, mul_comm c, ha.mul_le_mul_iff_left]
-#align mul_le_cancellable.mul_le_mul_iff_right MulLECancellable.mul_le_mul_iff_right
-#align add_le_cancellable.add_le_add_iff_right AddLECancellable.add_le_add_iff_right
--/
+#align mul_le_cancellable.mul_le_mul_iff_right MulLECancellable.mul_le_mul_iff_rightₓ
+#align add_le_cancellable.add_le_add_iff_right AddLECancellable.add_le_add_iff_rightₓ
#print MulLECancellable.le_mul_iff_one_le_right /-
@[to_additive]
@@ -1869,23 +1857,19 @@ protected theorem mul_le_iff_le_one_right [MulOneClass α] [CovariantClass α α
#align add_le_cancellable.add_le_iff_nonpos_right AddLECancellable.add_le_iff_nonpos_right
-/
-#print MulLECancellable.le_mul_iff_one_le_left /-
@[to_additive]
protected theorem le_mul_iff_one_le_left [CommMonoid α] [CovariantClass α α (· * ·) (· ≤ ·)]
{a b : α} (ha : MulLECancellable a) : a ≤ b * a ↔ 1 ≤ b := by
rw [mul_comm, ha.le_mul_iff_one_le_right]
-#align mul_le_cancellable.le_mul_iff_one_le_left MulLECancellable.le_mul_iff_one_le_left
-#align add_le_cancellable.le_add_iff_nonneg_left AddLECancellable.le_add_iff_nonneg_left
--/
+#align mul_le_cancellable.le_mul_iff_one_le_left MulLECancellable.le_mul_iff_one_le_leftₓ
+#align add_le_cancellable.le_add_iff_nonneg_left AddLECancellable.le_add_iff_nonneg_leftₓ
-#print MulLECancellable.mul_le_iff_le_one_left /-
@[to_additive]
protected theorem mul_le_iff_le_one_left [CommMonoid α] [CovariantClass α α (· * ·) (· ≤ ·)]
{a b : α} (ha : MulLECancellable a) : b * a ≤ a ↔ b ≤ 1 := by
rw [mul_comm, ha.mul_le_iff_le_one_right]
-#align mul_le_cancellable.mul_le_iff_le_one_left MulLECancellable.mul_le_iff_le_one_left
-#align add_le_cancellable.add_le_iff_nonpos_left AddLECancellable.add_le_iff_nonpos_left
--/
+#align mul_le_cancellable.mul_le_iff_le_one_left MulLECancellable.mul_le_iff_le_one_leftₓ
+#align add_le_cancellable.add_le_iff_nonpos_left AddLECancellable.add_le_iff_nonpos_leftₓ
end MulLECancellable
mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504
@@ -181,7 +181,7 @@ theorem mul_lt_mul_of_lt_of_lt [CovariantClass α α (· * ·) (· < ·)]
#align add_lt_add_of_lt_of_lt add_lt_add_of_lt_of_lt
-/
-alias add_lt_add_of_lt_of_lt ← add_lt_add
+alias add_lt_add := add_lt_add_of_lt_of_lt
#align add_lt_add add_lt_add
#print mul_lt_mul_of_le_of_lt /-
@@ -1114,19 +1114,19 @@ theorem Right.one_lt_mul' [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a
#align right.add_pos' Right.add_pos'
-/
-alias Left.mul_le_one ← mul_le_one'
+alias mul_le_one' := Left.mul_le_one
#align mul_le_one' mul_le_one'
-alias Left.mul_lt_one_of_le_of_lt ← mul_lt_one_of_le_of_lt
+alias mul_lt_one_of_le_of_lt := Left.mul_lt_one_of_le_of_lt
#align mul_lt_one_of_le_of_lt mul_lt_one_of_le_of_lt
-alias Left.mul_lt_one_of_lt_of_le ← mul_lt_one_of_lt_of_le
+alias mul_lt_one_of_lt_of_le := Left.mul_lt_one_of_lt_of_le
#align mul_lt_one_of_lt_of_le mul_lt_one_of_lt_of_le
-alias Left.mul_lt_one ← mul_lt_one
+alias mul_lt_one := Left.mul_lt_one
#align mul_lt_one mul_lt_one
-alias Left.mul_lt_one' ← mul_lt_one'
+alias mul_lt_one' := Left.mul_lt_one'
#align mul_lt_one' mul_lt_one'
attribute [to_additive add_nonpos "**Alias** of `left.add_nonpos`."] mul_le_one'
@@ -1141,19 +1141,19 @@ attribute [to_additive "**Alias** of `left.add_neg`."] mul_lt_one
attribute [to_additive "**Alias** of `left.add_neg'`."] mul_lt_one'
-alias Left.one_le_mul ← one_le_mul
+alias one_le_mul := Left.one_le_mul
#align one_le_mul one_le_mul
-alias Left.one_lt_mul_of_le_of_lt ← one_lt_mul_of_le_of_lt'
+alias one_lt_mul_of_le_of_lt' := Left.one_lt_mul_of_le_of_lt
#align one_lt_mul_of_le_of_lt' one_lt_mul_of_le_of_lt'
-alias Left.one_lt_mul_of_lt_of_le ← one_lt_mul_of_lt_of_le'
+alias one_lt_mul_of_lt_of_le' := Left.one_lt_mul_of_lt_of_le
#align one_lt_mul_of_lt_of_le' one_lt_mul_of_lt_of_le'
-alias Left.one_lt_mul ← one_lt_mul'
+alias one_lt_mul' := Left.one_lt_mul
#align one_lt_mul' one_lt_mul'
-alias Left.one_lt_mul' ← one_lt_mul''
+alias one_lt_mul'' := Left.one_lt_mul'
#align one_lt_mul'' one_lt_mul''
attribute [to_additive add_nonneg "**Alias** of `left.add_nonneg`."] one_le_mul
@@ -1417,7 +1417,7 @@ theorem Right.mul_eq_mul_iff_eq_and_eq [CovariantClass α α (· * ·) (· ≤
#align right.add_eq_add_iff_eq_and_eq Right.add_eq_add_iff_eq_and_eq
-/
-alias Left.mul_eq_mul_iff_eq_and_eq ← mul_eq_mul_iff_eq_and_eq
+alias mul_eq_mul_iff_eq_and_eq := Left.mul_eq_mul_iff_eq_and_eq
#align mul_eq_mul_iff_eq_and_eq mul_eq_mul_iff_eq_and_eq
attribute [to_additive] mul_eq_mul_iff_eq_and_eq
mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504
@@ -364,18 +364,18 @@ variable [LinearOrder α] [CovariantClass α α (· * ·) (· ≤ ·)]
[CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c d : α}
@[to_additive max_add_add_le_max_add_max]
-theorem max_mul_mul_le_max_mul_max' : max (a * b) (c * d) ≤ max a c * max b d :=
+theorem max_hMul_hMul_le_max_hMul_max' : max (a * b) (c * d) ≤ max a c * max b d :=
max_le (mul_le_mul' (le_max_left _ _) <| le_max_left _ _) <|
mul_le_mul' (le_max_right _ _) <| le_max_right _ _
-#align max_mul_mul_le_max_mul_max' max_mul_mul_le_max_mul_max'
+#align max_mul_mul_le_max_mul_max' max_hMul_hMul_le_max_hMul_max'
#align max_add_add_le_max_add_max max_add_add_le_max_add_max
--TODO: Also missing `min_mul_min_le_min_mul_mul`
@[to_additive min_add_min_le_min_add_add]
-theorem min_mul_min_le_min_mul_mul' : min a c * min b d ≤ min (a * b) (c * d) :=
+theorem min_hMul_min_le_min_hMul_mul' : min a c * min b d ≤ min (a * b) (c * d) :=
le_min (mul_le_mul' (min_le_left _ _) <| min_le_left _ _) <|
mul_le_mul' (min_le_right _ _) <| min_le_right _ _
-#align min_mul_min_le_min_mul_mul' min_mul_min_le_min_mul_mul'
+#align min_mul_min_le_min_mul_mul' min_hMul_min_le_min_hMul_mul'
#align min_add_min_le_min_add_add min_add_min_le_min_add_add
end LinearOrder
@@ -1364,7 +1364,7 @@ to the appropriate `covariant_class`. -/
"An additive semigroup with a partial order and satisfying `left_cancel_add_semigroup`\n(i.e. `c + a < c + b → a < b`) is a `left_cancel add_semigroup`."]
def Contravariant.toLeftCancelSemigroup [ContravariantClass α α (· * ·) (· ≤ ·)] :
LeftCancelSemigroup α :=
- { ‹Semigroup α› with mul_left_cancel := fun a b c => mul_left_cancel'' }
+ { ‹Semigroup α› with hMul_left_cancel := fun a b c => mul_left_cancel'' }
#align contravariant.to_left_cancel_semigroup Contravariant.toLeftCancelSemigroup
#align contravariant.to_left_cancel_add_semigroup Contravariant.toAddLeftCancelSemigroup
-/
@@ -1378,7 +1378,7 @@ to the appropriate `covariant_class`. -/
"An additive semigroup with a partial order and satisfying `right_cancel_add_semigroup`\n(`a + c < b + c → a < b`) is a `right_cancel add_semigroup`."]
def Contravariant.toRightCancelSemigroup [ContravariantClass α α (swap (· * ·)) (· ≤ ·)] :
RightCancelSemigroup α :=
- { ‹Semigroup α› with mul_right_cancel := fun a b c => mul_right_cancel'' }
+ { ‹Semigroup α› with hMul_right_cancel := fun a b c => mul_right_cancel'' }
#align contravariant.to_right_cancel_semigroup Contravariant.toRightCancelSemigroup
#align contravariant.to_right_cancel_add_semigroup Contravariant.toAddRightCancelSemigroup
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/48a058d7e39a80ed56858505719a0b2197900999
@@ -7,7 +7,7 @@ Yuyang Zhao
import Mathbin.Algebra.CovariantAndContravariant
import Mathbin.Order.MinMax
-#align_import algebra.order.monoid.lemmas from "leanprover-community/mathlib"@"448144f7ae193a8990cb7473c9e9a01990f64ac7"
+#align_import algebra.order.monoid.lemmas from "leanprover-community/mathlib"@"3ba15165bd6927679be7c22d6091a87337e3cd0c"
/-!
# Ordered monoids
@@ -358,6 +358,28 @@ theorem min_le_max_of_mul_le_mul (h : a * b ≤ c * d) : min a b ≤ max c d :=
end LinearOrder
+section LinearOrder
+
+variable [LinearOrder α] [CovariantClass α α (· * ·) (· ≤ ·)]
+ [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c d : α}
+
+@[to_additive max_add_add_le_max_add_max]
+theorem max_mul_mul_le_max_mul_max' : max (a * b) (c * d) ≤ max a c * max b d :=
+ max_le (mul_le_mul' (le_max_left _ _) <| le_max_left _ _) <|
+ mul_le_mul' (le_max_right _ _) <| le_max_right _ _
+#align max_mul_mul_le_max_mul_max' max_mul_mul_le_max_mul_max'
+#align max_add_add_le_max_add_max max_add_add_le_max_add_max
+
+--TODO: Also missing `min_mul_min_le_min_mul_mul`
+@[to_additive min_add_min_le_min_add_add]
+theorem min_mul_min_le_min_mul_mul' : min a c * min b d ≤ min (a * b) (c * d) :=
+ le_min (mul_le_mul' (min_le_left _ _) <| min_le_left _ _) <|
+ mul_le_mul' (min_le_right _ _) <| min_le_right _ _
+#align min_mul_min_le_min_mul_mul' min_mul_min_le_min_mul_mul'
+#align min_add_min_le_min_add_add min_add_min_le_min_add_add
+
+end LinearOrder
+
end Mul
-- using one
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -3,15 +3,12 @@ Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro, Johannes Hölzl, Damiano Testa,
Yuyang Zhao
-
-! This file was ported from Lean 3 source module algebra.order.monoid.lemmas
-! leanprover-community/mathlib commit 448144f7ae193a8990cb7473c9e9a01990f64ac7
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Algebra.CovariantAndContravariant
import Mathbin.Order.MinMax
+#align_import algebra.order.monoid.lemmas from "leanprover-community/mathlib"@"448144f7ae193a8990cb7473c9e9a01990f64ac7"
+
/-!
# Ordered monoids
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -351,11 +351,13 @@ section LinearOrder
variable [LinearOrder α] {a b c d : α} [CovariantClass α α (· * ·) (· < ·)]
[CovariantClass α α (swap (· * ·)) (· < ·)]
+#print min_le_max_of_mul_le_mul /-
@[to_additive]
theorem min_le_max_of_mul_le_mul (h : a * b ≤ c * d) : min a b ≤ max c d := by
simp_rw [min_le_iff, le_max_iff]; contrapose! h; exact mul_lt_mul_of_lt_of_lt h.1.1 h.2.2
#align min_le_max_of_mul_le_mul min_le_max_of_mul_le_mul
#align min_le_max_of_add_le_add min_le_max_of_add_le_add
+-/
end LinearOrder
@@ -370,6 +372,7 @@ section LE
variable [LE α]
+#print le_mul_of_one_le_right' /-
@[to_additive le_add_of_nonneg_right]
theorem le_mul_of_one_le_right' [CovariantClass α α (· * ·) (· ≤ ·)] {a b : α} (h : 1 ≤ b) :
a ≤ a * b :=
@@ -378,7 +381,9 @@ theorem le_mul_of_one_le_right' [CovariantClass α α (· * ·) (· ≤ ·)] {a
_ ≤ a * b := mul_le_mul_left' h a
#align le_mul_of_one_le_right' le_mul_of_one_le_right'
#align le_add_of_nonneg_right le_add_of_nonneg_right
+-/
+#print mul_le_of_le_one_right' /-
@[to_additive add_le_of_nonpos_right]
theorem mul_le_of_le_one_right' [CovariantClass α α (· * ·) (· ≤ ·)] {a b : α} (h : b ≤ 1) :
a * b ≤ a :=
@@ -387,7 +392,9 @@ theorem mul_le_of_le_one_right' [CovariantClass α α (· * ·) (· ≤ ·)] {a
_ = a := mul_one a
#align mul_le_of_le_one_right' mul_le_of_le_one_right'
#align add_le_of_nonpos_right add_le_of_nonpos_right
+-/
+#print le_mul_of_one_le_left' /-
@[to_additive le_add_of_nonneg_left]
theorem le_mul_of_one_le_left' [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b : α} (h : 1 ≤ b) :
a ≤ b * a :=
@@ -396,7 +403,9 @@ theorem le_mul_of_one_le_left' [CovariantClass α α (swap (· * ·)) (· ≤ ·
_ ≤ b * a := mul_le_mul_right' h a
#align le_mul_of_one_le_left' le_mul_of_one_le_left'
#align le_add_of_nonneg_left le_add_of_nonneg_left
+-/
+#print mul_le_of_le_one_left' /-
@[to_additive add_le_of_nonpos_left]
theorem mul_le_of_le_one_left' [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b : α} (h : b ≤ 1) :
b * a ≤ a :=
@@ -405,62 +414,79 @@ theorem mul_le_of_le_one_left' [CovariantClass α α (swap (· * ·)) (· ≤ ·
_ = a := one_mul a
#align mul_le_of_le_one_left' mul_le_of_le_one_left'
#align add_le_of_nonpos_left add_le_of_nonpos_left
+-/
+#print one_le_of_le_mul_right /-
@[to_additive]
theorem one_le_of_le_mul_right [ContravariantClass α α (· * ·) (· ≤ ·)] {a b : α} (h : a ≤ a * b) :
1 ≤ b :=
le_of_mul_le_mul_left' <| by simpa only [mul_one]
#align one_le_of_le_mul_right one_le_of_le_mul_right
#align nonneg_of_le_add_right nonneg_of_le_add_right
+-/
+#print le_one_of_mul_le_right /-
@[to_additive]
theorem le_one_of_mul_le_right [ContravariantClass α α (· * ·) (· ≤ ·)] {a b : α} (h : a * b ≤ a) :
b ≤ 1 :=
le_of_mul_le_mul_left' <| by simpa only [mul_one]
#align le_one_of_mul_le_right le_one_of_mul_le_right
#align nonpos_of_add_le_right nonpos_of_add_le_right
+-/
+#print one_le_of_le_mul_left /-
@[to_additive]
theorem one_le_of_le_mul_left [ContravariantClass α α (swap (· * ·)) (· ≤ ·)] {a b : α}
(h : b ≤ a * b) : 1 ≤ a :=
le_of_mul_le_mul_right' <| by simpa only [one_mul]
#align one_le_of_le_mul_left one_le_of_le_mul_left
#align nonneg_of_le_add_left nonneg_of_le_add_left
+-/
+#print le_one_of_mul_le_left /-
@[to_additive]
theorem le_one_of_mul_le_left [ContravariantClass α α (swap (· * ·)) (· ≤ ·)] {a b : α}
(h : a * b ≤ b) : a ≤ 1 :=
le_of_mul_le_mul_right' <| by simpa only [one_mul]
#align le_one_of_mul_le_left le_one_of_mul_le_left
#align nonpos_of_add_le_left nonpos_of_add_le_left
+-/
+#print le_mul_iff_one_le_right' /-
@[simp, to_additive le_add_iff_nonneg_right]
theorem le_mul_iff_one_le_right' [CovariantClass α α (· * ·) (· ≤ ·)]
[ContravariantClass α α (· * ·) (· ≤ ·)] (a : α) {b : α} : a ≤ a * b ↔ 1 ≤ b :=
Iff.trans (by rw [mul_one]) (mul_le_mul_iff_left a)
#align le_mul_iff_one_le_right' le_mul_iff_one_le_right'
#align le_add_iff_nonneg_right le_add_iff_nonneg_right
+-/
+#print le_mul_iff_one_le_left' /-
@[simp, to_additive le_add_iff_nonneg_left]
theorem le_mul_iff_one_le_left' [CovariantClass α α (swap (· * ·)) (· ≤ ·)]
[ContravariantClass α α (swap (· * ·)) (· ≤ ·)] (a : α) {b : α} : a ≤ b * a ↔ 1 ≤ b :=
Iff.trans (by rw [one_mul]) (mul_le_mul_iff_right a)
#align le_mul_iff_one_le_left' le_mul_iff_one_le_left'
#align le_add_iff_nonneg_left le_add_iff_nonneg_left
+-/
+#print mul_le_iff_le_one_right' /-
@[simp, to_additive add_le_iff_nonpos_right]
theorem mul_le_iff_le_one_right' [CovariantClass α α (· * ·) (· ≤ ·)]
[ContravariantClass α α (· * ·) (· ≤ ·)] (a : α) {b : α} : a * b ≤ a ↔ b ≤ 1 :=
Iff.trans (by rw [mul_one]) (mul_le_mul_iff_left a)
#align mul_le_iff_le_one_right' mul_le_iff_le_one_right'
#align add_le_iff_nonpos_right add_le_iff_nonpos_right
+-/
+#print mul_le_iff_le_one_left' /-
@[simp, to_additive add_le_iff_nonpos_left]
theorem mul_le_iff_le_one_left' [CovariantClass α α (swap (· * ·)) (· ≤ ·)]
[ContravariantClass α α (swap (· * ·)) (· ≤ ·)] {a b : α} : a * b ≤ b ↔ a ≤ 1 :=
Iff.trans (by rw [one_mul]) (mul_le_mul_iff_right b)
#align mul_le_iff_le_one_left' mul_le_iff_le_one_left'
#align add_le_iff_nonpos_left add_le_iff_nonpos_left
+-/
end LE
@@ -468,6 +494,7 @@ section LT
variable [LT α]
+#print lt_mul_of_one_lt_right' /-
@[to_additive lt_add_of_pos_right]
theorem lt_mul_of_one_lt_right' [CovariantClass α α (· * ·) (· < ·)] (a : α) {b : α} (h : 1 < b) :
a < a * b :=
@@ -476,7 +503,9 @@ theorem lt_mul_of_one_lt_right' [CovariantClass α α (· * ·) (· < ·)] (a :
_ < a * b := mul_lt_mul_left' h a
#align lt_mul_of_one_lt_right' lt_mul_of_one_lt_right'
#align lt_add_of_pos_right lt_add_of_pos_right
+-/
+#print mul_lt_of_lt_one_right' /-
@[to_additive add_lt_of_neg_right]
theorem mul_lt_of_lt_one_right' [CovariantClass α α (· * ·) (· < ·)] (a : α) {b : α} (h : b < 1) :
a * b < a :=
@@ -485,7 +514,9 @@ theorem mul_lt_of_lt_one_right' [CovariantClass α α (· * ·) (· < ·)] (a :
_ = a := mul_one a
#align mul_lt_of_lt_one_right' mul_lt_of_lt_one_right'
#align add_lt_of_neg_right add_lt_of_neg_right
+-/
+#print lt_mul_of_one_lt_left' /-
@[to_additive lt_add_of_pos_left]
theorem lt_mul_of_one_lt_left' [CovariantClass α α (swap (· * ·)) (· < ·)] (a : α) {b : α}
(h : 1 < b) : a < b * a :=
@@ -494,7 +525,9 @@ theorem lt_mul_of_one_lt_left' [CovariantClass α α (swap (· * ·)) (· < ·)]
_ < b * a := mul_lt_mul_right' h a
#align lt_mul_of_one_lt_left' lt_mul_of_one_lt_left'
#align lt_add_of_pos_left lt_add_of_pos_left
+-/
+#print mul_lt_of_lt_one_left' /-
@[to_additive add_lt_of_neg_left]
theorem mul_lt_of_lt_one_left' [CovariantClass α α (swap (· * ·)) (· < ·)] (a : α) {b : α}
(h : b < 1) : b * a < a :=
@@ -503,62 +536,79 @@ theorem mul_lt_of_lt_one_left' [CovariantClass α α (swap (· * ·)) (· < ·)]
_ = a := one_mul a
#align mul_lt_of_lt_one_left' mul_lt_of_lt_one_left'
#align add_lt_of_neg_left add_lt_of_neg_left
+-/
+#print one_lt_of_lt_mul_right /-
@[to_additive]
theorem one_lt_of_lt_mul_right [ContravariantClass α α (· * ·) (· < ·)] {a b : α} (h : a < a * b) :
1 < b :=
lt_of_mul_lt_mul_left' <| by simpa only [mul_one]
#align one_lt_of_lt_mul_right one_lt_of_lt_mul_right
#align pos_of_lt_add_right pos_of_lt_add_right
+-/
+#print lt_one_of_mul_lt_right /-
@[to_additive]
theorem lt_one_of_mul_lt_right [ContravariantClass α α (· * ·) (· < ·)] {a b : α} (h : a * b < a) :
b < 1 :=
lt_of_mul_lt_mul_left' <| by simpa only [mul_one]
#align lt_one_of_mul_lt_right lt_one_of_mul_lt_right
#align neg_of_add_lt_right neg_of_add_lt_right
+-/
+#print one_lt_of_lt_mul_left /-
@[to_additive]
theorem one_lt_of_lt_mul_left [ContravariantClass α α (swap (· * ·)) (· < ·)] {a b : α}
(h : b < a * b) : 1 < a :=
lt_of_mul_lt_mul_right' <| by simpa only [one_mul]
#align one_lt_of_lt_mul_left one_lt_of_lt_mul_left
#align pos_of_lt_add_left pos_of_lt_add_left
+-/
+#print lt_one_of_mul_lt_left /-
@[to_additive]
theorem lt_one_of_mul_lt_left [ContravariantClass α α (swap (· * ·)) (· < ·)] {a b : α}
(h : a * b < b) : a < 1 :=
lt_of_mul_lt_mul_right' <| by simpa only [one_mul]
#align lt_one_of_mul_lt_left lt_one_of_mul_lt_left
#align neg_of_add_lt_left neg_of_add_lt_left
+-/
+#print lt_mul_iff_one_lt_right' /-
@[simp, to_additive lt_add_iff_pos_right]
theorem lt_mul_iff_one_lt_right' [CovariantClass α α (· * ·) (· < ·)]
[ContravariantClass α α (· * ·) (· < ·)] (a : α) {b : α} : a < a * b ↔ 1 < b :=
Iff.trans (by rw [mul_one]) (mul_lt_mul_iff_left a)
#align lt_mul_iff_one_lt_right' lt_mul_iff_one_lt_right'
#align lt_add_iff_pos_right lt_add_iff_pos_right
+-/
+#print lt_mul_iff_one_lt_left' /-
@[simp, to_additive lt_add_iff_pos_left]
theorem lt_mul_iff_one_lt_left' [CovariantClass α α (swap (· * ·)) (· < ·)]
[ContravariantClass α α (swap (· * ·)) (· < ·)] (a : α) {b : α} : a < b * a ↔ 1 < b :=
Iff.trans (by rw [one_mul]) (mul_lt_mul_iff_right a)
#align lt_mul_iff_one_lt_left' lt_mul_iff_one_lt_left'
#align lt_add_iff_pos_left lt_add_iff_pos_left
+-/
+#print mul_lt_iff_lt_one_left' /-
@[simp, to_additive add_lt_iff_neg_left]
theorem mul_lt_iff_lt_one_left' [CovariantClass α α (· * ·) (· < ·)]
[ContravariantClass α α (· * ·) (· < ·)] {a b : α} : a * b < a ↔ b < 1 :=
Iff.trans (by rw [mul_one]) (mul_lt_mul_iff_left a)
#align mul_lt_iff_lt_one_left' mul_lt_iff_lt_one_left'
#align add_lt_iff_neg_left add_lt_iff_neg_left
+-/
+#print mul_lt_iff_lt_one_right' /-
@[simp, to_additive add_lt_iff_neg_right]
theorem mul_lt_iff_lt_one_right' [CovariantClass α α (swap (· * ·)) (· < ·)]
[ContravariantClass α α (swap (· * ·)) (· < ·)] {a : α} (b : α) : a * b < b ↔ a < 1 :=
Iff.trans (by rw [one_mul]) (mul_lt_mul_iff_right b)
#align mul_lt_iff_lt_one_right' mul_lt_iff_lt_one_right'
#align add_lt_iff_neg_right add_lt_iff_neg_right
+-/
end LT
@@ -570,6 +620,7 @@ variable [Preorder α]
which assume left covariance. -/
+#print mul_le_of_le_of_le_one /-
@[to_additive]
theorem mul_le_of_le_of_le_one [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (hbc : b ≤ c)
(ha : a ≤ 1) : b * a ≤ c :=
@@ -579,7 +630,9 @@ theorem mul_le_of_le_of_le_one [CovariantClass α α (· * ·) (· ≤ ·)] {a b
_ ≤ c := hbc
#align mul_le_of_le_of_le_one mul_le_of_le_of_le_one
#align add_le_of_le_of_nonpos add_le_of_le_of_nonpos
+-/
+#print mul_lt_of_le_of_lt_one /-
@[to_additive]
theorem mul_lt_of_le_of_lt_one [CovariantClass α α (· * ·) (· < ·)] {a b c : α} (hbc : b ≤ c)
(ha : a < 1) : b * a < c :=
@@ -589,7 +642,9 @@ theorem mul_lt_of_le_of_lt_one [CovariantClass α α (· * ·) (· < ·)] {a b c
_ ≤ c := hbc
#align mul_lt_of_le_of_lt_one mul_lt_of_le_of_lt_one
#align add_lt_of_le_of_neg add_lt_of_le_of_neg
+-/
+#print mul_lt_of_lt_of_le_one /-
@[to_additive]
theorem mul_lt_of_lt_of_le_one [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (hbc : b < c)
(ha : a ≤ 1) : b * a < c :=
@@ -599,7 +654,9 @@ theorem mul_lt_of_lt_of_le_one [CovariantClass α α (· * ·) (· ≤ ·)] {a b
_ < c := hbc
#align mul_lt_of_lt_of_le_one mul_lt_of_lt_of_le_one
#align add_lt_of_lt_of_nonpos add_lt_of_lt_of_nonpos
+-/
+#print mul_lt_of_lt_of_lt_one /-
@[to_additive]
theorem mul_lt_of_lt_of_lt_one [CovariantClass α α (· * ·) (· < ·)] {a b c : α} (hbc : b < c)
(ha : a < 1) : b * a < c :=
@@ -609,14 +666,18 @@ theorem mul_lt_of_lt_of_lt_one [CovariantClass α α (· * ·) (· < ·)] {a b c
_ < c := hbc
#align mul_lt_of_lt_of_lt_one mul_lt_of_lt_of_lt_one
#align add_lt_of_lt_of_neg add_lt_of_lt_of_neg
+-/
+#print mul_lt_of_lt_of_lt_one' /-
@[to_additive]
theorem mul_lt_of_lt_of_lt_one' [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (hbc : b < c)
(ha : a < 1) : b * a < c :=
mul_lt_of_lt_of_le_one hbc ha.le
#align mul_lt_of_lt_of_lt_one' mul_lt_of_lt_of_lt_one'
#align add_lt_of_lt_of_neg' add_lt_of_lt_of_neg'
+-/
+#print Left.mul_le_one /-
/-- Assumes left covariance.
The lemma assuming right covariance is `right.mul_le_one`. -/
@[to_additive
@@ -626,7 +687,9 @@ theorem Left.mul_le_one [CovariantClass α α (· * ·) (· ≤ ·)] {a b : α}
mul_le_of_le_of_le_one ha hb
#align left.mul_le_one Left.mul_le_one
#align left.add_nonpos Left.add_nonpos
+-/
+#print Left.mul_lt_one_of_le_of_lt /-
/-- Assumes left covariance.
The lemma assuming right covariance is `right.mul_lt_one_of_le_of_lt`. -/
@[to_additive Left.add_neg_of_nonpos_of_neg
@@ -636,7 +699,9 @@ theorem Left.mul_lt_one_of_le_of_lt [CovariantClass α α (· * ·) (· < ·)] {
mul_lt_of_le_of_lt_one ha hb
#align left.mul_lt_one_of_le_of_lt Left.mul_lt_one_of_le_of_lt
#align left.add_neg_of_nonpos_of_neg Left.add_neg_of_nonpos_of_neg
+-/
+#print Left.mul_lt_one_of_lt_of_le /-
/-- Assumes left covariance.
The lemma assuming right covariance is `right.mul_lt_one_of_lt_of_le`. -/
@[to_additive Left.add_neg_of_neg_of_nonpos
@@ -646,7 +711,9 @@ theorem Left.mul_lt_one_of_lt_of_le [CovariantClass α α (· * ·) (· ≤ ·)]
mul_lt_of_lt_of_le_one ha hb
#align left.mul_lt_one_of_lt_of_le Left.mul_lt_one_of_lt_of_le
#align left.add_neg_of_neg_of_nonpos Left.add_neg_of_neg_of_nonpos
+-/
+#print Left.mul_lt_one /-
/-- Assumes left covariance.
The lemma assuming right covariance is `right.mul_lt_one`. -/
@[to_additive "Assumes left covariance.\nThe lemma assuming right covariance is `right.add_neg`."]
@@ -655,7 +722,9 @@ theorem Left.mul_lt_one [CovariantClass α α (· * ·) (· < ·)] {a b : α} (h
mul_lt_of_lt_of_lt_one ha hb
#align left.mul_lt_one Left.mul_lt_one
#align left.add_neg Left.add_neg
+-/
+#print Left.mul_lt_one' /-
/-- Assumes left covariance.
The lemma assuming right covariance is `right.mul_lt_one'`. -/
@[to_additive "Assumes left covariance.\nThe lemma assuming right covariance is `right.add_neg'`."]
@@ -664,11 +733,13 @@ theorem Left.mul_lt_one' [CovariantClass α α (· * ·) (· ≤ ·)] {a b : α}
mul_lt_of_lt_of_lt_one' ha hb
#align left.mul_lt_one' Left.mul_lt_one'
#align left.add_neg' Left.add_neg'
+-/
/-! Lemmas of the form `b ≤ c → 1 ≤ a → b ≤ c * a`,
which assume left covariance. -/
+#print le_mul_of_le_of_one_le /-
@[to_additive]
theorem le_mul_of_le_of_one_le [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (hbc : b ≤ c)
(ha : 1 ≤ a) : b ≤ c * a :=
@@ -678,7 +749,9 @@ theorem le_mul_of_le_of_one_le [CovariantClass α α (· * ·) (· ≤ ·)] {a b
_ ≤ c * a := mul_le_mul_left' ha c
#align le_mul_of_le_of_one_le le_mul_of_le_of_one_le
#align le_add_of_le_of_nonneg le_add_of_le_of_nonneg
+-/
+#print lt_mul_of_le_of_one_lt /-
@[to_additive]
theorem lt_mul_of_le_of_one_lt [CovariantClass α α (· * ·) (· < ·)] {a b c : α} (hbc : b ≤ c)
(ha : 1 < a) : b < c * a :=
@@ -688,7 +761,9 @@ theorem lt_mul_of_le_of_one_lt [CovariantClass α α (· * ·) (· < ·)] {a b c
_ < c * a := mul_lt_mul_left' ha c
#align lt_mul_of_le_of_one_lt lt_mul_of_le_of_one_lt
#align lt_add_of_le_of_pos lt_add_of_le_of_pos
+-/
+#print lt_mul_of_lt_of_one_le /-
@[to_additive]
theorem lt_mul_of_lt_of_one_le [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (hbc : b < c)
(ha : 1 ≤ a) : b < c * a :=
@@ -698,7 +773,9 @@ theorem lt_mul_of_lt_of_one_le [CovariantClass α α (· * ·) (· ≤ ·)] {a b
_ ≤ c * a := mul_le_mul_left' ha c
#align lt_mul_of_lt_of_one_le lt_mul_of_lt_of_one_le
#align lt_add_of_lt_of_nonneg lt_add_of_lt_of_nonneg
+-/
+#print lt_mul_of_lt_of_one_lt /-
@[to_additive]
theorem lt_mul_of_lt_of_one_lt [CovariantClass α α (· * ·) (· < ·)] {a b c : α} (hbc : b < c)
(ha : 1 < a) : b < c * a :=
@@ -708,14 +785,18 @@ theorem lt_mul_of_lt_of_one_lt [CovariantClass α α (· * ·) (· < ·)] {a b c
_ < c * a := mul_lt_mul_left' ha c
#align lt_mul_of_lt_of_one_lt lt_mul_of_lt_of_one_lt
#align lt_add_of_lt_of_pos lt_add_of_lt_of_pos
+-/
+#print lt_mul_of_lt_of_one_lt' /-
@[to_additive]
theorem lt_mul_of_lt_of_one_lt' [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (hbc : b < c)
(ha : 1 < a) : b < c * a :=
lt_mul_of_lt_of_one_le hbc ha.le
#align lt_mul_of_lt_of_one_lt' lt_mul_of_lt_of_one_lt'
#align lt_add_of_lt_of_pos' lt_add_of_lt_of_pos'
+-/
+#print Left.one_le_mul /-
/-- Assumes left covariance.
The lemma assuming right covariance is `right.one_le_mul`. -/
@[to_additive Left.add_nonneg
@@ -725,7 +806,9 @@ theorem Left.one_le_mul [CovariantClass α α (· * ·) (· ≤ ·)] {a b : α}
le_mul_of_le_of_one_le ha hb
#align left.one_le_mul Left.one_le_mul
#align left.add_nonneg Left.add_nonneg
+-/
+#print Left.one_lt_mul_of_le_of_lt /-
/-- Assumes left covariance.
The lemma assuming right covariance is `right.one_lt_mul_of_le_of_lt`. -/
@[to_additive Left.add_pos_of_nonneg_of_pos
@@ -735,7 +818,9 @@ theorem Left.one_lt_mul_of_le_of_lt [CovariantClass α α (· * ·) (· < ·)] {
lt_mul_of_le_of_one_lt ha hb
#align left.one_lt_mul_of_le_of_lt Left.one_lt_mul_of_le_of_lt
#align left.add_pos_of_nonneg_of_pos Left.add_pos_of_nonneg_of_pos
+-/
+#print Left.one_lt_mul_of_lt_of_le /-
/-- Assumes left covariance.
The lemma assuming right covariance is `right.one_lt_mul_of_lt_of_le`. -/
@[to_additive Left.add_pos_of_pos_of_nonneg
@@ -745,7 +830,9 @@ theorem Left.one_lt_mul_of_lt_of_le [CovariantClass α α (· * ·) (· ≤ ·)]
lt_mul_of_lt_of_one_le ha hb
#align left.one_lt_mul_of_lt_of_le Left.one_lt_mul_of_lt_of_le
#align left.add_pos_of_pos_of_nonneg Left.add_pos_of_pos_of_nonneg
+-/
+#print Left.one_lt_mul /-
/-- Assumes left covariance.
The lemma assuming right covariance is `right.one_lt_mul`. -/
@[to_additive Left.add_pos
@@ -755,7 +842,9 @@ theorem Left.one_lt_mul [CovariantClass α α (· * ·) (· < ·)] {a b : α} (h
lt_mul_of_lt_of_one_lt ha hb
#align left.one_lt_mul Left.one_lt_mul
#align left.add_pos Left.add_pos
+-/
+#print Left.one_lt_mul' /-
/-- Assumes left covariance.
The lemma assuming right covariance is `right.one_lt_mul'`. -/
@[to_additive Left.add_pos'
@@ -765,11 +854,13 @@ theorem Left.one_lt_mul' [CovariantClass α α (· * ·) (· ≤ ·)] {a b : α}
lt_mul_of_lt_of_one_lt' ha hb
#align left.one_lt_mul' Left.one_lt_mul'
#align left.add_pos' Left.add_pos'
+-/
/-! Lemmas of the form `a ≤ 1 → b ≤ c → a * b ≤ c`,
which assume right covariance. -/
+#print mul_le_of_le_one_of_le /-
@[to_additive]
theorem mul_le_of_le_one_of_le [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α} (ha : a ≤ 1)
(hbc : b ≤ c) : a * b ≤ c :=
@@ -779,7 +870,9 @@ theorem mul_le_of_le_one_of_le [CovariantClass α α (swap (· * ·)) (· ≤ ·
_ ≤ c := hbc
#align mul_le_of_le_one_of_le mul_le_of_le_one_of_le
#align add_le_of_nonpos_of_le add_le_of_nonpos_of_le
+-/
+#print mul_lt_of_lt_one_of_le /-
@[to_additive]
theorem mul_lt_of_lt_one_of_le [CovariantClass α α (swap (· * ·)) (· < ·)] {a b c : α} (ha : a < 1)
(hbc : b ≤ c) : a * b < c :=
@@ -789,7 +882,9 @@ theorem mul_lt_of_lt_one_of_le [CovariantClass α α (swap (· * ·)) (· < ·)]
_ ≤ c := hbc
#align mul_lt_of_lt_one_of_le mul_lt_of_lt_one_of_le
#align add_lt_of_neg_of_le add_lt_of_neg_of_le
+-/
+#print mul_lt_of_le_one_of_lt /-
@[to_additive]
theorem mul_lt_of_le_one_of_lt [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α} (ha : a ≤ 1)
(hb : b < c) : a * b < c :=
@@ -799,7 +894,9 @@ theorem mul_lt_of_le_one_of_lt [CovariantClass α α (swap (· * ·)) (· ≤ ·
_ < c := hb
#align mul_lt_of_le_one_of_lt mul_lt_of_le_one_of_lt
#align add_lt_of_nonpos_of_lt add_lt_of_nonpos_of_lt
+-/
+#print mul_lt_of_lt_one_of_lt /-
@[to_additive]
theorem mul_lt_of_lt_one_of_lt [CovariantClass α α (swap (· * ·)) (· < ·)] {a b c : α} (ha : a < 1)
(hb : b < c) : a * b < c :=
@@ -809,14 +906,18 @@ theorem mul_lt_of_lt_one_of_lt [CovariantClass α α (swap (· * ·)) (· < ·)]
_ < c := hb
#align mul_lt_of_lt_one_of_lt mul_lt_of_lt_one_of_lt
#align add_lt_of_neg_of_lt add_lt_of_neg_of_lt
+-/
+#print mul_lt_of_lt_one_of_lt' /-
@[to_additive]
theorem mul_lt_of_lt_one_of_lt' [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α} (ha : a < 1)
(hbc : b < c) : a * b < c :=
mul_lt_of_le_one_of_lt ha.le hbc
#align mul_lt_of_lt_one_of_lt' mul_lt_of_lt_one_of_lt'
#align add_lt_of_neg_of_lt' add_lt_of_neg_of_lt'
+-/
+#print Right.mul_le_one /-
/-- Assumes right covariance.
The lemma assuming left covariance is `left.mul_le_one`. -/
@[to_additive "Assumes right covariance.\nThe lemma assuming left covariance is `left.add_nonpos`."]
@@ -825,7 +926,9 @@ theorem Right.mul_le_one [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a
mul_le_of_le_one_of_le ha hb
#align right.mul_le_one Right.mul_le_one
#align right.add_nonpos Right.add_nonpos
+-/
+#print Right.mul_lt_one_of_lt_of_le /-
/-- Assumes right covariance.
The lemma assuming left covariance is `left.mul_lt_one_of_lt_of_le`. -/
@[to_additive Right.add_neg_of_neg_of_nonpos
@@ -835,7 +938,9 @@ theorem Right.mul_lt_one_of_lt_of_le [CovariantClass α α (swap (· * ·)) (·
mul_lt_of_lt_one_of_le ha hb
#align right.mul_lt_one_of_lt_of_le Right.mul_lt_one_of_lt_of_le
#align right.add_neg_of_neg_of_nonpos Right.add_neg_of_neg_of_nonpos
+-/
+#print Right.mul_lt_one_of_le_of_lt /-
/-- Assumes right covariance.
The lemma assuming left covariance is `left.mul_lt_one_of_le_of_lt`. -/
@[to_additive Right.add_neg_of_nonpos_of_neg
@@ -845,7 +950,9 @@ theorem Right.mul_lt_one_of_le_of_lt [CovariantClass α α (swap (· * ·)) (·
mul_lt_of_le_one_of_lt ha hb
#align right.mul_lt_one_of_le_of_lt Right.mul_lt_one_of_le_of_lt
#align right.add_neg_of_nonpos_of_neg Right.add_neg_of_nonpos_of_neg
+-/
+#print Right.mul_lt_one /-
/-- Assumes right covariance.
The lemma assuming left covariance is `left.mul_lt_one`. -/
@[to_additive "Assumes right covariance.\nThe lemma assuming left covariance is `left.add_neg`."]
@@ -854,7 +961,9 @@ theorem Right.mul_lt_one [CovariantClass α α (swap (· * ·)) (· < ·)] {a b
mul_lt_of_lt_one_of_lt ha hb
#align right.mul_lt_one Right.mul_lt_one
#align right.add_neg Right.add_neg
+-/
+#print Right.mul_lt_one' /-
/-- Assumes right covariance.
The lemma assuming left covariance is `left.mul_lt_one'`. -/
@[to_additive "Assumes right covariance.\nThe lemma assuming left covariance is `left.add_neg'`."]
@@ -863,11 +972,13 @@ theorem Right.mul_lt_one' [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a
mul_lt_of_lt_one_of_lt' ha hb
#align right.mul_lt_one' Right.mul_lt_one'
#align right.add_neg' Right.add_neg'
+-/
/-! Lemmas of the form `1 ≤ a → b ≤ c → b ≤ a * c`,
which assume right covariance. -/
+#print le_mul_of_one_le_of_le /-
@[to_additive]
theorem le_mul_of_one_le_of_le [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α} (ha : 1 ≤ a)
(hbc : b ≤ c) : b ≤ a * c :=
@@ -877,7 +988,9 @@ theorem le_mul_of_one_le_of_le [CovariantClass α α (swap (· * ·)) (· ≤ ·
_ ≤ a * c := mul_le_mul_right' ha c
#align le_mul_of_one_le_of_le le_mul_of_one_le_of_le
#align le_add_of_nonneg_of_le le_add_of_nonneg_of_le
+-/
+#print lt_mul_of_one_lt_of_le /-
@[to_additive]
theorem lt_mul_of_one_lt_of_le [CovariantClass α α (swap (· * ·)) (· < ·)] {a b c : α} (ha : 1 < a)
(hbc : b ≤ c) : b < a * c :=
@@ -887,7 +1000,9 @@ theorem lt_mul_of_one_lt_of_le [CovariantClass α α (swap (· * ·)) (· < ·)]
_ < a * c := mul_lt_mul_right' ha c
#align lt_mul_of_one_lt_of_le lt_mul_of_one_lt_of_le
#align lt_add_of_pos_of_le lt_add_of_pos_of_le
+-/
+#print lt_mul_of_one_le_of_lt /-
@[to_additive]
theorem lt_mul_of_one_le_of_lt [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α} (ha : 1 ≤ a)
(hbc : b < c) : b < a * c :=
@@ -897,7 +1012,9 @@ theorem lt_mul_of_one_le_of_lt [CovariantClass α α (swap (· * ·)) (· ≤ ·
_ ≤ a * c := mul_le_mul_right' ha c
#align lt_mul_of_one_le_of_lt lt_mul_of_one_le_of_lt
#align lt_add_of_nonneg_of_lt lt_add_of_nonneg_of_lt
+-/
+#print lt_mul_of_one_lt_of_lt /-
@[to_additive]
theorem lt_mul_of_one_lt_of_lt [CovariantClass α α (swap (· * ·)) (· < ·)] {a b c : α} (ha : 1 < a)
(hbc : b < c) : b < a * c :=
@@ -907,14 +1024,18 @@ theorem lt_mul_of_one_lt_of_lt [CovariantClass α α (swap (· * ·)) (· < ·)]
_ < a * c := mul_lt_mul_right' ha c
#align lt_mul_of_one_lt_of_lt lt_mul_of_one_lt_of_lt
#align lt_add_of_pos_of_lt lt_add_of_pos_of_lt
+-/
+#print lt_mul_of_one_lt_of_lt' /-
@[to_additive]
theorem lt_mul_of_one_lt_of_lt' [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α} (ha : 1 < a)
(hbc : b < c) : b < a * c :=
lt_mul_of_one_le_of_lt ha.le hbc
#align lt_mul_of_one_lt_of_lt' lt_mul_of_one_lt_of_lt'
#align lt_add_of_pos_of_lt' lt_add_of_pos_of_lt'
+-/
+#print Right.one_le_mul /-
/-- Assumes right covariance.
The lemma assuming left covariance is `left.one_le_mul`. -/
@[to_additive Right.add_nonneg
@@ -924,7 +1045,9 @@ theorem Right.one_le_mul [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a
le_mul_of_one_le_of_le ha hb
#align right.one_le_mul Right.one_le_mul
#align right.add_nonneg Right.add_nonneg
+-/
+#print Right.one_lt_mul_of_lt_of_le /-
/-- Assumes right covariance.
The lemma assuming left covariance is `left.one_lt_mul_of_lt_of_le`. -/
@[to_additive Right.add_pos_of_pos_of_nonneg
@@ -934,7 +1057,9 @@ theorem Right.one_lt_mul_of_lt_of_le [CovariantClass α α (swap (· * ·)) (·
lt_mul_of_one_lt_of_le ha hb
#align right.one_lt_mul_of_lt_of_le Right.one_lt_mul_of_lt_of_le
#align right.add_pos_of_pos_of_nonneg Right.add_pos_of_pos_of_nonneg
+-/
+#print Right.one_lt_mul_of_le_of_lt /-
/-- Assumes right covariance.
The lemma assuming left covariance is `left.one_lt_mul_of_le_of_lt`. -/
@[to_additive Right.add_pos_of_nonneg_of_pos
@@ -944,7 +1069,9 @@ theorem Right.one_lt_mul_of_le_of_lt [CovariantClass α α (swap (· * ·)) (·
lt_mul_of_one_le_of_lt ha hb
#align right.one_lt_mul_of_le_of_lt Right.one_lt_mul_of_le_of_lt
#align right.add_pos_of_nonneg_of_pos Right.add_pos_of_nonneg_of_pos
+-/
+#print Right.one_lt_mul /-
/-- Assumes right covariance.
The lemma assuming left covariance is `left.one_lt_mul`. -/
@[to_additive Right.add_pos
@@ -954,7 +1081,9 @@ theorem Right.one_lt_mul [CovariantClass α α (swap (· * ·)) (· < ·)] {a b
lt_mul_of_one_lt_of_lt ha hb
#align right.one_lt_mul Right.one_lt_mul
#align right.add_pos Right.add_pos
+-/
+#print Right.one_lt_mul' /-
/-- Assumes right covariance.
The lemma assuming left covariance is `left.one_lt_mul'`. -/
@[to_additive Right.add_pos'
@@ -964,6 +1093,7 @@ theorem Right.one_lt_mul' [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a
lt_mul_of_one_lt_of_lt' ha hb
#align right.one_lt_mul' Right.one_lt_mul'
#align right.add_pos' Right.add_pos'
+-/
alias Left.mul_le_one ← mul_le_one'
#align mul_le_one' mul_le_one'
@@ -1019,61 +1149,77 @@ attribute [to_additive add_pos "**Alias** of `left.add_pos`."] one_lt_mul'
attribute [to_additive add_pos' "**Alias** of `left.add_pos'`."] one_lt_mul''
+#print lt_of_mul_lt_of_one_le_left /-
@[to_additive]
theorem lt_of_mul_lt_of_one_le_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (h : a * b < c)
(hle : 1 ≤ b) : a < c :=
(le_mul_of_one_le_right' hle).trans_lt h
#align lt_of_mul_lt_of_one_le_left lt_of_mul_lt_of_one_le_left
#align lt_of_add_lt_of_nonneg_left lt_of_add_lt_of_nonneg_left
+-/
+#print le_of_mul_le_of_one_le_left /-
@[to_additive]
theorem le_of_mul_le_of_one_le_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (h : a * b ≤ c)
(hle : 1 ≤ b) : a ≤ c :=
(le_mul_of_one_le_right' hle).trans h
#align le_of_mul_le_of_one_le_left le_of_mul_le_of_one_le_left
#align le_of_add_le_of_nonneg_left le_of_add_le_of_nonneg_left
+-/
+#print lt_of_lt_mul_of_le_one_left /-
@[to_additive]
theorem lt_of_lt_mul_of_le_one_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (h : a < b * c)
(hle : c ≤ 1) : a < b :=
h.trans_le (mul_le_of_le_one_right' hle)
#align lt_of_lt_mul_of_le_one_left lt_of_lt_mul_of_le_one_left
#align lt_of_lt_add_of_nonpos_left lt_of_lt_add_of_nonpos_left
+-/
+#print le_of_le_mul_of_le_one_left /-
@[to_additive]
theorem le_of_le_mul_of_le_one_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (h : a ≤ b * c)
(hle : c ≤ 1) : a ≤ b :=
h.trans (mul_le_of_le_one_right' hle)
#align le_of_le_mul_of_le_one_left le_of_le_mul_of_le_one_left
#align le_of_le_add_of_nonpos_left le_of_le_add_of_nonpos_left
+-/
+#print lt_of_mul_lt_of_one_le_right /-
@[to_additive]
theorem lt_of_mul_lt_of_one_le_right [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α}
(h : a * b < c) (hle : 1 ≤ a) : b < c :=
(le_mul_of_one_le_left' hle).trans_lt h
#align lt_of_mul_lt_of_one_le_right lt_of_mul_lt_of_one_le_right
#align lt_of_add_lt_of_nonneg_right lt_of_add_lt_of_nonneg_right
+-/
+#print le_of_mul_le_of_one_le_right /-
@[to_additive]
theorem le_of_mul_le_of_one_le_right [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α}
(h : a * b ≤ c) (hle : 1 ≤ a) : b ≤ c :=
(le_mul_of_one_le_left' hle).trans h
#align le_of_mul_le_of_one_le_right le_of_mul_le_of_one_le_right
#align le_of_add_le_of_nonneg_right le_of_add_le_of_nonneg_right
+-/
+#print lt_of_lt_mul_of_le_one_right /-
@[to_additive]
theorem lt_of_lt_mul_of_le_one_right [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α}
(h : a < b * c) (hle : b ≤ 1) : a < c :=
h.trans_le (mul_le_of_le_one_left' hle)
#align lt_of_lt_mul_of_le_one_right lt_of_lt_mul_of_le_one_right
#align lt_of_lt_add_of_nonpos_right lt_of_lt_add_of_nonpos_right
+-/
+#print le_of_le_mul_of_le_one_right /-
@[to_additive]
theorem le_of_le_mul_of_le_one_right [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α}
(h : a ≤ b * c) (hle : b ≤ 1) : a ≤ c :=
h.trans (mul_le_of_le_one_left' hle)
#align le_of_le_mul_of_le_one_right le_of_le_mul_of_le_one_right
#align le_of_le_add_of_nonpos_right le_of_le_add_of_nonpos_right
+-/
end Preorder
@@ -1081,6 +1227,7 @@ section PartialOrder
variable [PartialOrder α]
+#print mul_eq_one_iff' /-
@[to_additive]
theorem mul_eq_one_iff' [CovariantClass α α (· * ·) (· ≤ ·)]
[CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b : α} (ha : 1 ≤ a) (hb : 1 ≤ b) :
@@ -1095,7 +1242,9 @@ theorem mul_eq_one_iff' [CovariantClass α α (· * ·) (· ≤ ·)]
fun ⟨ha', hb'⟩ => by rw [ha', hb', mul_one]
#align mul_eq_one_iff' mul_eq_one_iff'
#align add_eq_zero_iff' add_eq_zero_iff'
+-/
+#print mul_le_mul_iff_of_ge /-
@[to_additive]
theorem mul_le_mul_iff_of_ge [CovariantClass α α (· * ·) (· ≤ ·)]
[CovariantClass α α (swap (· * ·)) (· ≤ ·)] [CovariantClass α α (· * ·) (· < ·)]
@@ -1109,22 +1258,27 @@ theorem mul_le_mul_iff_of_ge [CovariantClass α α (· * ·) (· ≤ ·)]
· exact mul_lt_mul_of_le_of_lt ha hb
#align mul_le_mul_iff_of_ge mul_le_mul_iff_of_ge
#align add_le_add_iff_of_ge add_le_add_iff_of_ge
+-/
section Left
variable [CovariantClass α α (· * ·) (· ≤ ·)] {a b : α}
+#print eq_one_of_one_le_mul_left /-
@[to_additive eq_zero_of_add_nonneg_left]
theorem eq_one_of_one_le_mul_left (ha : a ≤ 1) (hb : b ≤ 1) (hab : 1 ≤ a * b) : a = 1 :=
ha.eq_of_not_lt fun h => hab.not_lt <| mul_lt_one_of_lt_of_le h hb
#align eq_one_of_one_le_mul_left eq_one_of_one_le_mul_left
#align eq_zero_of_add_nonneg_left eq_zero_of_add_nonneg_left
+-/
+#print eq_one_of_mul_le_one_left /-
@[to_additive]
theorem eq_one_of_mul_le_one_left (ha : 1 ≤ a) (hb : 1 ≤ b) (hab : a * b ≤ 1) : a = 1 :=
ha.eq_of_not_gt fun h => hab.not_lt <| one_lt_mul_of_lt_of_le' h hb
#align eq_one_of_mul_le_one_left eq_one_of_mul_le_one_left
#align eq_zero_of_add_nonpos_left eq_zero_of_add_nonpos_left
+-/
end Left
@@ -1132,17 +1286,21 @@ section Right
variable [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b : α}
+#print eq_one_of_one_le_mul_right /-
@[to_additive eq_zero_of_add_nonneg_right]
theorem eq_one_of_one_le_mul_right (ha : a ≤ 1) (hb : b ≤ 1) (hab : 1 ≤ a * b) : b = 1 :=
hb.eq_of_not_lt fun h => hab.not_lt <| Right.mul_lt_one_of_le_of_lt ha h
#align eq_one_of_one_le_mul_right eq_one_of_one_le_mul_right
#align eq_zero_of_add_nonneg_right eq_zero_of_add_nonneg_right
+-/
+#print eq_one_of_mul_le_one_right /-
@[to_additive]
theorem eq_one_of_mul_le_one_right (ha : 1 ≤ a) (hb : 1 ≤ b) (hab : a * b ≤ 1) : b = 1 :=
hb.eq_of_not_gt fun h => hab.not_lt <| Right.one_lt_mul_of_le_of_lt ha h
#align eq_one_of_mul_le_one_right eq_one_of_mul_le_one_right
#align eq_zero_of_add_nonpos_right eq_zero_of_add_nonpos_right
+-/
end Right
@@ -1152,6 +1310,7 @@ section LinearOrder
variable [LinearOrder α]
+#print exists_square_le /-
theorem exists_square_le [CovariantClass α α (· * ·) (· < ·)] (a : α) : ∃ b : α, b * b ≤ a :=
by
by_cases h : a < 1
@@ -1163,6 +1322,7 @@ theorem exists_square_le [CovariantClass α α (· * ·) (· < ·)] (a : α) :
push_neg at h
rwa [mul_one]
#align exists_square_le exists_square_le
+-/
end LinearOrder
@@ -1176,6 +1336,7 @@ section PartialOrder
variable [PartialOrder α]
+#print Contravariant.toLeftCancelSemigroup /-
/- This is not instance, since we want to have an instance from `left_cancel_semigroup`s
to the appropriate `covariant_class`. -/
/-- A semigroup with a partial order and satisfying `left_cancel_semigroup`
@@ -1187,7 +1348,9 @@ def Contravariant.toLeftCancelSemigroup [ContravariantClass α α (· * ·) (·
{ ‹Semigroup α› with mul_left_cancel := fun a b c => mul_left_cancel'' }
#align contravariant.to_left_cancel_semigroup Contravariant.toLeftCancelSemigroup
#align contravariant.to_left_cancel_add_semigroup Contravariant.toAddLeftCancelSemigroup
+-/
+#print Contravariant.toRightCancelSemigroup /-
/- This is not instance, since we want to have an instance from `right_cancel_semigroup`s
to the appropriate `covariant_class`. -/
/-- A semigroup with a partial order and satisfying `right_cancel_semigroup`
@@ -1199,7 +1362,9 @@ def Contravariant.toRightCancelSemigroup [ContravariantClass α α (swap (· *
{ ‹Semigroup α› with mul_right_cancel := fun a b c => mul_right_cancel'' }
#align contravariant.to_right_cancel_semigroup Contravariant.toRightCancelSemigroup
#align contravariant.to_right_cancel_add_semigroup Contravariant.toAddRightCancelSemigroup
+-/
+#print Left.mul_eq_mul_iff_eq_and_eq /-
@[to_additive]
theorem Left.mul_eq_mul_iff_eq_and_eq [CovariantClass α α (· * ·) (· < ·)]
[CovariantClass α α (swap (· * ·)) (· ≤ ·)] [ContravariantClass α α (· * ·) (· ≤ ·)]
@@ -1214,7 +1379,9 @@ theorem Left.mul_eq_mul_iff_eq_and_eq [CovariantClass α α (· * ·) (· < ·)]
exact ((Left.mul_lt_mul hac hbd).Ne h).elim
#align left.mul_eq_mul_iff_eq_and_eq Left.mul_eq_mul_iff_eq_and_eq
#align left.add_eq_add_iff_eq_and_eq Left.add_eq_add_iff_eq_and_eq
+-/
+#print Right.mul_eq_mul_iff_eq_and_eq /-
@[to_additive]
theorem Right.mul_eq_mul_iff_eq_and_eq [CovariantClass α α (· * ·) (· ≤ ·)]
[ContravariantClass α α (· * ·) (· ≤ ·)] [CovariantClass α α (swap (· * ·)) (· < ·)]
@@ -1229,6 +1396,7 @@ theorem Right.mul_eq_mul_iff_eq_and_eq [CovariantClass α α (· * ·) (· ≤
exact ((Right.mul_lt_mul hac hbd).Ne h).elim
#align right.mul_eq_mul_iff_eq_and_eq Right.mul_eq_mul_iff_eq_and_eq
#align right.add_eq_add_iff_eq_and_eq Right.add_eq_add_iff_eq_and_eq
+-/
alias Left.mul_eq_mul_iff_eq_and_eq ← mul_eq_mul_iff_eq_and_eq
#align mul_eq_mul_iff_eq_and_eq mul_eq_mul_iff_eq_and_eq
@@ -1243,54 +1411,71 @@ section Mono
variable [Mul α] [Preorder α] [Preorder β] {f g : β → α} {s : Set β}
+#print Monotone.const_mul' /-
@[to_additive const_add]
theorem Monotone.const_mul' [CovariantClass α α (· * ·) (· ≤ ·)] (hf : Monotone f) (a : α) :
Monotone fun x => a * f x := fun x y h => mul_le_mul_left' (hf h) a
#align monotone.const_mul' Monotone.const_mul'
#align monotone.const_add Monotone.const_add
+-/
+#print MonotoneOn.const_mul' /-
@[to_additive const_add]
theorem MonotoneOn.const_mul' [CovariantClass α α (· * ·) (· ≤ ·)] (hf : MonotoneOn f s) (a : α) :
MonotoneOn (fun x => a * f x) s := fun x hx y hy h => mul_le_mul_left' (hf hx hy h) a
#align monotone_on.const_mul' MonotoneOn.const_mul'
#align monotone_on.const_add MonotoneOn.const_add
+-/
+#print Antitone.const_mul' /-
@[to_additive const_add]
theorem Antitone.const_mul' [CovariantClass α α (· * ·) (· ≤ ·)] (hf : Antitone f) (a : α) :
Antitone fun x => a * f x := fun x y h => mul_le_mul_left' (hf h) a
#align antitone.const_mul' Antitone.const_mul'
#align antitone.const_add Antitone.const_add
+-/
+#print AntitoneOn.const_mul' /-
@[to_additive const_add]
theorem AntitoneOn.const_mul' [CovariantClass α α (· * ·) (· ≤ ·)] (hf : AntitoneOn f s) (a : α) :
AntitoneOn (fun x => a * f x) s := fun x hx y hy h => mul_le_mul_left' (hf hx hy h) a
#align antitone_on.const_mul' AntitoneOn.const_mul'
#align antitone_on.const_add AntitoneOn.const_add
+-/
+#print Monotone.mul_const' /-
@[to_additive add_const]
theorem Monotone.mul_const' [CovariantClass α α (swap (· * ·)) (· ≤ ·)] (hf : Monotone f) (a : α) :
Monotone fun x => f x * a := fun x y h => mul_le_mul_right' (hf h) a
#align monotone.mul_const' Monotone.mul_const'
#align monotone.add_const Monotone.add_const
+-/
+#print MonotoneOn.mul_const' /-
@[to_additive add_const]
theorem MonotoneOn.mul_const' [CovariantClass α α (swap (· * ·)) (· ≤ ·)] (hf : MonotoneOn f s)
(a : α) : MonotoneOn (fun x => f x * a) s := fun x hx y hy h => mul_le_mul_right' (hf hx hy h) a
#align monotone_on.mul_const' MonotoneOn.mul_const'
#align monotone_on.add_const MonotoneOn.add_const
+-/
+#print Antitone.mul_const' /-
@[to_additive add_const]
theorem Antitone.mul_const' [CovariantClass α α (swap (· * ·)) (· ≤ ·)] (hf : Antitone f) (a : α) :
Antitone fun x => f x * a := fun x y h => mul_le_mul_right' (hf h) a
#align antitone.mul_const' Antitone.mul_const'
#align antitone.add_const Antitone.add_const
+-/
+#print AntitoneOn.mul_const' /-
@[to_additive add_const]
theorem AntitoneOn.mul_const' [CovariantClass α α (swap (· * ·)) (· ≤ ·)] (hf : AntitoneOn f s)
(a : α) : AntitoneOn (fun x => f x * a) s := fun x hx y hy h => mul_le_mul_right' (hf hx hy h) a
#align antitone_on.mul_const' AntitoneOn.mul_const'
#align antitone_on.add_const AntitoneOn.add_const
+-/
+#print Monotone.mul' /-
/-- The product of two monotone functions is monotone. -/
@[to_additive add "The sum of two monotone functions is monotone."]
theorem Monotone.mul' [CovariantClass α α (· * ·) (· ≤ ·)]
@@ -1298,7 +1483,9 @@ theorem Monotone.mul' [CovariantClass α α (· * ·) (· ≤ ·)]
Monotone fun x => f x * g x := fun x y h => mul_le_mul' (hf h) (hg h)
#align monotone.mul' Monotone.mul'
#align monotone.add Monotone.add
+-/
+#print MonotoneOn.mul' /-
/-- The product of two monotone functions is monotone. -/
@[to_additive add "The sum of two monotone functions is monotone."]
theorem MonotoneOn.mul' [CovariantClass α α (· * ·) (· ≤ ·)]
@@ -1306,7 +1493,9 @@ theorem MonotoneOn.mul' [CovariantClass α α (· * ·) (· ≤ ·)]
MonotoneOn (fun x => f x * g x) s := fun x hx y hy h => mul_le_mul' (hf hx hy h) (hg hx hy h)
#align monotone_on.mul' MonotoneOn.mul'
#align monotone_on.add MonotoneOn.add
+-/
+#print Antitone.mul' /-
/-- The product of two antitone functions is antitone. -/
@[to_additive add "The sum of two antitone functions is antitone."]
theorem Antitone.mul' [CovariantClass α α (· * ·) (· ≤ ·)]
@@ -1314,7 +1503,9 @@ theorem Antitone.mul' [CovariantClass α α (· * ·) (· ≤ ·)]
Antitone fun x => f x * g x := fun x y h => mul_le_mul' (hf h) (hg h)
#align antitone.mul' Antitone.mul'
#align antitone.add Antitone.add
+-/
+#print AntitoneOn.mul' /-
/-- The product of two antitone functions is antitone. -/
@[to_additive add "The sum of two antitone functions is antitone."]
theorem AntitoneOn.mul' [CovariantClass α α (· * ·) (· ≤ ·)]
@@ -1322,6 +1513,7 @@ theorem AntitoneOn.mul' [CovariantClass α α (· * ·) (· ≤ ·)]
AntitoneOn (fun x => f x * g x) s := fun x hx y hy h => mul_le_mul' (hf hx hy h) (hg hx hy h)
#align antitone_on.mul' AntitoneOn.mul'
#align antitone_on.add AntitoneOn.add
+-/
section Left
@@ -1399,6 +1591,7 @@ theorem StrictAntiOn.mul_const' (hf : StrictAntiOn f s) (c : α) :
end Right
+#print StrictMono.mul' /-
/-- The product of two strictly monotone functions is strictly monotone. -/
@[to_additive add "The sum of two strictly monotone functions is strictly monotone."]
theorem StrictMono.mul' [CovariantClass α α (· * ·) (· < ·)]
@@ -1406,7 +1599,9 @@ theorem StrictMono.mul' [CovariantClass α α (· * ·) (· < ·)]
StrictMono fun x => f x * g x := fun a b ab => mul_lt_mul_of_lt_of_lt (hf ab) (hg ab)
#align strict_mono.mul' StrictMono.mul'
#align strict_mono.add StrictMono.add
+-/
+#print StrictMonoOn.mul' /-
/-- The product of two strictly monotone functions is strictly monotone. -/
@[to_additive add "The sum of two strictly monotone functions is strictly monotone."]
theorem StrictMonoOn.mul' [CovariantClass α α (· * ·) (· < ·)]
@@ -1415,7 +1610,9 @@ theorem StrictMonoOn.mul' [CovariantClass α α (· * ·) (· < ·)]
mul_lt_mul_of_lt_of_lt (hf ha hb ab) (hg ha hb ab)
#align strict_mono_on.mul' StrictMonoOn.mul'
#align strict_mono_on.add StrictMonoOn.add
+-/
+#print StrictAnti.mul' /-
/-- The product of two strictly antitone functions is strictly antitone. -/
@[to_additive add "The sum of two strictly antitone functions is strictly antitone."]
theorem StrictAnti.mul' [CovariantClass α α (· * ·) (· < ·)]
@@ -1423,7 +1620,9 @@ theorem StrictAnti.mul' [CovariantClass α α (· * ·) (· < ·)]
StrictAnti fun x => f x * g x := fun a b ab => mul_lt_mul_of_lt_of_lt (hf ab) (hg ab)
#align strict_anti.mul' StrictAnti.mul'
#align strict_anti.add StrictAnti.add
+-/
+#print StrictAntiOn.mul' /-
/-- The product of two strictly antitone functions is strictly antitone. -/
@[to_additive add "The sum of two strictly antitone functions is strictly antitone."]
theorem StrictAntiOn.mul' [CovariantClass α α (· * ·) (· < ·)]
@@ -1432,7 +1631,9 @@ theorem StrictAntiOn.mul' [CovariantClass α α (· * ·) (· < ·)]
mul_lt_mul_of_lt_of_lt (hf ha hb ab) (hg ha hb ab)
#align strict_anti_on.mul' StrictAntiOn.mul'
#align strict_anti_on.add StrictAntiOn.add
+-/
+#print Monotone.mul_strictMono' /-
/-- The product of a monotone function and a strictly monotone function is strictly monotone. -/
@[to_additive add_strict_mono
"The sum of a monotone function and a strictly monotone function is strictly monotone."]
@@ -1442,7 +1643,9 @@ theorem Monotone.mul_strictMono' [CovariantClass α α (· * ·) (· < ·)]
mul_lt_mul_of_le_of_lt (hf h.le) (hg h)
#align monotone.mul_strict_mono' Monotone.mul_strictMono'
#align monotone.add_strict_mono Monotone.add_strictMono
+-/
+#print MonotoneOn.mul_strictMono' /-
/-- The product of a monotone function and a strictly monotone function is strictly monotone. -/
@[to_additive add_strict_mono
"The sum of a monotone function and a strictly monotone function is strictly monotone."]
@@ -1452,7 +1655,9 @@ theorem MonotoneOn.mul_strictMono' [CovariantClass α α (· * ·) (· < ·)]
mul_lt_mul_of_le_of_lt (hf hx hy h.le) (hg hx hy h)
#align monotone_on.mul_strict_mono' MonotoneOn.mul_strictMono'
#align monotone_on.add_strict_mono MonotoneOn.add_strictMono
+-/
+#print Antitone.mul_strictAnti' /-
/-- The product of a antitone function and a strictly antitone function is strictly antitone. -/
@[to_additive add_strict_anti
"The sum of a antitone function and a strictly antitone function is strictly antitone."]
@@ -1462,7 +1667,9 @@ theorem Antitone.mul_strictAnti' [CovariantClass α α (· * ·) (· < ·)]
mul_lt_mul_of_le_of_lt (hf h.le) (hg h)
#align antitone.mul_strict_anti' Antitone.mul_strictAnti'
#align antitone.add_strict_anti Antitone.add_strictAnti
+-/
+#print AntitoneOn.mul_strictAnti' /-
/-- The product of a antitone function and a strictly antitone function is strictly antitone. -/
@[to_additive add_strict_anti
"The sum of a antitone function and a strictly antitone function is strictly antitone."]
@@ -1472,6 +1679,7 @@ theorem AntitoneOn.mul_strictAnti' [CovariantClass α α (· * ·) (· < ·)]
mul_lt_mul_of_le_of_lt (hf hx hy h.le) (hg hx hy h)
#align antitone_on.mul_strict_anti' AntitoneOn.mul_strictAnti'
#align antitone_on.add_strict_anti AntitoneOn.add_strictAnti
+-/
variable [CovariantClass α α (· * ·) (· ≤ ·)] [CovariantClass α α (swap (· * ·)) (· < ·)]
@@ -1559,11 +1767,13 @@ theorem Contravariant.MulLECancellable [Mul α] [LE α] [ContravariantClass α
#align contravariant.add_le_cancellable Contravariant.AddLECancellable
-/
+#print mulLECancellable_one /-
@[to_additive]
theorem mulLECancellable_one [Monoid α] [LE α] : MulLECancellable (1 : α) := fun a b => by
simpa only [one_mul] using id
#align mul_le_cancellable_one mulLECancellable_one
#align add_le_cancellable_zero addLECancellable_zero
+-/
namespace MulLECancellable
@@ -1584,19 +1794,23 @@ protected theorem inj [Mul α] [PartialOrder α] {a b c : α} (ha : MulLECancell
#align add_le_cancellable.inj AddLECancellable.inj
-/
+#print MulLECancellable.injective_left /-
@[to_additive]
protected theorem injective_left [CommSemigroup α] [PartialOrder α] {a : α}
(ha : MulLECancellable a) : Injective (· * a) := fun b c h =>
ha.Injective <| by rwa [mul_comm a, mul_comm a]
#align mul_le_cancellable.injective_left MulLECancellable.injective_left
#align add_le_cancellable.injective_left AddLECancellable.injective_left
+-/
+#print MulLECancellable.inj_left /-
@[to_additive]
protected theorem inj_left [CommSemigroup α] [PartialOrder α] {a b c : α}
(hc : MulLECancellable c) : a * c = b * c ↔ a = b :=
hc.injective_left.eq_iff
#align mul_le_cancellable.inj_left MulLECancellable.inj_left
#align add_le_cancellable.inj_left AddLECancellable.inj_left
+-/
variable [LE α]
@@ -1609,40 +1823,50 @@ protected theorem mul_le_mul_iff_left [Mul α] [CovariantClass α α (· * ·) (
#align add_le_cancellable.add_le_add_iff_left AddLECancellable.add_le_add_iff_left
-/
+#print MulLECancellable.mul_le_mul_iff_right /-
@[to_additive]
protected theorem mul_le_mul_iff_right [CommSemigroup α] [CovariantClass α α (· * ·) (· ≤ ·)]
{a b c : α} (ha : MulLECancellable a) : b * a ≤ c * a ↔ b ≤ c := by
rw [mul_comm b, mul_comm c, ha.mul_le_mul_iff_left]
#align mul_le_cancellable.mul_le_mul_iff_right MulLECancellable.mul_le_mul_iff_right
#align add_le_cancellable.add_le_add_iff_right AddLECancellable.add_le_add_iff_right
+-/
+#print MulLECancellable.le_mul_iff_one_le_right /-
@[to_additive]
protected theorem le_mul_iff_one_le_right [MulOneClass α] [CovariantClass α α (· * ·) (· ≤ ·)]
{a b : α} (ha : MulLECancellable a) : a ≤ a * b ↔ 1 ≤ b :=
Iff.trans (by rw [mul_one]) ha.mul_le_mul_iff_left
#align mul_le_cancellable.le_mul_iff_one_le_right MulLECancellable.le_mul_iff_one_le_right
#align add_le_cancellable.le_add_iff_nonneg_right AddLECancellable.le_add_iff_nonneg_right
+-/
+#print MulLECancellable.mul_le_iff_le_one_right /-
@[to_additive]
protected theorem mul_le_iff_le_one_right [MulOneClass α] [CovariantClass α α (· * ·) (· ≤ ·)]
{a b : α} (ha : MulLECancellable a) : a * b ≤ a ↔ b ≤ 1 :=
Iff.trans (by rw [mul_one]) ha.mul_le_mul_iff_left
#align mul_le_cancellable.mul_le_iff_le_one_right MulLECancellable.mul_le_iff_le_one_right
#align add_le_cancellable.add_le_iff_nonpos_right AddLECancellable.add_le_iff_nonpos_right
+-/
+#print MulLECancellable.le_mul_iff_one_le_left /-
@[to_additive]
protected theorem le_mul_iff_one_le_left [CommMonoid α] [CovariantClass α α (· * ·) (· ≤ ·)]
{a b : α} (ha : MulLECancellable a) : a ≤ b * a ↔ 1 ≤ b := by
rw [mul_comm, ha.le_mul_iff_one_le_right]
#align mul_le_cancellable.le_mul_iff_one_le_left MulLECancellable.le_mul_iff_one_le_left
#align add_le_cancellable.le_add_iff_nonneg_left AddLECancellable.le_add_iff_nonneg_left
+-/
+#print MulLECancellable.mul_le_iff_le_one_left /-
@[to_additive]
protected theorem mul_le_iff_le_one_left [CommMonoid α] [CovariantClass α α (· * ·) (· ≤ ·)]
{a b : α} (ha : MulLECancellable a) : b * a ≤ a ↔ b ≤ 1 := by
rw [mul_comm, ha.mul_le_iff_le_one_right]
#align mul_le_cancellable.mul_le_iff_le_one_left MulLECancellable.mul_le_iff_le_one_left
#align add_le_cancellable.add_le_iff_nonpos_left AddLECancellable.add_le_iff_nonpos_left
+-/
end MulLECancellable
mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0
@@ -180,7 +180,6 @@ theorem mul_lt_mul_of_lt_of_lt [CovariantClass α α (· * ·) (· < ·)]
calc
a * c < a * d := mul_lt_mul_left' h₂ a
_ < b * d := mul_lt_mul_right' h₁ d
-
#align mul_lt_mul_of_lt_of_lt mul_lt_mul_of_lt_of_lt
#align add_lt_add_of_lt_of_lt add_lt_add_of_lt_of_lt
-/
@@ -377,7 +376,6 @@ theorem le_mul_of_one_le_right' [CovariantClass α α (· * ·) (· ≤ ·)] {a
calc
a = a * 1 := (mul_one a).symm
_ ≤ a * b := mul_le_mul_left' h a
-
#align le_mul_of_one_le_right' le_mul_of_one_le_right'
#align le_add_of_nonneg_right le_add_of_nonneg_right
@@ -387,7 +385,6 @@ theorem mul_le_of_le_one_right' [CovariantClass α α (· * ·) (· ≤ ·)] {a
calc
a * b ≤ a * 1 := mul_le_mul_left' h a
_ = a := mul_one a
-
#align mul_le_of_le_one_right' mul_le_of_le_one_right'
#align add_le_of_nonpos_right add_le_of_nonpos_right
@@ -397,7 +394,6 @@ theorem le_mul_of_one_le_left' [CovariantClass α α (swap (· * ·)) (· ≤ ·
calc
a = 1 * a := (one_mul a).symm
_ ≤ b * a := mul_le_mul_right' h a
-
#align le_mul_of_one_le_left' le_mul_of_one_le_left'
#align le_add_of_nonneg_left le_add_of_nonneg_left
@@ -407,7 +403,6 @@ theorem mul_le_of_le_one_left' [CovariantClass α α (swap (· * ·)) (· ≤ ·
calc
b * a ≤ 1 * a := mul_le_mul_right' h a
_ = a := one_mul a
-
#align mul_le_of_le_one_left' mul_le_of_le_one_left'
#align add_le_of_nonpos_left add_le_of_nonpos_left
@@ -479,7 +474,6 @@ theorem lt_mul_of_one_lt_right' [CovariantClass α α (· * ·) (· < ·)] (a :
calc
a = a * 1 := (mul_one a).symm
_ < a * b := mul_lt_mul_left' h a
-
#align lt_mul_of_one_lt_right' lt_mul_of_one_lt_right'
#align lt_add_of_pos_right lt_add_of_pos_right
@@ -489,7 +483,6 @@ theorem mul_lt_of_lt_one_right' [CovariantClass α α (· * ·) (· < ·)] (a :
calc
a * b < a * 1 := mul_lt_mul_left' h a
_ = a := mul_one a
-
#align mul_lt_of_lt_one_right' mul_lt_of_lt_one_right'
#align add_lt_of_neg_right add_lt_of_neg_right
@@ -499,7 +492,6 @@ theorem lt_mul_of_one_lt_left' [CovariantClass α α (swap (· * ·)) (· < ·)]
calc
a = 1 * a := (one_mul a).symm
_ < b * a := mul_lt_mul_right' h a
-
#align lt_mul_of_one_lt_left' lt_mul_of_one_lt_left'
#align lt_add_of_pos_left lt_add_of_pos_left
@@ -509,7 +501,6 @@ theorem mul_lt_of_lt_one_left' [CovariantClass α α (swap (· * ·)) (· < ·)]
calc
b * a < 1 * a := mul_lt_mul_right' h a
_ = a := one_mul a
-
#align mul_lt_of_lt_one_left' mul_lt_of_lt_one_left'
#align add_lt_of_neg_left add_lt_of_neg_left
@@ -586,7 +577,6 @@ theorem mul_le_of_le_of_le_one [CovariantClass α α (· * ·) (· ≤ ·)] {a b
b * a ≤ b * 1 := mul_le_mul_left' ha b
_ = b := (mul_one b)
_ ≤ c := hbc
-
#align mul_le_of_le_of_le_one mul_le_of_le_of_le_one
#align add_le_of_le_of_nonpos add_le_of_le_of_nonpos
@@ -597,7 +587,6 @@ theorem mul_lt_of_le_of_lt_one [CovariantClass α α (· * ·) (· < ·)] {a b c
b * a < b * 1 := mul_lt_mul_left' ha b
_ = b := (mul_one b)
_ ≤ c := hbc
-
#align mul_lt_of_le_of_lt_one mul_lt_of_le_of_lt_one
#align add_lt_of_le_of_neg add_lt_of_le_of_neg
@@ -608,7 +597,6 @@ theorem mul_lt_of_lt_of_le_one [CovariantClass α α (· * ·) (· ≤ ·)] {a b
b * a ≤ b * 1 := mul_le_mul_left' ha b
_ = b := (mul_one b)
_ < c := hbc
-
#align mul_lt_of_lt_of_le_one mul_lt_of_lt_of_le_one
#align add_lt_of_lt_of_nonpos add_lt_of_lt_of_nonpos
@@ -619,7 +607,6 @@ theorem mul_lt_of_lt_of_lt_one [CovariantClass α α (· * ·) (· < ·)] {a b c
b * a < b * 1 := mul_lt_mul_left' ha b
_ = b := (mul_one b)
_ < c := hbc
-
#align mul_lt_of_lt_of_lt_one mul_lt_of_lt_of_lt_one
#align add_lt_of_lt_of_neg add_lt_of_lt_of_neg
@@ -689,7 +676,6 @@ theorem le_mul_of_le_of_one_le [CovariantClass α α (· * ·) (· ≤ ·)] {a b
b ≤ c := hbc
_ = c * 1 := (mul_one c).symm
_ ≤ c * a := mul_le_mul_left' ha c
-
#align le_mul_of_le_of_one_le le_mul_of_le_of_one_le
#align le_add_of_le_of_nonneg le_add_of_le_of_nonneg
@@ -700,7 +686,6 @@ theorem lt_mul_of_le_of_one_lt [CovariantClass α α (· * ·) (· < ·)] {a b c
b ≤ c := hbc
_ = c * 1 := (mul_one c).symm
_ < c * a := mul_lt_mul_left' ha c
-
#align lt_mul_of_le_of_one_lt lt_mul_of_le_of_one_lt
#align lt_add_of_le_of_pos lt_add_of_le_of_pos
@@ -711,7 +696,6 @@ theorem lt_mul_of_lt_of_one_le [CovariantClass α α (· * ·) (· ≤ ·)] {a b
b < c := hbc
_ = c * 1 := (mul_one c).symm
_ ≤ c * a := mul_le_mul_left' ha c
-
#align lt_mul_of_lt_of_one_le lt_mul_of_lt_of_one_le
#align lt_add_of_lt_of_nonneg lt_add_of_lt_of_nonneg
@@ -722,7 +706,6 @@ theorem lt_mul_of_lt_of_one_lt [CovariantClass α α (· * ·) (· < ·)] {a b c
b < c := hbc
_ = c * 1 := (mul_one c).symm
_ < c * a := mul_lt_mul_left' ha c
-
#align lt_mul_of_lt_of_one_lt lt_mul_of_lt_of_one_lt
#align lt_add_of_lt_of_pos lt_add_of_lt_of_pos
@@ -794,7 +777,6 @@ theorem mul_le_of_le_one_of_le [CovariantClass α α (swap (· * ·)) (· ≤ ·
a * b ≤ 1 * b := mul_le_mul_right' ha b
_ = b := (one_mul b)
_ ≤ c := hbc
-
#align mul_le_of_le_one_of_le mul_le_of_le_one_of_le
#align add_le_of_nonpos_of_le add_le_of_nonpos_of_le
@@ -805,7 +787,6 @@ theorem mul_lt_of_lt_one_of_le [CovariantClass α α (swap (· * ·)) (· < ·)]
a * b < 1 * b := mul_lt_mul_right' ha b
_ = b := (one_mul b)
_ ≤ c := hbc
-
#align mul_lt_of_lt_one_of_le mul_lt_of_lt_one_of_le
#align add_lt_of_neg_of_le add_lt_of_neg_of_le
@@ -816,7 +797,6 @@ theorem mul_lt_of_le_one_of_lt [CovariantClass α α (swap (· * ·)) (· ≤ ·
a * b ≤ 1 * b := mul_le_mul_right' ha b
_ = b := (one_mul b)
_ < c := hb
-
#align mul_lt_of_le_one_of_lt mul_lt_of_le_one_of_lt
#align add_lt_of_nonpos_of_lt add_lt_of_nonpos_of_lt
@@ -827,7 +807,6 @@ theorem mul_lt_of_lt_one_of_lt [CovariantClass α α (swap (· * ·)) (· < ·)]
a * b < 1 * b := mul_lt_mul_right' ha b
_ = b := (one_mul b)
_ < c := hb
-
#align mul_lt_of_lt_one_of_lt mul_lt_of_lt_one_of_lt
#align add_lt_of_neg_of_lt add_lt_of_neg_of_lt
@@ -896,7 +875,6 @@ theorem le_mul_of_one_le_of_le [CovariantClass α α (swap (· * ·)) (· ≤ ·
b ≤ c := hbc
_ = 1 * c := (one_mul c).symm
_ ≤ a * c := mul_le_mul_right' ha c
-
#align le_mul_of_one_le_of_le le_mul_of_one_le_of_le
#align le_add_of_nonneg_of_le le_add_of_nonneg_of_le
@@ -907,7 +885,6 @@ theorem lt_mul_of_one_lt_of_le [CovariantClass α α (swap (· * ·)) (· < ·)]
b ≤ c := hbc
_ = 1 * c := (one_mul c).symm
_ < a * c := mul_lt_mul_right' ha c
-
#align lt_mul_of_one_lt_of_le lt_mul_of_one_lt_of_le
#align lt_add_of_pos_of_le lt_add_of_pos_of_le
@@ -918,7 +895,6 @@ theorem lt_mul_of_one_le_of_lt [CovariantClass α α (swap (· * ·)) (· ≤ ·
b < c := hbc
_ = 1 * c := (one_mul c).symm
_ ≤ a * c := mul_le_mul_right' ha c
-
#align lt_mul_of_one_le_of_lt lt_mul_of_one_le_of_lt
#align lt_add_of_nonneg_of_lt lt_add_of_nonneg_of_lt
@@ -929,7 +905,6 @@ theorem lt_mul_of_one_lt_of_lt [CovariantClass α α (swap (· * ·)) (· < ·)]
b < c := hbc
_ = 1 * c := (one_mul c).symm
_ < a * c := mul_lt_mul_right' ha c
-
#align lt_mul_of_one_lt_of_lt lt_mul_of_one_lt_of_lt
#align lt_add_of_pos_of_lt lt_add_of_pos_of_lt
mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297
@@ -1185,7 +1185,7 @@ theorem exists_square_le [CovariantClass α α (· * ·) (· < ·)] (a : α) :
rw [mul_one] at this
exact le_of_lt this
· use 1
- push_neg at h
+ push_neg at h
rwa [mul_one]
#align exists_square_le exists_square_le
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -1182,10 +1182,10 @@ theorem exists_square_le [CovariantClass α α (· * ·) (· < ·)] (a : α) :
by_cases h : a < 1
· use a
have : a * a < a * 1 := mul_lt_mul_left' h a
- rw [mul_one] at this
+ rw [mul_one] at this
exact le_of_lt this
· use 1
- push_neg at h
+ push_neg at h
rwa [mul_one]
#align exists_square_le exists_square_le
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -172,6 +172,7 @@ section Preorder
variable [Preorder α]
+#print mul_lt_mul_of_lt_of_lt /-
@[to_additive]
theorem mul_lt_mul_of_lt_of_lt [CovariantClass α α (· * ·) (· < ·)]
[CovariantClass α α (swap (· * ·)) (· < ·)] {a b c d : α} (h₁ : a < b) (h₂ : c < d) :
@@ -182,10 +183,12 @@ theorem mul_lt_mul_of_lt_of_lt [CovariantClass α α (· * ·) (· < ·)]
#align mul_lt_mul_of_lt_of_lt mul_lt_mul_of_lt_of_lt
#align add_lt_add_of_lt_of_lt add_lt_add_of_lt_of_lt
+-/
alias add_lt_add_of_lt_of_lt ← add_lt_add
#align add_lt_add add_lt_add
+#print mul_lt_mul_of_le_of_lt /-
@[to_additive]
theorem mul_lt_mul_of_le_of_lt [CovariantClass α α (· * ·) (· < ·)]
[CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c d : α} (h₁ : a ≤ b) (h₂ : c < d) :
@@ -193,7 +196,9 @@ theorem mul_lt_mul_of_le_of_lt [CovariantClass α α (· * ·) (· < ·)]
(mul_le_mul_right' h₁ _).trans_lt (mul_lt_mul_left' h₂ b)
#align mul_lt_mul_of_le_of_lt mul_lt_mul_of_le_of_lt
#align add_lt_add_of_le_of_lt add_lt_add_of_le_of_lt
+-/
+#print mul_lt_mul_of_lt_of_le /-
@[to_additive]
theorem mul_lt_mul_of_lt_of_le [CovariantClass α α (· * ·) (· ≤ ·)]
[CovariantClass α α (swap (· * ·)) (· < ·)] {a b c d : α} (h₁ : a < b) (h₂ : c ≤ d) :
@@ -201,7 +206,9 @@ theorem mul_lt_mul_of_lt_of_le [CovariantClass α α (· * ·) (· ≤ ·)]
(mul_le_mul_left' h₂ _).trans_lt (mul_lt_mul_right' h₁ d)
#align mul_lt_mul_of_lt_of_le mul_lt_mul_of_lt_of_le
#align add_lt_add_of_lt_of_le add_lt_add_of_lt_of_le
+-/
+#print Left.mul_lt_mul /-
/-- Only assumes left strict covariance. -/
@[to_additive "Only assumes left strict covariance"]
theorem Left.mul_lt_mul [CovariantClass α α (· * ·) (· < ·)]
@@ -210,7 +217,9 @@ theorem Left.mul_lt_mul [CovariantClass α α (· * ·) (· < ·)]
mul_lt_mul_of_le_of_lt h₁.le h₂
#align left.mul_lt_mul Left.mul_lt_mul
#align left.add_lt_add Left.add_lt_add
+-/
+#print Right.mul_lt_mul /-
/-- Only assumes right strict covariance. -/
@[to_additive "Only assumes right strict covariance"]
theorem Right.mul_lt_mul [CovariantClass α α (· * ·) (· ≤ ·)]
@@ -219,14 +228,18 @@ theorem Right.mul_lt_mul [CovariantClass α α (· * ·) (· ≤ ·)]
mul_lt_mul_of_lt_of_le h₁ h₂.le
#align right.mul_lt_mul Right.mul_lt_mul
#align right.add_lt_add Right.add_lt_add
+-/
+#print mul_le_mul' /-
@[to_additive add_le_add]
theorem mul_le_mul' [CovariantClass α α (· * ·) (· ≤ ·)] [CovariantClass α α (swap (· * ·)) (· ≤ ·)]
{a b c d : α} (h₁ : a ≤ b) (h₂ : c ≤ d) : a * c ≤ b * d :=
(mul_le_mul_left' h₂ _).trans (mul_le_mul_right' h₁ d)
#align mul_le_mul' mul_le_mul'
#align add_le_add add_le_add
+-/
+#print mul_le_mul_three /-
@[to_additive]
theorem mul_le_mul_three [CovariantClass α α (· * ·) (· ≤ ·)]
[CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c d e f : α} (h₁ : a ≤ d) (h₂ : b ≤ e)
@@ -234,62 +247,79 @@ theorem mul_le_mul_three [CovariantClass α α (· * ·) (· ≤ ·)]
mul_le_mul' (mul_le_mul' h₁ h₂) h₃
#align mul_le_mul_three mul_le_mul_three
#align add_le_add_three add_le_add_three
+-/
+#print mul_lt_of_mul_lt_left /-
@[to_additive]
theorem mul_lt_of_mul_lt_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b c d : α} (h : a * b < c)
(hle : d ≤ b) : a * d < c :=
(mul_le_mul_left' hle a).trans_lt h
#align mul_lt_of_mul_lt_left mul_lt_of_mul_lt_left
#align add_lt_of_add_lt_left add_lt_of_add_lt_left
+-/
+#print mul_le_of_mul_le_left /-
@[to_additive]
theorem mul_le_of_mul_le_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b c d : α} (h : a * b ≤ c)
(hle : d ≤ b) : a * d ≤ c :=
@act_rel_of_rel_of_act_rel _ _ _ (· ≤ ·) _ ⟨fun _ _ _ => le_trans⟩ a _ _ _ hle h
#align mul_le_of_mul_le_left mul_le_of_mul_le_left
#align add_le_of_add_le_left add_le_of_add_le_left
+-/
+#print mul_lt_of_mul_lt_right /-
@[to_additive]
theorem mul_lt_of_mul_lt_right [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c d : α}
(h : a * b < c) (hle : d ≤ a) : d * b < c :=
(mul_le_mul_right' hle b).trans_lt h
#align mul_lt_of_mul_lt_right mul_lt_of_mul_lt_right
#align add_lt_of_add_lt_right add_lt_of_add_lt_right
+-/
+#print mul_le_of_mul_le_right /-
@[to_additive]
theorem mul_le_of_mul_le_right [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c d : α}
(h : a * b ≤ c) (hle : d ≤ a) : d * b ≤ c :=
(mul_le_mul_right' hle b).trans h
#align mul_le_of_mul_le_right mul_le_of_mul_le_right
#align add_le_of_add_le_right add_le_of_add_le_right
+-/
+#print lt_mul_of_lt_mul_left /-
@[to_additive]
theorem lt_mul_of_lt_mul_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b c d : α} (h : a < b * c)
(hle : c ≤ d) : a < b * d :=
h.trans_le (mul_le_mul_left' hle b)
#align lt_mul_of_lt_mul_left lt_mul_of_lt_mul_left
#align lt_add_of_lt_add_left lt_add_of_lt_add_left
+-/
+#print le_mul_of_le_mul_left /-
@[to_additive]
theorem le_mul_of_le_mul_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b c d : α} (h : a ≤ b * c)
(hle : c ≤ d) : a ≤ b * d :=
@rel_act_of_rel_of_rel_act _ _ _ (· ≤ ·) _ ⟨fun _ _ _ => le_trans⟩ b _ _ _ hle h
#align le_mul_of_le_mul_left le_mul_of_le_mul_left
#align le_add_of_le_add_left le_add_of_le_add_left
+-/
+#print lt_mul_of_lt_mul_right /-
@[to_additive]
theorem lt_mul_of_lt_mul_right [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c d : α}
(h : a < b * c) (hle : b ≤ d) : a < d * c :=
h.trans_le (mul_le_mul_right' hle c)
#align lt_mul_of_lt_mul_right lt_mul_of_lt_mul_right
#align lt_add_of_lt_add_right lt_add_of_lt_add_right
+-/
+#print le_mul_of_le_mul_right /-
@[to_additive]
theorem le_mul_of_le_mul_right [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c d : α}
(h : a ≤ b * c) (hle : b ≤ d) : a ≤ d * c :=
h.trans (mul_le_mul_right' hle c)
#align le_mul_of_le_mul_right le_mul_of_le_mul_right
#align le_add_of_le_add_right le_add_of_le_add_right
+-/
end Preorder
@@ -297,19 +327,23 @@ section PartialOrder
variable [PartialOrder α]
+#print mul_left_cancel'' /-
@[to_additive]
theorem mul_left_cancel'' [ContravariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (h : a * b = a * c) :
b = c :=
(le_of_mul_le_mul_left' h.le).antisymm (le_of_mul_le_mul_left' h.ge)
#align mul_left_cancel'' mul_left_cancel''
#align add_left_cancel'' add_left_cancel''
+-/
+#print mul_right_cancel'' /-
@[to_additive]
theorem mul_right_cancel'' [ContravariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α}
(h : a * b = c * b) : a = c :=
le_antisymm (le_of_mul_le_mul_right' h.le) (le_of_mul_le_mul_right' h.ge)
#align mul_right_cancel'' mul_right_cancel''
#align add_right_cancel'' add_right_cancel''
+-/
end PartialOrder
@@ -1318,29 +1352,37 @@ section Left
variable [CovariantClass α α (· * ·) (· < ·)]
+#print StrictMono.const_mul' /-
@[to_additive const_add]
theorem StrictMono.const_mul' (hf : StrictMono f) (c : α) : StrictMono fun x => c * f x :=
fun a b ab => mul_lt_mul_left' (hf ab) c
#align strict_mono.const_mul' StrictMono.const_mul'
#align strict_mono.const_add StrictMono.const_add
+-/
+#print StrictMonoOn.const_mul' /-
@[to_additive const_add]
theorem StrictMonoOn.const_mul' (hf : StrictMonoOn f s) (c : α) :
StrictMonoOn (fun x => c * f x) s := fun a ha b hb ab => mul_lt_mul_left' (hf ha hb ab) c
#align strict_mono_on.const_mul' StrictMonoOn.const_mul'
#align strict_mono_on.const_add StrictMonoOn.const_add
+-/
+#print StrictAnti.const_mul' /-
@[to_additive const_add]
theorem StrictAnti.const_mul' (hf : StrictAnti f) (c : α) : StrictAnti fun x => c * f x :=
fun a b ab => mul_lt_mul_left' (hf ab) c
#align strict_anti.const_mul' StrictAnti.const_mul'
#align strict_anti.const_add StrictAnti.const_add
+-/
+#print StrictAntiOn.const_mul' /-
@[to_additive const_add]
theorem StrictAntiOn.const_mul' (hf : StrictAntiOn f s) (c : α) :
StrictAntiOn (fun x => c * f x) s := fun a ha b hb ab => mul_lt_mul_left' (hf ha hb ab) c
#align strict_anti_on.const_mul' StrictAntiOn.const_mul'
#align strict_anti_on.const_add StrictAntiOn.const_add
+-/
end Left
@@ -1348,29 +1390,37 @@ section Right
variable [CovariantClass α α (swap (· * ·)) (· < ·)]
+#print StrictMono.mul_const' /-
@[to_additive add_const]
theorem StrictMono.mul_const' (hf : StrictMono f) (c : α) : StrictMono fun x => f x * c :=
fun a b ab => mul_lt_mul_right' (hf ab) c
#align strict_mono.mul_const' StrictMono.mul_const'
#align strict_mono.add_const StrictMono.add_const
+-/
+#print StrictMonoOn.mul_const' /-
@[to_additive add_const]
theorem StrictMonoOn.mul_const' (hf : StrictMonoOn f s) (c : α) :
StrictMonoOn (fun x => f x * c) s := fun a ha b hb ab => mul_lt_mul_right' (hf ha hb ab) c
#align strict_mono_on.mul_const' StrictMonoOn.mul_const'
#align strict_mono_on.add_const StrictMonoOn.add_const
+-/
+#print StrictAnti.mul_const' /-
@[to_additive add_const]
theorem StrictAnti.mul_const' (hf : StrictAnti f) (c : α) : StrictAnti fun x => f x * c :=
fun a b ab => mul_lt_mul_right' (hf ab) c
#align strict_anti.mul_const' StrictAnti.mul_const'
#align strict_anti.add_const StrictAnti.add_const
+-/
+#print StrictAntiOn.mul_const' /-
@[to_additive add_const]
theorem StrictAntiOn.mul_const' (hf : StrictAntiOn f s) (c : α) :
StrictAntiOn (fun x => f x * c) s := fun a ha b hb ab => mul_lt_mul_right' (hf ha hb ab) c
#align strict_anti_on.mul_const' StrictAntiOn.mul_const'
#align strict_anti_on.add_const StrictAntiOn.add_const
+-/
end Right
@@ -1450,6 +1500,7 @@ theorem AntitoneOn.mul_strictAnti' [CovariantClass α α (· * ·) (· < ·)]
variable [CovariantClass α α (· * ·) (· ≤ ·)] [CovariantClass α α (swap (· * ·)) (· < ·)]
+#print StrictMono.mul_monotone' /-
/-- The product of a strictly monotone function and a monotone function is strictly monotone. -/
@[to_additive add_monotone
"The sum of a strictly monotone function and a monotone function is strictly monotone."]
@@ -1457,7 +1508,9 @@ theorem StrictMono.mul_monotone' (hf : StrictMono f) (hg : Monotone g) :
StrictMono fun x => f x * g x := fun x y h => mul_lt_mul_of_lt_of_le (hf h) (hg h.le)
#align strict_mono.mul_monotone' StrictMono.mul_monotone'
#align strict_mono.add_monotone StrictMono.add_monotone
+-/
+#print StrictMonoOn.mul_monotone' /-
/-- The product of a strictly monotone function and a monotone function is strictly monotone. -/
@[to_additive add_monotone
"The sum of a strictly monotone function and a monotone function is strictly monotone."]
@@ -1466,7 +1519,9 @@ theorem StrictMonoOn.mul_monotone' (hf : StrictMonoOn f s) (hg : MonotoneOn g s)
mul_lt_mul_of_lt_of_le (hf hx hy h) (hg hx hy h.le)
#align strict_mono_on.mul_monotone' StrictMonoOn.mul_monotone'
#align strict_mono_on.add_monotone StrictMonoOn.add_monotone
+-/
+#print StrictAnti.mul_antitone' /-
/-- The product of a strictly antitone function and a antitone function is strictly antitone. -/
@[to_additive add_antitone
"The sum of a strictly antitone function and a antitone function is strictly antitone."]
@@ -1474,7 +1529,9 @@ theorem StrictAnti.mul_antitone' (hf : StrictAnti f) (hg : Antitone g) :
StrictAnti fun x => f x * g x := fun x y h => mul_lt_mul_of_lt_of_le (hf h) (hg h.le)
#align strict_anti.mul_antitone' StrictAnti.mul_antitone'
#align strict_anti.add_antitone StrictAnti.add_antitone
+-/
+#print StrictAntiOn.mul_antitone' /-
/-- The product of a strictly antitone function and a antitone function is strictly antitone. -/
@[to_additive add_antitone
"The sum of a strictly antitone function and a antitone function is strictly antitone."]
@@ -1483,20 +1540,25 @@ theorem StrictAntiOn.mul_antitone' (hf : StrictAntiOn f s) (hg : AntitoneOn g s)
mul_lt_mul_of_lt_of_le (hf hx hy h) (hg hx hy h.le)
#align strict_anti_on.mul_antitone' StrictAntiOn.mul_antitone'
#align strict_anti_on.add_antitone StrictAntiOn.add_antitone
+-/
+#print cmp_mul_left' /-
@[simp, to_additive cmp_add_left]
theorem cmp_mul_left' {α : Type _} [Mul α] [LinearOrder α] [CovariantClass α α (· * ·) (· < ·)]
(a b c : α) : cmp (a * b) (a * c) = cmp b c :=
(strictMono_id.const_mul' a).cmp_map_eq b c
#align cmp_mul_left' cmp_mul_left'
#align cmp_add_left cmp_add_left
+-/
+#print cmp_mul_right' /-
@[simp, to_additive cmp_add_right]
theorem cmp_mul_right' {α : Type _} [Mul α] [LinearOrder α]
[CovariantClass α α (swap (· * ·)) (· < ·)] (a b c : α) : cmp (a * c) (b * c) = cmp a b :=
(strictMono_id.mul_const' c).cmp_map_eq a b
#align cmp_mul_right' cmp_mul_right'
#align cmp_add_right cmp_add_right
+-/
end Mono
@@ -1530,18 +1592,22 @@ theorem mulLECancellable_one [Monoid α] [LE α] : MulLECancellable (1 : α) :=
namespace MulLECancellable
+#print MulLECancellable.Injective /-
@[to_additive]
protected theorem Injective [Mul α] [PartialOrder α] {a : α} (ha : MulLECancellable a) :
Injective ((· * ·) a) := fun b c h => le_antisymm (ha h.le) (ha h.ge)
#align mul_le_cancellable.injective MulLECancellable.Injective
#align add_le_cancellable.injective AddLECancellable.Injective
+-/
+#print MulLECancellable.inj /-
@[to_additive]
protected theorem inj [Mul α] [PartialOrder α] {a b c : α} (ha : MulLECancellable a) :
a * b = a * c ↔ b = c :=
ha.Injective.eq_iff
#align mul_le_cancellable.inj MulLECancellable.inj
#align add_le_cancellable.inj AddLECancellable.inj
+-/
@[to_additive]
protected theorem injective_left [CommSemigroup α] [PartialOrder α] {a : α}
@@ -1609,14 +1675,18 @@ section Bit
variable [Add α] [Preorder α]
+#print bit0_mono /-
theorem bit0_mono [CovariantClass α α (· + ·) (· ≤ ·)] [CovariantClass α α (swap (· + ·)) (· ≤ ·)] :
Monotone (bit0 : α → α) := fun a b h => add_le_add h h
#align bit0_mono bit0_mono
+-/
+#print bit0_strictMono /-
theorem bit0_strictMono [CovariantClass α α (· + ·) (· < ·)]
[CovariantClass α α (swap (· + ·)) (· < ·)] : StrictMono (bit0 : α → α) := fun a b h =>
add_lt_add h h
#align bit0_strict_mono bit0_strictMono
+-/
end Bit
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -172,12 +172,6 @@ section Preorder
variable [Preorder α]
-/- warning: mul_lt_mul_of_lt_of_lt -> mul_lt_mul_of_lt_of_lt is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] {a : α} {b : α} {c : α} {d : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a b) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) c d) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b d))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1146 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1148 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1146 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1148) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1161 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1163 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1161 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1163)] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1183 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1185 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1183 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1185)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1198 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1200 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1198 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1200)] {a : α} {b : α} {c : α} {d : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) c d) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b d))
-Case conversion may be inaccurate. Consider using '#align mul_lt_mul_of_lt_of_lt mul_lt_mul_of_lt_of_ltₓ'. -/
@[to_additive]
theorem mul_lt_mul_of_lt_of_lt [CovariantClass α α (· * ·) (· < ·)]
[CovariantClass α α (swap (· * ·)) (· < ·)] {a b c d : α} (h₁ : a < b) (h₂ : c < d) :
@@ -189,21 +183,9 @@ theorem mul_lt_mul_of_lt_of_lt [CovariantClass α α (· * ·) (· < ·)]
#align mul_lt_mul_of_lt_of_lt mul_lt_mul_of_lt_of_lt
#align add_lt_add_of_lt_of_lt add_lt_add_of_lt_of_lt
-/- warning: add_lt_add -> add_lt_add is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Add.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] {a : α} {b : α} {c : α} {d : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a b) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) c d) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α _inst_1) a c) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α _inst_1) b d))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Add.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1146 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1148 : α) => HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1146 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1148) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1161 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1163 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1161 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1163)] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1183 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1185 : α) => HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1183 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1185)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1198 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1200 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1198 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1200)] {a : α} {b : α} {c : α} {d : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) c d) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α _inst_1) a c) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α _inst_1) b d))
-Case conversion may be inaccurate. Consider using '#align add_lt_add add_lt_addₓ'. -/
alias add_lt_add_of_lt_of_lt ← add_lt_add
#align add_lt_add add_lt_add
-/- warning: mul_lt_mul_of_le_of_lt -> mul_lt_mul_of_le_of_lt is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a b) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) c d) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b d))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1286 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1288 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1286 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1288) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1301 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1303 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1301 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1303)] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1323 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1325 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1323 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1325)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1338 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1340 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1338 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1340)] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) c d) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b d))
-Case conversion may be inaccurate. Consider using '#align mul_lt_mul_of_le_of_lt mul_lt_mul_of_le_of_ltₓ'. -/
@[to_additive]
theorem mul_lt_mul_of_le_of_lt [CovariantClass α α (· * ·) (· < ·)]
[CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c d : α} (h₁ : a ≤ b) (h₂ : c < d) :
@@ -212,12 +194,6 @@ theorem mul_lt_mul_of_le_of_lt [CovariantClass α α (· * ·) (· < ·)]
#align mul_lt_mul_of_le_of_lt mul_lt_mul_of_le_of_lt
#align add_lt_add_of_le_of_lt add_lt_add_of_le_of_lt
-/- warning: mul_lt_mul_of_lt_of_le -> mul_lt_mul_of_lt_of_le is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] {a : α} {b : α} {c : α} {d : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a b) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) c d) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b d))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1402 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1404 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1402 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1404) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1417 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1419 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1417 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1419)] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1439 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1441 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1439 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1441)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1454 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1456 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1454 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1456)] {a : α} {b : α} {c : α} {d : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) c d) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b d))
-Case conversion may be inaccurate. Consider using '#align mul_lt_mul_of_lt_of_le mul_lt_mul_of_lt_of_leₓ'. -/
@[to_additive]
theorem mul_lt_mul_of_lt_of_le [CovariantClass α α (· * ·) (· ≤ ·)]
[CovariantClass α α (swap (· * ·)) (· < ·)] {a b c d : α} (h₁ : a < b) (h₂ : c ≤ d) :
@@ -226,12 +202,6 @@ theorem mul_lt_mul_of_lt_of_le [CovariantClass α α (· * ·) (· ≤ ·)]
#align mul_lt_mul_of_lt_of_le mul_lt_mul_of_lt_of_le
#align add_lt_add_of_lt_of_le add_lt_add_of_lt_of_le
-/- warning: left.mul_lt_mul -> Left.mul_lt_mul is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α} {d : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a b) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) c d) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b d))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1521 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1523 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1521 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1523) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1536 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1538 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1536 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1538)] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1558 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1560 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1558 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1560)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1573 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1575 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1573 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1575)] {a : α} {b : α} {c : α} {d : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) c d) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b d))
-Case conversion may be inaccurate. Consider using '#align left.mul_lt_mul Left.mul_lt_mulₓ'. -/
/-- Only assumes left strict covariance. -/
@[to_additive "Only assumes left strict covariance"]
theorem Left.mul_lt_mul [CovariantClass α α (· * ·) (· < ·)]
@@ -241,12 +211,6 @@ theorem Left.mul_lt_mul [CovariantClass α α (· * ·) (· < ·)]
#align left.mul_lt_mul Left.mul_lt_mul
#align left.add_lt_add Left.add_lt_add
-/- warning: right.mul_lt_mul -> Right.mul_lt_mul is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] {a : α} {b : α} {c : α} {d : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a b) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) c d) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b d))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1633 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1635 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1633 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1635) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1648 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1650 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1648 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1650)] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1670 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1672 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1670 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1672)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1685 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1687 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1685 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1687)] {a : α} {b : α} {c : α} {d : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) c d) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b d))
-Case conversion may be inaccurate. Consider using '#align right.mul_lt_mul Right.mul_lt_mulₓ'. -/
/-- Only assumes right strict covariance. -/
@[to_additive "Only assumes right strict covariance"]
theorem Right.mul_lt_mul [CovariantClass α α (· * ·) (· ≤ ·)]
@@ -256,12 +220,6 @@ theorem Right.mul_lt_mul [CovariantClass α α (· * ·) (· ≤ ·)]
#align right.mul_lt_mul Right.mul_lt_mul
#align right.add_lt_add Right.add_lt_add
-/- warning: mul_le_mul' -> mul_le_mul' is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a b) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) c d) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b d))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1742 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1744 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1742 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1744) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1757 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1759 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1757 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1759)] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1779 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1781 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1779 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1781)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1794 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1796 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1794 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1796)] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) c d) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b d))
-Case conversion may be inaccurate. Consider using '#align mul_le_mul' mul_le_mul'ₓ'. -/
@[to_additive add_le_add]
theorem mul_le_mul' [CovariantClass α α (· * ·) (· ≤ ·)] [CovariantClass α α (swap (· * ·)) (· ≤ ·)]
{a b c d : α} (h₁ : a ≤ b) (h₂ : c ≤ d) : a * c ≤ b * d :=
@@ -269,12 +227,6 @@ theorem mul_le_mul' [CovariantClass α α (· * ·) (· ≤ ·)] [CovariantClass
#align mul_le_mul' mul_le_mul'
#align add_le_add add_le_add
-/- warning: mul_le_mul_three -> mul_le_mul_three is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α} {d : α} {e : α} {f : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a d) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) b e) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) c f) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a b) c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) d e) f))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1858 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1860 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1858 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1860) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1873 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1875 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1873 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1875)] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1895 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1897 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1895 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1897)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1910 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1912 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1910 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1912)] {a : α} {b : α} {c : α} {d : α} {e : α} {f : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a d) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b e) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) c f) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a b) c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) d e) f))
-Case conversion may be inaccurate. Consider using '#align mul_le_mul_three mul_le_mul_threeₓ'. -/
@[to_additive]
theorem mul_le_mul_three [CovariantClass α α (· * ·) (· ≤ ·)]
[CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c d e f : α} (h₁ : a ≤ d) (h₂ : b ≤ e)
@@ -283,12 +235,6 @@ theorem mul_le_mul_three [CovariantClass α α (· * ·) (· ≤ ·)]
#align mul_le_mul_three mul_le_mul_three
#align add_le_add_three add_le_add_three
-/- warning: mul_lt_of_mul_lt_left -> mul_lt_of_mul_lt_left is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α} {d : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a b) c) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) d b) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a d) c)
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1981 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1983 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1981 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1983) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1996 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1998 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1996 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1998)] {a : α} {b : α} {c : α} {d : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a b) c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) d b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a d) c)
-Case conversion may be inaccurate. Consider using '#align mul_lt_of_mul_lt_left mul_lt_of_mul_lt_leftₓ'. -/
@[to_additive]
theorem mul_lt_of_mul_lt_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b c d : α} (h : a * b < c)
(hle : d ≤ b) : a * d < c :=
@@ -296,12 +242,6 @@ theorem mul_lt_of_mul_lt_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b
#align mul_lt_of_mul_lt_left mul_lt_of_mul_lt_left
#align add_lt_of_add_lt_left add_lt_of_add_lt_left
-/- warning: mul_le_of_mul_le_left -> mul_le_of_mul_le_left is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a b) c) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) d b) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a d) c)
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2056 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2058 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2056 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2058) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2071 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2073 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2071 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2073)] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a b) c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) d b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a d) c)
-Case conversion may be inaccurate. Consider using '#align mul_le_of_mul_le_left mul_le_of_mul_le_leftₓ'. -/
@[to_additive]
theorem mul_le_of_mul_le_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b c d : α} (h : a * b ≤ c)
(hle : d ≤ b) : a * d ≤ c :=
@@ -309,12 +249,6 @@ theorem mul_le_of_mul_le_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b
#align mul_le_of_mul_le_left mul_le_of_mul_le_left
#align add_le_of_add_le_left add_le_of_add_le_left
-/- warning: mul_lt_of_mul_lt_right -> mul_lt_of_mul_lt_right is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α} {d : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a b) c) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) d a) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) d b) c)
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2152 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2154 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2152 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2154)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2167 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2169 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2167 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2169)] {a : α} {b : α} {c : α} {d : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a b) c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) d a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) d b) c)
-Case conversion may be inaccurate. Consider using '#align mul_lt_of_mul_lt_right mul_lt_of_mul_lt_rightₓ'. -/
@[to_additive]
theorem mul_lt_of_mul_lt_right [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c d : α}
(h : a * b < c) (hle : d ≤ a) : d * b < c :=
@@ -322,12 +256,6 @@ theorem mul_lt_of_mul_lt_right [CovariantClass α α (swap (· * ·)) (· ≤ ·
#align mul_lt_of_mul_lt_right mul_lt_of_mul_lt_right
#align add_lt_of_add_lt_right add_lt_of_add_lt_right
-/- warning: mul_le_of_mul_le_right -> mul_le_of_mul_le_right is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a b) c) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) d a) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) d b) c)
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2230 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2232 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2230 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2232)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2245 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2247 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2245 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2247)] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a b) c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) d a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) d b) c)
-Case conversion may be inaccurate. Consider using '#align mul_le_of_mul_le_right mul_le_of_mul_le_rightₓ'. -/
@[to_additive]
theorem mul_le_of_mul_le_right [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c d : α}
(h : a * b ≤ c) (hle : d ≤ a) : d * b ≤ c :=
@@ -335,12 +263,6 @@ theorem mul_le_of_mul_le_right [CovariantClass α α (swap (· * ·)) (· ≤ ·
#align mul_le_of_mul_le_right mul_le_of_mul_le_right
#align add_le_of_add_le_right add_le_of_add_le_right
-/- warning: lt_mul_of_lt_mul_left -> lt_mul_of_lt_mul_left is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α} {d : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b c)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) c d) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b d))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2305 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2307 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2305 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2307) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2320 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2322 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2320 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2322)] {a : α} {b : α} {c : α} {d : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b c)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) c d) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b d))
-Case conversion may be inaccurate. Consider using '#align lt_mul_of_lt_mul_left lt_mul_of_lt_mul_leftₓ'. -/
@[to_additive]
theorem lt_mul_of_lt_mul_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b c d : α} (h : a < b * c)
(hle : c ≤ d) : a < b * d :=
@@ -348,12 +270,6 @@ theorem lt_mul_of_lt_mul_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b
#align lt_mul_of_lt_mul_left lt_mul_of_lt_mul_left
#align lt_add_of_lt_add_left lt_add_of_lt_add_left
-/- warning: le_mul_of_le_mul_left -> le_mul_of_le_mul_left is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b c)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) c d) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b d))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2379 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2381 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2379 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2381) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2394 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2396 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2394 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2396)] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b c)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) c d) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b d))
-Case conversion may be inaccurate. Consider using '#align le_mul_of_le_mul_left le_mul_of_le_mul_leftₓ'. -/
@[to_additive]
theorem le_mul_of_le_mul_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b c d : α} (h : a ≤ b * c)
(hle : c ≤ d) : a ≤ b * d :=
@@ -361,12 +277,6 @@ theorem le_mul_of_le_mul_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b
#align le_mul_of_le_mul_left le_mul_of_le_mul_left
#align le_add_of_le_add_left le_add_of_le_add_left
-/- warning: lt_mul_of_lt_mul_right -> lt_mul_of_lt_mul_right is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α} {d : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b c)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) b d) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) d c))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2475 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2477 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2475 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2477)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2490 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2492 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2490 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2492)] {a : α} {b : α} {c : α} {d : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b c)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b d) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) d c))
-Case conversion may be inaccurate. Consider using '#align lt_mul_of_lt_mul_right lt_mul_of_lt_mul_rightₓ'. -/
@[to_additive]
theorem lt_mul_of_lt_mul_right [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c d : α}
(h : a < b * c) (hle : b ≤ d) : a < d * c :=
@@ -374,12 +284,6 @@ theorem lt_mul_of_lt_mul_right [CovariantClass α α (swap (· * ·)) (· ≤ ·
#align lt_mul_of_lt_mul_right lt_mul_of_lt_mul_right
#align lt_add_of_lt_add_right lt_add_of_lt_add_right
-/- warning: le_mul_of_le_mul_right -> le_mul_of_le_mul_right is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b c)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) b d) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) d c))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2552 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2554 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2552 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2554)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2567 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2569 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2567 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2569)] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b c)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b d) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) d c))
-Case conversion may be inaccurate. Consider using '#align le_mul_of_le_mul_right le_mul_of_le_mul_rightₓ'. -/
@[to_additive]
theorem le_mul_of_le_mul_right [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c d : α}
(h : a ≤ b * c) (hle : b ≤ d) : a ≤ d * c :=
@@ -393,12 +297,6 @@ section PartialOrder
variable [PartialOrder α]
-/- warning: mul_left_cancel'' -> mul_left_cancel'' is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a : α} {b : α} {c : α}, (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a c)) -> (Eq.{succ u1} α b c)
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2638 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2640 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2638 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2640) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2653 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2655 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2653 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2655)] {a : α} {b : α} {c : α}, (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a c)) -> (Eq.{succ u1} α b c)
-Case conversion may be inaccurate. Consider using '#align mul_left_cancel'' mul_left_cancel''ₓ'. -/
@[to_additive]
theorem mul_left_cancel'' [ContravariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (h : a * b = a * c) :
b = c :=
@@ -406,12 +304,6 @@ theorem mul_left_cancel'' [ContravariantClass α α (· * ·) (· ≤ ·)] {a b
#align mul_left_cancel'' mul_left_cancel''
#align add_left_cancel'' add_left_cancel''
-/- warning: mul_right_cancel'' -> mul_right_cancel'' is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a : α} {b : α} {c : α}, (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) c b)) -> (Eq.{succ u1} α a c)
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2712 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2714 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2712 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2714)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2727 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2729 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2727 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2729)] {a : α} {b : α} {c : α}, (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) c b)) -> (Eq.{succ u1} α a c)
-Case conversion may be inaccurate. Consider using '#align mul_right_cancel'' mul_right_cancel''ₓ'. -/
@[to_additive]
theorem mul_right_cancel'' [ContravariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α}
(h : a * b = c * b) : a = c :=
@@ -426,12 +318,6 @@ section LinearOrder
variable [LinearOrder α] {a b c d : α} [CovariantClass α α (· * ·) (· < ·)]
[CovariantClass α α (swap (· * ·)) (· < ·)]
-/- warning: min_le_max_of_mul_le_mul -> min_le_max_of_mul_le_mul is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : LinearOrder.{u1} α] {a : α} {b : α} {c : α} {d : α} [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))))], (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) c d)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (LinearOrder.min.{u1} α _inst_2 a b) (LinearOrder.max.{u1} α _inst_2 c d))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : LinearOrder.{u1} α] {a : α} {b : α} {c : α} {d : α} [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2882 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2884 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2882 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2884) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2897 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2899 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2897 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2899)] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2919 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2921 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2919 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2921)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2934 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2936 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2934 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2936)], (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) c d)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (Min.min.{u1} α (LinearOrder.toMin.{u1} α _inst_2) a b) (Max.max.{u1} α (LinearOrder.toMax.{u1} α _inst_2) c d))
-Case conversion may be inaccurate. Consider using '#align min_le_max_of_mul_le_mul min_le_max_of_mul_le_mulₓ'. -/
@[to_additive]
theorem min_le_max_of_mul_le_mul (h : a * b ≤ c * d) : min a b ≤ max c d := by
simp_rw [min_le_iff, le_max_iff]; contrapose! h; exact mul_lt_mul_of_lt_of_lt h.1.1 h.2.2
@@ -451,12 +337,6 @@ section LE
variable [LE α]
-/- warning: le_mul_of_one_le_right' -> le_mul_of_one_le_right' is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α _inst_2)] {a : α} {b : α}, (LE.le.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LE.le.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3032 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3034 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3032 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3034) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3047 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3049 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3047 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3049)] {a : α} {b : α}, (LE.le.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LE.le.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
-Case conversion may be inaccurate. Consider using '#align le_mul_of_one_le_right' le_mul_of_one_le_right'ₓ'. -/
@[to_additive le_add_of_nonneg_right]
theorem le_mul_of_one_le_right' [CovariantClass α α (· * ·) (· ≤ ·)] {a b : α} (h : 1 ≤ b) :
a ≤ a * b :=
@@ -467,12 +347,6 @@ theorem le_mul_of_one_le_right' [CovariantClass α α (· * ·) (· ≤ ·)] {a
#align le_mul_of_one_le_right' le_mul_of_one_le_right'
#align le_add_of_nonneg_right le_add_of_nonneg_right
-/- warning: mul_le_of_le_one_right' -> mul_le_of_le_one_right' is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α _inst_2)] {a : α} {b : α}, (LE.le.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) a)
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3124 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3126 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3124 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3126) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3139 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3141 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3139 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3141)] {a : α} {b : α}, (LE.le.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) a)
-Case conversion may be inaccurate. Consider using '#align mul_le_of_le_one_right' mul_le_of_le_one_right'ₓ'. -/
@[to_additive add_le_of_nonpos_right]
theorem mul_le_of_le_one_right' [CovariantClass α α (· * ·) (· ≤ ·)] {a b : α} (h : b ≤ 1) :
a * b ≤ a :=
@@ -483,12 +357,6 @@ theorem mul_le_of_le_one_right' [CovariantClass α α (· * ·) (· ≤ ·)] {a
#align mul_le_of_le_one_right' mul_le_of_le_one_right'
#align add_le_of_nonpos_right add_le_of_nonpos_right
-/- warning: le_mul_of_one_le_left' -> le_mul_of_one_le_left' is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α _inst_2)] {a : α} {b : α}, (LE.le.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LE.le.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b a))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3216 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3218 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3216 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3218)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3231 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3233 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3231 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3233)] {a : α} {b : α}, (LE.le.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LE.le.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b a))
-Case conversion may be inaccurate. Consider using '#align le_mul_of_one_le_left' le_mul_of_one_le_left'ₓ'. -/
@[to_additive le_add_of_nonneg_left]
theorem le_mul_of_one_le_left' [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b : α} (h : 1 ≤ b) :
a ≤ b * a :=
@@ -499,12 +367,6 @@ theorem le_mul_of_one_le_left' [CovariantClass α α (swap (· * ·)) (· ≤ ·
#align le_mul_of_one_le_left' le_mul_of_one_le_left'
#align le_add_of_nonneg_left le_add_of_nonneg_left
-/- warning: mul_le_of_le_one_left' -> mul_le_of_le_one_left' is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α _inst_2)] {a : α} {b : α}, (LE.le.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b a) a)
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3311 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3313 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3311 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3313)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3326 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3328 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3326 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3328)] {a : α} {b : α}, (LE.le.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b a) a)
-Case conversion may be inaccurate. Consider using '#align mul_le_of_le_one_left' mul_le_of_le_one_left'ₓ'. -/
@[to_additive add_le_of_nonpos_left]
theorem mul_le_of_le_one_left' [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b : α} (h : b ≤ 1) :
b * a ≤ a :=
@@ -515,12 +377,6 @@ theorem mul_le_of_le_one_left' [CovariantClass α α (swap (· * ·)) (· ≤ ·
#align mul_le_of_le_one_left' mul_le_of_le_one_left'
#align add_le_of_nonpos_left add_le_of_nonpos_left
-/- warning: one_le_of_le_mul_right -> one_le_of_le_mul_right is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α _inst_2)] {a : α} {b : α}, (LE.le.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b)) -> (LE.le.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b)
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3400 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3402 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3400 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3402) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3415 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3417 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3415 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3417)] {a : α} {b : α}, (LE.le.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b)) -> (LE.le.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b)
-Case conversion may be inaccurate. Consider using '#align one_le_of_le_mul_right one_le_of_le_mul_rightₓ'. -/
@[to_additive]
theorem one_le_of_le_mul_right [ContravariantClass α α (· * ·) (· ≤ ·)] {a b : α} (h : a ≤ a * b) :
1 ≤ b :=
@@ -528,12 +384,6 @@ theorem one_le_of_le_mul_right [ContravariantClass α α (· * ·) (· ≤ ·)]
#align one_le_of_le_mul_right one_le_of_le_mul_right
#align nonneg_of_le_add_right nonneg_of_le_add_right
-/- warning: le_one_of_mul_le_right -> le_one_of_mul_le_right is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3466 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3468 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3466 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3468) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3481 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3483 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3481 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3483)] {a : α} {b : α}, (LE.le.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) a) -> (LE.le.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
-Case conversion may be inaccurate. Consider using '#align le_one_of_mul_le_right le_one_of_mul_le_rightₓ'. -/
@[to_additive]
theorem le_one_of_mul_le_right [ContravariantClass α α (· * ·) (· ≤ ·)] {a b : α} (h : a * b ≤ a) :
b ≤ 1 :=
@@ -541,12 +391,6 @@ theorem le_one_of_mul_le_right [ContravariantClass α α (· * ·) (· ≤ ·)]
#align le_one_of_mul_le_right le_one_of_mul_le_right
#align nonpos_of_add_le_right nonpos_of_add_le_right
-/- warning: one_le_of_le_mul_left -> one_le_of_le_mul_left is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align one_le_of_le_mul_left one_le_of_le_mul_leftₓ'. -/
@[to_additive]
theorem one_le_of_le_mul_left [ContravariantClass α α (swap (· * ·)) (· ≤ ·)] {a b : α}
(h : b ≤ a * b) : 1 ≤ a :=
@@ -554,12 +398,6 @@ theorem one_le_of_le_mul_left [ContravariantClass α α (swap (· * ·)) (· ≤
#align one_le_of_le_mul_left one_le_of_le_mul_left
#align nonneg_of_le_add_left nonneg_of_le_add_left
-/- warning: le_one_of_mul_le_left -> le_one_of_mul_le_left is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align le_one_of_mul_le_left le_one_of_mul_le_leftₓ'. -/
@[to_additive]
theorem le_one_of_mul_le_left [ContravariantClass α α (swap (· * ·)) (· ≤ ·)] {a b : α}
(h : a * b ≤ b) : a ≤ 1 :=
@@ -567,12 +405,6 @@ theorem le_one_of_mul_le_left [ContravariantClass α α (swap (· * ·)) (· ≤
#align le_one_of_mul_le_left le_one_of_mul_le_left
#align nonpos_of_add_le_left nonpos_of_add_le_left
-/- warning: le_mul_iff_one_le_right' -> le_mul_iff_one_le_right' is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α _inst_2)] [_inst_4 : ContravariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α _inst_2)] (a : α) {b : α}, Iff (LE.le.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b)) (LE.le.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b)
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3670 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3672 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3670 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3672) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3685 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3687 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3685 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3687)] [_inst_4 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3704 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3706 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3704 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3706) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3719 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3721 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3719 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3721)] (a : α) {b : α}, Iff (LE.le.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b)) (LE.le.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b)
-Case conversion may be inaccurate. Consider using '#align le_mul_iff_one_le_right' le_mul_iff_one_le_right'ₓ'. -/
@[simp, to_additive le_add_iff_nonneg_right]
theorem le_mul_iff_one_le_right' [CovariantClass α α (· * ·) (· ≤ ·)]
[ContravariantClass α α (· * ·) (· ≤ ·)] (a : α) {b : α} : a ≤ a * b ↔ 1 ≤ b :=
@@ -580,12 +412,6 @@ theorem le_mul_iff_one_le_right' [CovariantClass α α (· * ·) (· ≤ ·)]
#align le_mul_iff_one_le_right' le_mul_iff_one_le_right'
#align le_add_iff_nonneg_right le_add_iff_nonneg_right
-/- warning: le_mul_iff_one_le_left' -> le_mul_iff_one_le_left' is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α _inst_2)] [_inst_4 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α _inst_2)] (a : α) {b : α}, Iff (LE.le.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b a)) (LE.le.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b)
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3804 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3806 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3804 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3806)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3819 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3821 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3819 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3821)] [_inst_4 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3841 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3843 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3841 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3843)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3856 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3858 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3856 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3858)] (a : α) {b : α}, Iff (LE.le.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b a)) (LE.le.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b)
-Case conversion may be inaccurate. Consider using '#align le_mul_iff_one_le_left' le_mul_iff_one_le_left'ₓ'. -/
@[simp, to_additive le_add_iff_nonneg_left]
theorem le_mul_iff_one_le_left' [CovariantClass α α (swap (· * ·)) (· ≤ ·)]
[ContravariantClass α α (swap (· * ·)) (· ≤ ·)] (a : α) {b : α} : a ≤ b * a ↔ 1 ≤ b :=
@@ -593,12 +419,6 @@ theorem le_mul_iff_one_le_left' [CovariantClass α α (swap (· * ·)) (· ≤
#align le_mul_iff_one_le_left' le_mul_iff_one_le_left'
#align le_add_iff_nonneg_left le_add_iff_nonneg_left
-/- warning: mul_le_iff_le_one_right' -> mul_le_iff_le_one_right' is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α _inst_2)] [_inst_4 : ContravariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α _inst_2)] (a : α) {b : α}, Iff (LE.le.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) a) (LE.le.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3938 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3940 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3938 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3940) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3953 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3955 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3953 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3955)] [_inst_4 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3972 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3974 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3972 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3974) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3987 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3989 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3987 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3989)] (a : α) {b : α}, Iff (LE.le.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) a) (LE.le.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
-Case conversion may be inaccurate. Consider using '#align mul_le_iff_le_one_right' mul_le_iff_le_one_right'ₓ'. -/
@[simp, to_additive add_le_iff_nonpos_right]
theorem mul_le_iff_le_one_right' [CovariantClass α α (· * ·) (· ≤ ·)]
[ContravariantClass α α (· * ·) (· ≤ ·)] (a : α) {b : α} : a * b ≤ a ↔ b ≤ 1 :=
@@ -606,12 +426,6 @@ theorem mul_le_iff_le_one_right' [CovariantClass α α (· * ·) (· ≤ ·)]
#align mul_le_iff_le_one_right' mul_le_iff_le_one_right'
#align add_le_iff_nonpos_right add_le_iff_nonpos_right
-/- warning: mul_le_iff_le_one_left' -> mul_le_iff_le_one_left' is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α _inst_2)] [_inst_4 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α _inst_2)] {a : α} {b : α}, Iff (LE.le.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) b) (LE.le.{u1} α _inst_2 a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4072 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4074 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4072 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4074)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4087 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4089 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4087 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4089)] [_inst_4 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4109 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4111 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4109 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4111)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4124 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4126 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4124 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4126)] {a : α} {b : α}, Iff (LE.le.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) b) (LE.le.{u1} α _inst_2 a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
-Case conversion may be inaccurate. Consider using '#align mul_le_iff_le_one_left' mul_le_iff_le_one_left'ₓ'. -/
@[simp, to_additive add_le_iff_nonpos_left]
theorem mul_le_iff_le_one_left' [CovariantClass α α (swap (· * ·)) (· ≤ ·)]
[ContravariantClass α α (swap (· * ·)) (· ≤ ·)] {a b : α} : a * b ≤ b ↔ a ≤ 1 :=
@@ -625,12 +439,6 @@ section LT
variable [LT α]
-/- warning: lt_mul_of_one_lt_right' -> lt_mul_of_one_lt_right' is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α _inst_2)] (a : α) {b : α}, (LT.lt.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4218 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4220 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4218 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4220) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4233 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4235 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4233 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4235)] (a : α) {b : α}, (LT.lt.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
-Case conversion may be inaccurate. Consider using '#align lt_mul_of_one_lt_right' lt_mul_of_one_lt_right'ₓ'. -/
@[to_additive lt_add_of_pos_right]
theorem lt_mul_of_one_lt_right' [CovariantClass α α (· * ·) (· < ·)] (a : α) {b : α} (h : 1 < b) :
a < a * b :=
@@ -641,12 +449,6 @@ theorem lt_mul_of_one_lt_right' [CovariantClass α α (· * ·) (· < ·)] (a :
#align lt_mul_of_one_lt_right' lt_mul_of_one_lt_right'
#align lt_add_of_pos_right lt_add_of_pos_right
-/- warning: mul_lt_of_lt_one_right' -> mul_lt_of_lt_one_right' is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α _inst_2)] (a : α) {b : α}, (LT.lt.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) a)
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4310 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4312 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4310 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4312) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4325 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4327 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4325 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4327)] (a : α) {b : α}, (LT.lt.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) a)
-Case conversion may be inaccurate. Consider using '#align mul_lt_of_lt_one_right' mul_lt_of_lt_one_right'ₓ'. -/
@[to_additive add_lt_of_neg_right]
theorem mul_lt_of_lt_one_right' [CovariantClass α α (· * ·) (· < ·)] (a : α) {b : α} (h : b < 1) :
a * b < a :=
@@ -657,12 +459,6 @@ theorem mul_lt_of_lt_one_right' [CovariantClass α α (· * ·) (· < ·)] (a :
#align mul_lt_of_lt_one_right' mul_lt_of_lt_one_right'
#align add_lt_of_neg_right add_lt_of_neg_right
-/- warning: lt_mul_of_one_lt_left' -> lt_mul_of_one_lt_left' is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α _inst_2)] (a : α) {b : α}, (LT.lt.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b a))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4402 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4404 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4402 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4404)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4417 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4419 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4417 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4419)] (a : α) {b : α}, (LT.lt.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b a))
-Case conversion may be inaccurate. Consider using '#align lt_mul_of_one_lt_left' lt_mul_of_one_lt_left'ₓ'. -/
@[to_additive lt_add_of_pos_left]
theorem lt_mul_of_one_lt_left' [CovariantClass α α (swap (· * ·)) (· < ·)] (a : α) {b : α}
(h : 1 < b) : a < b * a :=
@@ -673,12 +469,6 @@ theorem lt_mul_of_one_lt_left' [CovariantClass α α (swap (· * ·)) (· < ·)]
#align lt_mul_of_one_lt_left' lt_mul_of_one_lt_left'
#align lt_add_of_pos_left lt_add_of_pos_left
-/- warning: mul_lt_of_lt_one_left' -> mul_lt_of_lt_one_left' is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α _inst_2)] (a : α) {b : α}, (LT.lt.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b a) a)
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4497 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4499 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4497 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4499)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4512 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4514 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4512 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4514)] (a : α) {b : α}, (LT.lt.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b a) a)
-Case conversion may be inaccurate. Consider using '#align mul_lt_of_lt_one_left' mul_lt_of_lt_one_left'ₓ'. -/
@[to_additive add_lt_of_neg_left]
theorem mul_lt_of_lt_one_left' [CovariantClass α α (swap (· * ·)) (· < ·)] (a : α) {b : α}
(h : b < 1) : b * a < a :=
@@ -689,12 +479,6 @@ theorem mul_lt_of_lt_one_left' [CovariantClass α α (swap (· * ·)) (· < ·)]
#align mul_lt_of_lt_one_left' mul_lt_of_lt_one_left'
#align add_lt_of_neg_left add_lt_of_neg_left
-/- warning: one_lt_of_lt_mul_right -> one_lt_of_lt_mul_right is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α _inst_2)] {a : α} {b : α}, (LT.lt.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b)) -> (LT.lt.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b)
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4586 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4588 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4586 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4588) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4601 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4603 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4601 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4603)] {a : α} {b : α}, (LT.lt.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b)) -> (LT.lt.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b)
-Case conversion may be inaccurate. Consider using '#align one_lt_of_lt_mul_right one_lt_of_lt_mul_rightₓ'. -/
@[to_additive]
theorem one_lt_of_lt_mul_right [ContravariantClass α α (· * ·) (· < ·)] {a b : α} (h : a < a * b) :
1 < b :=
@@ -702,12 +486,6 @@ theorem one_lt_of_lt_mul_right [ContravariantClass α α (· * ·) (· < ·)] {a
#align one_lt_of_lt_mul_right one_lt_of_lt_mul_right
#align pos_of_lt_add_right pos_of_lt_add_right
-/- warning: lt_one_of_mul_lt_right -> lt_one_of_mul_lt_right is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α _inst_2)] {a : α} {b : α}, (LT.lt.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) a) -> (LT.lt.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4652 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4654 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4652 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4654) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4667 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4669 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4667 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4669)] {a : α} {b : α}, (LT.lt.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) a) -> (LT.lt.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
-Case conversion may be inaccurate. Consider using '#align lt_one_of_mul_lt_right lt_one_of_mul_lt_rightₓ'. -/
@[to_additive]
theorem lt_one_of_mul_lt_right [ContravariantClass α α (· * ·) (· < ·)] {a b : α} (h : a * b < a) :
b < 1 :=
@@ -715,12 +493,6 @@ theorem lt_one_of_mul_lt_right [ContravariantClass α α (· * ·) (· < ·)] {a
#align lt_one_of_mul_lt_right lt_one_of_mul_lt_right
#align neg_of_add_lt_right neg_of_add_lt_right
-/- warning: one_lt_of_lt_mul_left -> one_lt_of_lt_mul_left is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4721 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4723 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4721 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4723)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4736 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4738 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4736 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4738)] {a : α} {b : α}, (LT.lt.{u1} α _inst_2 b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b)) -> (LT.lt.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a)
-Case conversion may be inaccurate. Consider using '#align one_lt_of_lt_mul_left one_lt_of_lt_mul_leftₓ'. -/
@[to_additive]
theorem one_lt_of_lt_mul_left [ContravariantClass α α (swap (· * ·)) (· < ·)] {a b : α}
(h : b < a * b) : 1 < a :=
@@ -728,12 +500,6 @@ theorem one_lt_of_lt_mul_left [ContravariantClass α α (swap (· * ·)) (· <
#align one_lt_of_lt_mul_left one_lt_of_lt_mul_left
#align pos_of_lt_add_left pos_of_lt_add_left
-/- warning: lt_one_of_mul_lt_left -> lt_one_of_mul_lt_left is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align lt_one_of_mul_lt_left lt_one_of_mul_lt_leftₓ'. -/
@[to_additive]
theorem lt_one_of_mul_lt_left [ContravariantClass α α (swap (· * ·)) (· < ·)] {a b : α}
(h : a * b < b) : a < 1 :=
@@ -741,12 +507,6 @@ theorem lt_one_of_mul_lt_left [ContravariantClass α α (swap (· * ·)) (· <
#align lt_one_of_mul_lt_left lt_one_of_mul_lt_left
#align neg_of_add_lt_left neg_of_add_lt_left
-/- warning: lt_mul_iff_one_lt_right' -> lt_mul_iff_one_lt_right' is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α _inst_2)] [_inst_4 : ContravariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α _inst_2)] (a : α) {b : α}, Iff (LT.lt.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b)) (LT.lt.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b)
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4856 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4858 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4856 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4858) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4871 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4873 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4871 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4873)] [_inst_4 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4890 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4892 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4890 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4892) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4905 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4907 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4905 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4907)] (a : α) {b : α}, Iff (LT.lt.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b)) (LT.lt.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b)
-Case conversion may be inaccurate. Consider using '#align lt_mul_iff_one_lt_right' lt_mul_iff_one_lt_right'ₓ'. -/
@[simp, to_additive lt_add_iff_pos_right]
theorem lt_mul_iff_one_lt_right' [CovariantClass α α (· * ·) (· < ·)]
[ContravariantClass α α (· * ·) (· < ·)] (a : α) {b : α} : a < a * b ↔ 1 < b :=
@@ -754,12 +514,6 @@ theorem lt_mul_iff_one_lt_right' [CovariantClass α α (· * ·) (· < ·)]
#align lt_mul_iff_one_lt_right' lt_mul_iff_one_lt_right'
#align lt_add_iff_pos_right lt_add_iff_pos_right
-/- warning: lt_mul_iff_one_lt_left' -> lt_mul_iff_one_lt_left' is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α _inst_2)] [_inst_4 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α _inst_2)] (a : α) {b : α}, Iff (LT.lt.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b a)) (LT.lt.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b)
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4990 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4992 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4990 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4992)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5005 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5007 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5005 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5007)] [_inst_4 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5027 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5029 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5027 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5029)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5042 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5044 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5042 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5044)] (a : α) {b : α}, Iff (LT.lt.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b a)) (LT.lt.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b)
-Case conversion may be inaccurate. Consider using '#align lt_mul_iff_one_lt_left' lt_mul_iff_one_lt_left'ₓ'. -/
@[simp, to_additive lt_add_iff_pos_left]
theorem lt_mul_iff_one_lt_left' [CovariantClass α α (swap (· * ·)) (· < ·)]
[ContravariantClass α α (swap (· * ·)) (· < ·)] (a : α) {b : α} : a < b * a ↔ 1 < b :=
@@ -767,12 +521,6 @@ theorem lt_mul_iff_one_lt_left' [CovariantClass α α (swap (· * ·)) (· < ·)
#align lt_mul_iff_one_lt_left' lt_mul_iff_one_lt_left'
#align lt_add_iff_pos_left lt_add_iff_pos_left
-/- warning: mul_lt_iff_lt_one_left' -> mul_lt_iff_lt_one_left' is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α _inst_2)] [_inst_4 : ContravariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α _inst_2)] {a : α} {b : α}, Iff (LT.lt.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) a) (LT.lt.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5124 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5126 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5124 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5126) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5139 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5141 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5139 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5141)] [_inst_4 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5158 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5160 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5158 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5160) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5173 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5175 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5173 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5175)] {a : α} {b : α}, Iff (LT.lt.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) a) (LT.lt.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
-Case conversion may be inaccurate. Consider using '#align mul_lt_iff_lt_one_left' mul_lt_iff_lt_one_left'ₓ'. -/
@[simp, to_additive add_lt_iff_neg_left]
theorem mul_lt_iff_lt_one_left' [CovariantClass α α (· * ·) (· < ·)]
[ContravariantClass α α (· * ·) (· < ·)] {a b : α} : a * b < a ↔ b < 1 :=
@@ -780,12 +528,6 @@ theorem mul_lt_iff_lt_one_left' [CovariantClass α α (· * ·) (· < ·)]
#align mul_lt_iff_lt_one_left' mul_lt_iff_lt_one_left'
#align add_lt_iff_neg_left add_lt_iff_neg_left
-/- warning: mul_lt_iff_lt_one_right' -> mul_lt_iff_lt_one_right' is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α _inst_2)] [_inst_4 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α _inst_2)] {a : α} (b : α), Iff (LT.lt.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) b) (LT.lt.{u1} α _inst_2 a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5258 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5260 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5258 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5260)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5273 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5275 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5273 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5275)] [_inst_4 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5295 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5297 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5295 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5297)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5310 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5312 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5310 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5312)] {a : α} (b : α), Iff (LT.lt.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) b) (LT.lt.{u1} α _inst_2 a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
-Case conversion may be inaccurate. Consider using '#align mul_lt_iff_lt_one_right' mul_lt_iff_lt_one_right'ₓ'. -/
@[simp, to_additive add_lt_iff_neg_right]
theorem mul_lt_iff_lt_one_right' [CovariantClass α α (swap (· * ·)) (· < ·)]
[ContravariantClass α α (swap (· * ·)) (· < ·)] {a : α} (b : α) : a * b < b ↔ a < 1 :=
@@ -803,12 +545,6 @@ variable [Preorder α]
which assume left covariance. -/
-/- warning: mul_le_of_le_of_le_one -> mul_le_of_le_of_le_one is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b a) c)
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5405 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5407 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5405 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5407) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5420 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5422 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5420 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5422)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b a) c)
-Case conversion may be inaccurate. Consider using '#align mul_le_of_le_of_le_one mul_le_of_le_of_le_oneₓ'. -/
@[to_additive]
theorem mul_le_of_le_of_le_one [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (hbc : b ≤ c)
(ha : a ≤ 1) : b * a ≤ c :=
@@ -820,12 +556,6 @@ theorem mul_le_of_le_of_le_one [CovariantClass α α (· * ·) (· ≤ ·)] {a b
#align mul_le_of_le_of_le_one mul_le_of_le_of_le_one
#align add_le_of_le_of_nonpos add_le_of_le_of_nonpos
-/- warning: mul_lt_of_le_of_lt_one -> mul_lt_of_le_of_lt_one is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b a) c)
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5515 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5517 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5515 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5517) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5530 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5532 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5530 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5532)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b a) c)
-Case conversion may be inaccurate. Consider using '#align mul_lt_of_le_of_lt_one mul_lt_of_le_of_lt_oneₓ'. -/
@[to_additive]
theorem mul_lt_of_le_of_lt_one [CovariantClass α α (· * ·) (· < ·)] {a b c : α} (hbc : b ≤ c)
(ha : a < 1) : b * a < c :=
@@ -837,12 +567,6 @@ theorem mul_lt_of_le_of_lt_one [CovariantClass α α (· * ·) (· < ·)] {a b c
#align mul_lt_of_le_of_lt_one mul_lt_of_le_of_lt_one
#align add_lt_of_le_of_neg add_lt_of_le_of_neg
-/- warning: mul_lt_of_lt_of_le_one -> mul_lt_of_lt_of_le_one is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b a) c)
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5625 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5627 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5625 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5627) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5640 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5642 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5640 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5642)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b a) c)
-Case conversion may be inaccurate. Consider using '#align mul_lt_of_lt_of_le_one mul_lt_of_lt_of_le_oneₓ'. -/
@[to_additive]
theorem mul_lt_of_lt_of_le_one [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (hbc : b < c)
(ha : a ≤ 1) : b * a < c :=
@@ -854,12 +578,6 @@ theorem mul_lt_of_lt_of_le_one [CovariantClass α α (· * ·) (· ≤ ·)] {a b
#align mul_lt_of_lt_of_le_one mul_lt_of_lt_of_le_one
#align add_lt_of_lt_of_nonpos add_lt_of_lt_of_nonpos
-/- warning: mul_lt_of_lt_of_lt_one -> mul_lt_of_lt_of_lt_one is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b a) c)
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5735 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5737 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5735 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5737) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5750 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5752 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5750 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5752)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b a) c)
-Case conversion may be inaccurate. Consider using '#align mul_lt_of_lt_of_lt_one mul_lt_of_lt_of_lt_oneₓ'. -/
@[to_additive]
theorem mul_lt_of_lt_of_lt_one [CovariantClass α α (· * ·) (· < ·)] {a b c : α} (hbc : b < c)
(ha : a < 1) : b * a < c :=
@@ -871,12 +589,6 @@ theorem mul_lt_of_lt_of_lt_one [CovariantClass α α (· * ·) (· < ·)] {a b c
#align mul_lt_of_lt_of_lt_one mul_lt_of_lt_of_lt_one
#align add_lt_of_lt_of_neg add_lt_of_lt_of_neg
-/- warning: mul_lt_of_lt_of_lt_one' -> mul_lt_of_lt_of_lt_one' is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b a) c)
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5845 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5847 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5845 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5847) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5860 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5862 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5860 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5862)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b a) c)
-Case conversion may be inaccurate. Consider using '#align mul_lt_of_lt_of_lt_one' mul_lt_of_lt_of_lt_one'ₓ'. -/
@[to_additive]
theorem mul_lt_of_lt_of_lt_one' [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (hbc : b < c)
(ha : a < 1) : b * a < c :=
@@ -884,12 +596,6 @@ theorem mul_lt_of_lt_of_lt_one' [CovariantClass α α (· * ·) (· ≤ ·)] {a
#align mul_lt_of_lt_of_lt_one' mul_lt_of_lt_of_lt_one'
#align add_lt_of_lt_of_neg' add_lt_of_lt_of_neg'
-/- warning: left.mul_le_one -> Left.mul_le_one is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align left.mul_le_one Left.mul_le_oneₓ'. -/
/-- Assumes left covariance.
The lemma assuming right covariance is `right.mul_le_one`. -/
@[to_additive
@@ -900,12 +606,6 @@ theorem Left.mul_le_one [CovariantClass α α (· * ·) (· ≤ ·)] {a b : α}
#align left.mul_le_one Left.mul_le_one
#align left.add_nonpos Left.add_nonpos
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-Case conversion may be inaccurate. Consider using '#align left.mul_lt_one_of_le_of_lt Left.mul_lt_one_of_le_of_ltₓ'. -/
/-- Assumes left covariance.
The lemma assuming right covariance is `right.mul_lt_one_of_le_of_lt`. -/
@[to_additive Left.add_neg_of_nonpos_of_neg
@@ -916,12 +616,6 @@ theorem Left.mul_lt_one_of_le_of_lt [CovariantClass α α (· * ·) (· < ·)] {
#align left.mul_lt_one_of_le_of_lt Left.mul_lt_one_of_le_of_lt
#align left.add_neg_of_nonpos_of_neg Left.add_neg_of_nonpos_of_neg
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/-- Assumes left covariance.
The lemma assuming right covariance is `right.mul_lt_one_of_lt_of_le`. -/
@[to_additive Left.add_neg_of_neg_of_nonpos
@@ -932,12 +626,6 @@ theorem Left.mul_lt_one_of_lt_of_le [CovariantClass α α (· * ·) (· ≤ ·)]
#align left.mul_lt_one_of_lt_of_le Left.mul_lt_one_of_lt_of_le
#align left.add_neg_of_neg_of_nonpos Left.add_neg_of_neg_of_nonpos
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/-- Assumes left covariance.
The lemma assuming right covariance is `right.mul_lt_one`. -/
@[to_additive "Assumes left covariance.\nThe lemma assuming right covariance is `right.add_neg`."]
@@ -947,12 +635,6 @@ theorem Left.mul_lt_one [CovariantClass α α (· * ·) (· < ·)] {a b : α} (h
#align left.mul_lt_one Left.mul_lt_one
#align left.add_neg Left.add_neg
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/-- Assumes left covariance.
The lemma assuming right covariance is `right.mul_lt_one'`. -/
@[to_additive "Assumes left covariance.\nThe lemma assuming right covariance is `right.add_neg'`."]
@@ -966,12 +648,6 @@ theorem Left.mul_lt_one' [CovariantClass α α (· * ·) (· ≤ ·)] {a b : α}
which assume left covariance. -/
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-Case conversion may be inaccurate. Consider using '#align le_mul_of_le_of_one_le le_mul_of_le_of_one_leₓ'. -/
@[to_additive]
theorem le_mul_of_le_of_one_le [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (hbc : b ≤ c)
(ha : 1 ≤ a) : b ≤ c * a :=
@@ -983,12 +659,6 @@ theorem le_mul_of_le_of_one_le [CovariantClass α α (· * ·) (· ≤ ·)] {a b
#align le_mul_of_le_of_one_le le_mul_of_le_of_one_le
#align le_add_of_le_of_nonneg le_add_of_le_of_nonneg
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-Case conversion may be inaccurate. Consider using '#align lt_mul_of_le_of_one_lt lt_mul_of_le_of_one_ltₓ'. -/
@[to_additive]
theorem lt_mul_of_le_of_one_lt [CovariantClass α α (· * ·) (· < ·)] {a b c : α} (hbc : b ≤ c)
(ha : 1 < a) : b < c * a :=
@@ -1000,12 +670,6 @@ theorem lt_mul_of_le_of_one_lt [CovariantClass α α (· * ·) (· < ·)] {a b c
#align lt_mul_of_le_of_one_lt lt_mul_of_le_of_one_lt
#align lt_add_of_le_of_pos lt_add_of_le_of_pos
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@[to_additive]
theorem lt_mul_of_lt_of_one_le [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (hbc : b < c)
(ha : 1 ≤ a) : b < c * a :=
@@ -1017,12 +681,6 @@ theorem lt_mul_of_lt_of_one_le [CovariantClass α α (· * ·) (· ≤ ·)] {a b
#align lt_mul_of_lt_of_one_le lt_mul_of_lt_of_one_le
#align lt_add_of_lt_of_nonneg lt_add_of_lt_of_nonneg
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@[to_additive]
theorem lt_mul_of_lt_of_one_lt [CovariantClass α α (· * ·) (· < ·)] {a b c : α} (hbc : b < c)
(ha : 1 < a) : b < c * a :=
@@ -1034,12 +692,6 @@ theorem lt_mul_of_lt_of_one_lt [CovariantClass α α (· * ·) (· < ·)] {a b c
#align lt_mul_of_lt_of_one_lt lt_mul_of_lt_of_one_lt
#align lt_add_of_lt_of_pos lt_add_of_lt_of_pos
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-Case conversion may be inaccurate. Consider using '#align lt_mul_of_lt_of_one_lt' lt_mul_of_lt_of_one_lt'ₓ'. -/
@[to_additive]
theorem lt_mul_of_lt_of_one_lt' [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (hbc : b < c)
(ha : 1 < a) : b < c * a :=
@@ -1047,12 +699,6 @@ theorem lt_mul_of_lt_of_one_lt' [CovariantClass α α (· * ·) (· ≤ ·)] {a
#align lt_mul_of_lt_of_one_lt' lt_mul_of_lt_of_one_lt'
#align lt_add_of_lt_of_pos' lt_add_of_lt_of_pos'
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/-- Assumes left covariance.
The lemma assuming right covariance is `right.one_le_mul`. -/
@[to_additive Left.add_nonneg
@@ -1063,12 +709,6 @@ theorem Left.one_le_mul [CovariantClass α α (· * ·) (· ≤ ·)] {a b : α}
#align left.one_le_mul Left.one_le_mul
#align left.add_nonneg Left.add_nonneg
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/-- Assumes left covariance.
The lemma assuming right covariance is `right.one_lt_mul_of_le_of_lt`. -/
@[to_additive Left.add_pos_of_nonneg_of_pos
@@ -1079,12 +719,6 @@ theorem Left.one_lt_mul_of_le_of_lt [CovariantClass α α (· * ·) (· < ·)] {
#align left.one_lt_mul_of_le_of_lt Left.one_lt_mul_of_le_of_lt
#align left.add_pos_of_nonneg_of_pos Left.add_pos_of_nonneg_of_pos
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/-- Assumes left covariance.
The lemma assuming right covariance is `right.one_lt_mul_of_lt_of_le`. -/
@[to_additive Left.add_pos_of_pos_of_nonneg
@@ -1095,12 +729,6 @@ theorem Left.one_lt_mul_of_lt_of_le [CovariantClass α α (· * ·) (· ≤ ·)]
#align left.one_lt_mul_of_lt_of_le Left.one_lt_mul_of_lt_of_le
#align left.add_pos_of_pos_of_nonneg Left.add_pos_of_pos_of_nonneg
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/-- Assumes left covariance.
The lemma assuming right covariance is `right.one_lt_mul`. -/
@[to_additive Left.add_pos
@@ -1111,12 +739,6 @@ theorem Left.one_lt_mul [CovariantClass α α (· * ·) (· < ·)] {a b : α} (h
#align left.one_lt_mul Left.one_lt_mul
#align left.add_pos Left.add_pos
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/-- Assumes left covariance.
The lemma assuming right covariance is `right.one_lt_mul'`. -/
@[to_additive Left.add_pos'
@@ -1131,12 +753,6 @@ theorem Left.one_lt_mul' [CovariantClass α α (· * ·) (· ≤ ·)] {a b : α}
which assume right covariance. -/
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-Case conversion may be inaccurate. Consider using '#align mul_le_of_le_one_of_le mul_le_of_le_one_of_leₓ'. -/
@[to_additive]
theorem mul_le_of_le_one_of_le [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α} (ha : a ≤ 1)
(hbc : b ≤ c) : a * b ≤ c :=
@@ -1148,12 +764,6 @@ theorem mul_le_of_le_one_of_le [CovariantClass α α (swap (· * ·)) (· ≤ ·
#align mul_le_of_le_one_of_le mul_le_of_le_one_of_le
#align add_le_of_nonpos_of_le add_le_of_nonpos_of_le
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-Case conversion may be inaccurate. Consider using '#align mul_lt_of_lt_one_of_le mul_lt_of_lt_one_of_leₓ'. -/
@[to_additive]
theorem mul_lt_of_lt_one_of_le [CovariantClass α α (swap (· * ·)) (· < ·)] {a b c : α} (ha : a < 1)
(hbc : b ≤ c) : a * b < c :=
@@ -1165,12 +775,6 @@ theorem mul_lt_of_lt_one_of_le [CovariantClass α α (swap (· * ·)) (· < ·)]
#align mul_lt_of_lt_one_of_le mul_lt_of_lt_one_of_le
#align add_lt_of_neg_of_le add_lt_of_neg_of_le
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-Case conversion may be inaccurate. Consider using '#align mul_lt_of_le_one_of_lt mul_lt_of_le_one_of_ltₓ'. -/
@[to_additive]
theorem mul_lt_of_le_one_of_lt [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α} (ha : a ≤ 1)
(hb : b < c) : a * b < c :=
@@ -1182,12 +786,6 @@ theorem mul_lt_of_le_one_of_lt [CovariantClass α α (swap (· * ·)) (· ≤ ·
#align mul_lt_of_le_one_of_lt mul_lt_of_le_one_of_lt
#align add_lt_of_nonpos_of_lt add_lt_of_nonpos_of_lt
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-Case conversion may be inaccurate. Consider using '#align mul_lt_of_lt_one_of_lt mul_lt_of_lt_one_of_ltₓ'. -/
@[to_additive]
theorem mul_lt_of_lt_one_of_lt [CovariantClass α α (swap (· * ·)) (· < ·)] {a b c : α} (ha : a < 1)
(hb : b < c) : a * b < c :=
@@ -1199,12 +797,6 @@ theorem mul_lt_of_lt_one_of_lt [CovariantClass α α (swap (· * ·)) (· < ·)]
#align mul_lt_of_lt_one_of_lt mul_lt_of_lt_one_of_lt
#align add_lt_of_neg_of_lt add_lt_of_neg_of_lt
-/- warning: mul_lt_of_lt_one_of_lt' -> mul_lt_of_lt_one_of_lt' is a dubious translation:
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- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) c)
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-Case conversion may be inaccurate. Consider using '#align mul_lt_of_lt_one_of_lt' mul_lt_of_lt_one_of_lt'ₓ'. -/
@[to_additive]
theorem mul_lt_of_lt_one_of_lt' [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α} (ha : a < 1)
(hbc : b < c) : a * b < c :=
@@ -1212,12 +804,6 @@ theorem mul_lt_of_lt_one_of_lt' [CovariantClass α α (swap (· * ·)) (· ≤
#align mul_lt_of_lt_one_of_lt' mul_lt_of_lt_one_of_lt'
#align add_lt_of_neg_of_lt' add_lt_of_neg_of_lt'
-/- warning: right.mul_le_one -> Right.mul_le_one is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align right.mul_le_one Right.mul_le_oneₓ'. -/
/-- Assumes right covariance.
The lemma assuming left covariance is `left.mul_le_one`. -/
@[to_additive "Assumes right covariance.\nThe lemma assuming left covariance is `left.add_nonpos`."]
@@ -1227,12 +813,6 @@ theorem Right.mul_le_one [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a
#align right.mul_le_one Right.mul_le_one
#align right.add_nonpos Right.add_nonpos
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-Case conversion may be inaccurate. Consider using '#align right.mul_lt_one_of_lt_of_le Right.mul_lt_one_of_lt_of_leₓ'. -/
/-- Assumes right covariance.
The lemma assuming left covariance is `left.mul_lt_one_of_lt_of_le`. -/
@[to_additive Right.add_neg_of_neg_of_nonpos
@@ -1243,12 +823,6 @@ theorem Right.mul_lt_one_of_lt_of_le [CovariantClass α α (swap (· * ·)) (·
#align right.mul_lt_one_of_lt_of_le Right.mul_lt_one_of_lt_of_le
#align right.add_neg_of_neg_of_nonpos Right.add_neg_of_neg_of_nonpos
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/-- Assumes right covariance.
The lemma assuming left covariance is `left.mul_lt_one_of_le_of_lt`. -/
@[to_additive Right.add_neg_of_nonpos_of_neg
@@ -1259,12 +833,6 @@ theorem Right.mul_lt_one_of_le_of_lt [CovariantClass α α (swap (· * ·)) (·
#align right.mul_lt_one_of_le_of_lt Right.mul_lt_one_of_le_of_lt
#align right.add_neg_of_nonpos_of_neg Right.add_neg_of_nonpos_of_neg
-/- warning: right.mul_lt_one -> Right.mul_lt_one is a dubious translation:
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- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7896 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7898 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7896 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7898)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7911 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7913 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7911 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7913)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
-Case conversion may be inaccurate. Consider using '#align right.mul_lt_one Right.mul_lt_oneₓ'. -/
/-- Assumes right covariance.
The lemma assuming left covariance is `left.mul_lt_one`. -/
@[to_additive "Assumes right covariance.\nThe lemma assuming left covariance is `left.add_neg`."]
@@ -1274,12 +842,6 @@ theorem Right.mul_lt_one [CovariantClass α α (swap (· * ·)) (· < ·)] {a b
#align right.mul_lt_one Right.mul_lt_one
#align right.add_neg Right.add_neg
-/- warning: right.mul_lt_one' -> Right.mul_lt_one' is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align right.mul_lt_one' Right.mul_lt_one'ₓ'. -/
/-- Assumes right covariance.
The lemma assuming left covariance is `left.mul_lt_one'`. -/
@[to_additive "Assumes right covariance.\nThe lemma assuming left covariance is `left.add_neg'`."]
@@ -1293,12 +855,6 @@ theorem Right.mul_lt_one' [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a
which assume right covariance. -/
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-Case conversion may be inaccurate. Consider using '#align le_mul_of_one_le_of_le le_mul_of_one_le_of_leₓ'. -/
@[to_additive]
theorem le_mul_of_one_le_of_le [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α} (ha : 1 ≤ a)
(hbc : b ≤ c) : b ≤ a * c :=
@@ -1310,12 +866,6 @@ theorem le_mul_of_one_le_of_le [CovariantClass α α (swap (· * ·)) (· ≤ ·
#align le_mul_of_one_le_of_le le_mul_of_one_le_of_le
#align le_add_of_nonneg_of_le le_add_of_nonneg_of_le
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-Case conversion may be inaccurate. Consider using '#align lt_mul_of_one_lt_of_le lt_mul_of_one_lt_of_leₓ'. -/
@[to_additive]
theorem lt_mul_of_one_lt_of_le [CovariantClass α α (swap (· * ·)) (· < ·)] {a b c : α} (ha : 1 < a)
(hbc : b ≤ c) : b < a * c :=
@@ -1327,12 +877,6 @@ theorem lt_mul_of_one_lt_of_le [CovariantClass α α (swap (· * ·)) (· < ·)]
#align lt_mul_of_one_lt_of_le lt_mul_of_one_lt_of_le
#align lt_add_of_pos_of_le lt_add_of_pos_of_le
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-Case conversion may be inaccurate. Consider using '#align lt_mul_of_one_le_of_lt lt_mul_of_one_le_of_ltₓ'. -/
@[to_additive]
theorem lt_mul_of_one_le_of_lt [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α} (ha : 1 ≤ a)
(hbc : b < c) : b < a * c :=
@@ -1344,12 +888,6 @@ theorem lt_mul_of_one_le_of_lt [CovariantClass α α (swap (· * ·)) (· ≤ ·
#align lt_mul_of_one_le_of_lt lt_mul_of_one_le_of_lt
#align lt_add_of_nonneg_of_lt lt_add_of_nonneg_of_lt
-/- warning: lt_mul_of_one_lt_of_lt -> lt_mul_of_one_lt_of_lt is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align lt_mul_of_one_lt_of_lt lt_mul_of_one_lt_of_ltₓ'. -/
@[to_additive]
theorem lt_mul_of_one_lt_of_lt [CovariantClass α α (swap (· * ·)) (· < ·)] {a b c : α} (ha : 1 < a)
(hbc : b < c) : b < a * c :=
@@ -1361,12 +899,6 @@ theorem lt_mul_of_one_lt_of_lt [CovariantClass α α (swap (· * ·)) (· < ·)]
#align lt_mul_of_one_lt_of_lt lt_mul_of_one_lt_of_lt
#align lt_add_of_pos_of_lt lt_add_of_pos_of_lt
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-Case conversion may be inaccurate. Consider using '#align lt_mul_of_one_lt_of_lt' lt_mul_of_one_lt_of_lt'ₓ'. -/
@[to_additive]
theorem lt_mul_of_one_lt_of_lt' [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α} (ha : 1 < a)
(hbc : b < c) : b < a * c :=
@@ -1374,12 +906,6 @@ theorem lt_mul_of_one_lt_of_lt' [CovariantClass α α (swap (· * ·)) (· ≤
#align lt_mul_of_one_lt_of_lt' lt_mul_of_one_lt_of_lt'
#align lt_add_of_pos_of_lt' lt_add_of_pos_of_lt'
-/- warning: right.one_le_mul -> Right.one_le_mul is a dubious translation:
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- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
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-Case conversion may be inaccurate. Consider using '#align right.one_le_mul Right.one_le_mulₓ'. -/
/-- Assumes right covariance.
The lemma assuming left covariance is `left.one_le_mul`. -/
@[to_additive Right.add_nonneg
@@ -1390,12 +916,6 @@ theorem Right.one_le_mul [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a
#align right.one_le_mul Right.one_le_mul
#align right.add_nonneg Right.add_nonneg
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/-- Assumes right covariance.
The lemma assuming left covariance is `left.one_lt_mul_of_lt_of_le`. -/
@[to_additive Right.add_pos_of_pos_of_nonneg
@@ -1406,12 +926,6 @@ theorem Right.one_lt_mul_of_lt_of_le [CovariantClass α α (swap (· * ·)) (·
#align right.one_lt_mul_of_lt_of_le Right.one_lt_mul_of_lt_of_le
#align right.add_pos_of_pos_of_nonneg Right.add_pos_of_pos_of_nonneg
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-Case conversion may be inaccurate. Consider using '#align right.one_lt_mul_of_le_of_lt Right.one_lt_mul_of_le_of_ltₓ'. -/
/-- Assumes right covariance.
The lemma assuming left covariance is `left.one_lt_mul_of_le_of_lt`. -/
@[to_additive Right.add_pos_of_nonneg_of_pos
@@ -1422,12 +936,6 @@ theorem Right.one_lt_mul_of_le_of_lt [CovariantClass α α (swap (· * ·)) (·
#align right.one_lt_mul_of_le_of_lt Right.one_lt_mul_of_le_of_lt
#align right.add_pos_of_nonneg_of_pos Right.add_pos_of_nonneg_of_pos
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- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
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-Case conversion may be inaccurate. Consider using '#align right.one_lt_mul Right.one_lt_mulₓ'. -/
/-- Assumes right covariance.
The lemma assuming left covariance is `left.one_lt_mul`. -/
@[to_additive Right.add_pos
@@ -1438,12 +946,6 @@ theorem Right.one_lt_mul [CovariantClass α α (swap (· * ·)) (· < ·)] {a b
#align right.one_lt_mul Right.one_lt_mul
#align right.add_pos Right.add_pos
-/- warning: right.one_lt_mul' -> Right.one_lt_mul' is a dubious translation:
-lean 3 declaration is
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/-- Assumes right covariance.
The lemma assuming left covariance is `left.one_lt_mul'`. -/
@[to_additive Right.add_pos'
@@ -1454,48 +956,18 @@ theorem Right.one_lt_mul' [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a
#align right.one_lt_mul' Right.one_lt_mul'
#align right.add_pos' Right.add_pos'
-/- warning: mul_le_one' -> mul_le_one' is a dubious translation:
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- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5916 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5918 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5916 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5918) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5931 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5933 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5931 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5933)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
-Case conversion may be inaccurate. Consider using '#align mul_le_one' mul_le_one'ₓ'. -/
alias Left.mul_le_one ← mul_le_one'
#align mul_le_one' mul_le_one'
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-Case conversion may be inaccurate. Consider using '#align mul_lt_one_of_le_of_lt mul_lt_one_of_le_of_ltₓ'. -/
alias Left.mul_lt_one_of_le_of_lt ← mul_lt_one_of_le_of_lt
#align mul_lt_one_of_le_of_lt mul_lt_one_of_le_of_lt
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-Case conversion may be inaccurate. Consider using '#align mul_lt_one_of_lt_of_le mul_lt_one_of_lt_of_leₓ'. -/
alias Left.mul_lt_one_of_lt_of_le ← mul_lt_one_of_lt_of_le
#align mul_lt_one_of_lt_of_le mul_lt_one_of_lt_of_le
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-Case conversion may be inaccurate. Consider using '#align mul_lt_one mul_lt_oneₓ'. -/
alias Left.mul_lt_one ← mul_lt_one
#align mul_lt_one mul_lt_one
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alias Left.mul_lt_one' ← mul_lt_one'
#align mul_lt_one' mul_lt_one'
@@ -1511,48 +983,18 @@ attribute [to_additive "**Alias** of `left.add_neg`."] mul_lt_one
attribute [to_additive "**Alias** of `left.add_neg'`."] mul_lt_one'
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alias Left.one_le_mul ← one_le_mul
#align one_le_mul one_le_mul
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alias Left.one_lt_mul_of_le_of_lt ← one_lt_mul_of_le_of_lt'
#align one_lt_mul_of_le_of_lt' one_lt_mul_of_le_of_lt'
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-Case conversion may be inaccurate. Consider using '#align one_lt_mul_of_lt_of_le' one_lt_mul_of_lt_of_le'ₓ'. -/
alias Left.one_lt_mul_of_lt_of_le ← one_lt_mul_of_lt_of_le'
#align one_lt_mul_of_lt_of_le' one_lt_mul_of_lt_of_le'
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-Case conversion may be inaccurate. Consider using '#align one_lt_mul' one_lt_mul'ₓ'. -/
alias Left.one_lt_mul ← one_lt_mul'
#align one_lt_mul' one_lt_mul'
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-Case conversion may be inaccurate. Consider using '#align one_lt_mul'' one_lt_mul''ₓ'. -/
alias Left.one_lt_mul' ← one_lt_mul''
#align one_lt_mul'' one_lt_mul''
@@ -1568,12 +1010,6 @@ attribute [to_additive add_pos "**Alias** of `left.add_pos`."] one_lt_mul'
attribute [to_additive add_pos' "**Alias** of `left.add_pos'`."] one_lt_mul''
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-Case conversion may be inaccurate. Consider using '#align lt_of_mul_lt_of_one_le_left lt_of_mul_lt_of_one_le_leftₓ'. -/
@[to_additive]
theorem lt_of_mul_lt_of_one_le_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (h : a * b < c)
(hle : 1 ≤ b) : a < c :=
@@ -1581,12 +1017,6 @@ theorem lt_of_mul_lt_of_one_le_left [CovariantClass α α (· * ·) (· ≤ ·)]
#align lt_of_mul_lt_of_one_le_left lt_of_mul_lt_of_one_le_left
#align lt_of_add_lt_of_nonneg_left lt_of_add_lt_of_nonneg_left
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align le_of_mul_le_of_one_le_left le_of_mul_le_of_one_le_leftₓ'. -/
@[to_additive]
theorem le_of_mul_le_of_one_le_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (h : a * b ≤ c)
(hle : 1 ≤ b) : a ≤ c :=
@@ -1594,12 +1024,6 @@ theorem le_of_mul_le_of_one_le_left [CovariantClass α α (· * ·) (· ≤ ·)]
#align le_of_mul_le_of_one_le_left le_of_mul_le_of_one_le_left
#align le_of_add_le_of_nonneg_left le_of_add_le_of_nonneg_left
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align lt_of_lt_mul_of_le_one_left lt_of_lt_mul_of_le_one_leftₓ'. -/
@[to_additive]
theorem lt_of_lt_mul_of_le_one_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (h : a < b * c)
(hle : c ≤ 1) : a < b :=
@@ -1607,12 +1031,6 @@ theorem lt_of_lt_mul_of_le_one_left [CovariantClass α α (· * ·) (· ≤ ·)]
#align lt_of_lt_mul_of_le_one_left lt_of_lt_mul_of_le_one_left
#align lt_of_lt_add_of_nonpos_left lt_of_lt_add_of_nonpos_left
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-Case conversion may be inaccurate. Consider using '#align le_of_le_mul_of_le_one_left le_of_le_mul_of_le_one_leftₓ'. -/
@[to_additive]
theorem le_of_le_mul_of_le_one_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (h : a ≤ b * c)
(hle : c ≤ 1) : a ≤ b :=
@@ -1620,12 +1038,6 @@ theorem le_of_le_mul_of_le_one_left [CovariantClass α α (· * ·) (· ≤ ·)]
#align le_of_le_mul_of_le_one_left le_of_le_mul_of_le_one_left
#align le_of_le_add_of_nonpos_left le_of_le_add_of_nonpos_left
-/- warning: lt_of_mul_lt_of_one_le_right -> lt_of_mul_lt_of_one_le_right is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align lt_of_mul_lt_of_one_le_right lt_of_mul_lt_of_one_le_rightₓ'. -/
@[to_additive]
theorem lt_of_mul_lt_of_one_le_right [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α}
(h : a * b < c) (hle : 1 ≤ a) : b < c :=
@@ -1633,12 +1045,6 @@ theorem lt_of_mul_lt_of_one_le_right [CovariantClass α α (swap (· * ·)) (·
#align lt_of_mul_lt_of_one_le_right lt_of_mul_lt_of_one_le_right
#align lt_of_add_lt_of_nonneg_right lt_of_add_lt_of_nonneg_right
-/- warning: le_of_mul_le_of_one_le_right -> le_of_mul_le_of_one_le_right is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9343 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9345 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9343 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9345)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9358 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9360 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9358 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9360)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c)
-Case conversion may be inaccurate. Consider using '#align le_of_mul_le_of_one_le_right le_of_mul_le_of_one_le_rightₓ'. -/
@[to_additive]
theorem le_of_mul_le_of_one_le_right [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α}
(h : a * b ≤ c) (hle : 1 ≤ a) : b ≤ c :=
@@ -1646,12 +1052,6 @@ theorem le_of_mul_le_of_one_le_right [CovariantClass α α (swap (· * ·)) (·
#align le_of_mul_le_of_one_le_right le_of_mul_le_of_one_le_right
#align le_of_add_le_of_nonneg_right le_of_add_le_of_nonneg_right
-/- warning: lt_of_lt_mul_of_le_one_right -> lt_of_lt_mul_of_le_one_right is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9417 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9419 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9417 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9419)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9432 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9434 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9432 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9434)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b c)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a c)
-Case conversion may be inaccurate. Consider using '#align lt_of_lt_mul_of_le_one_right lt_of_lt_mul_of_le_one_rightₓ'. -/
@[to_additive]
theorem lt_of_lt_mul_of_le_one_right [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α}
(h : a < b * c) (hle : b ≤ 1) : a < c :=
@@ -1659,12 +1059,6 @@ theorem lt_of_lt_mul_of_le_one_right [CovariantClass α α (swap (· * ·)) (·
#align lt_of_lt_mul_of_le_one_right lt_of_lt_mul_of_le_one_right
#align lt_of_lt_add_of_nonpos_right lt_of_lt_add_of_nonpos_right
-/- warning: le_of_le_mul_of_le_one_right -> le_of_le_mul_of_le_one_right is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b c)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a c)
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9490 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9492 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9490 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9492)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9505 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9507 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9505 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9507)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b c)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a c)
-Case conversion may be inaccurate. Consider using '#align le_of_le_mul_of_le_one_right le_of_le_mul_of_le_one_rightₓ'. -/
@[to_additive]
theorem le_of_le_mul_of_le_one_right [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α}
(h : a ≤ b * c) (hle : b ≤ 1) : a ≤ c :=
@@ -1678,12 +1072,6 @@ section PartialOrder
variable [PartialOrder α]
-/- warning: mul_eq_one_iff' -> mul_eq_one_iff' is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (Iff (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) (And (Eq.{succ u1} α a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) (Eq.{succ u1} α b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))))
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-Case conversion may be inaccurate. Consider using '#align mul_eq_one_iff' mul_eq_one_iff'ₓ'. -/
@[to_additive]
theorem mul_eq_one_iff' [CovariantClass α α (· * ·) (· ≤ ·)]
[CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b : α} (ha : 1 ≤ a) (hb : 1 ≤ b) :
@@ -1699,12 +1087,6 @@ theorem mul_eq_one_iff' [CovariantClass α α (· * ·) (· ≤ ·)]
#align mul_eq_one_iff' mul_eq_one_iff'
#align add_eq_zero_iff' add_eq_zero_iff'
-/- warning: mul_le_mul_iff_of_ge -> mul_le_mul_iff_of_ge is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_5 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_6 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a₁ : α} {a₂ : α} {b₁ : α} {b₂ : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a₁ a₂) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b₁ b₂) -> (Iff (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a₂ b₂) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a₁ b₁)) (And (Eq.{succ u1} α a₁ a₂) (Eq.{succ u1} α b₁ b₂)))
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- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9831 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9833 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9831 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9833) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9846 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9848 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9846 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9848)] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9868 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9870 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9868 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9870)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9883 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9885 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9883 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9885)] [_inst_5 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9902 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9904 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9902 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9904) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9917 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9919 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9917 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9919)] [_inst_6 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9939 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9941 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9939 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9941)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9954 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9956 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9954 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9956)] {a₁ : α} {a₂ : α} {b₁ : α} {b₂ : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a₁ a₂) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b₁ b₂) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a₂ b₂) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a₁ b₁)) (And (Eq.{succ u1} α a₁ a₂) (Eq.{succ u1} α b₁ b₂)))
-Case conversion may be inaccurate. Consider using '#align mul_le_mul_iff_of_ge mul_le_mul_iff_of_geₓ'. -/
@[to_additive]
theorem mul_le_mul_iff_of_ge [CovariantClass α α (· * ·) (· ≤ ·)]
[CovariantClass α α (swap (· * ·)) (· ≤ ·)] [CovariantClass α α (· * ·) (· < ·)]
@@ -1723,24 +1105,12 @@ section Left
variable [CovariantClass α α (· * ·) (· ≤ ·)] {a b : α}
-/- warning: eq_one_of_one_le_mul_left -> eq_one_of_one_le_mul_left is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b)) -> (Eq.{succ u1} α a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10119 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10121 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10119 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10121) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10134 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10136 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10134 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10136)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b)) -> (Eq.{succ u1} α a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
-Case conversion may be inaccurate. Consider using '#align eq_one_of_one_le_mul_left eq_one_of_one_le_mul_leftₓ'. -/
@[to_additive eq_zero_of_add_nonneg_left]
theorem eq_one_of_one_le_mul_left (ha : a ≤ 1) (hb : b ≤ 1) (hab : 1 ≤ a * b) : a = 1 :=
ha.eq_of_not_lt fun h => hab.not_lt <| mul_lt_one_of_lt_of_le h hb
#align eq_one_of_one_le_mul_left eq_one_of_one_le_mul_left
#align eq_zero_of_add_nonneg_left eq_zero_of_add_nonneg_left
-/- warning: eq_one_of_mul_le_one_left -> eq_one_of_mul_le_one_left is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (Eq.{succ u1} α a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10198 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10200 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10198 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10200) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10213 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10215 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10213 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10215)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (Eq.{succ u1} α a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
-Case conversion may be inaccurate. Consider using '#align eq_one_of_mul_le_one_left eq_one_of_mul_le_one_leftₓ'. -/
@[to_additive]
theorem eq_one_of_mul_le_one_left (ha : 1 ≤ a) (hb : 1 ≤ b) (hab : a * b ≤ 1) : a = 1 :=
ha.eq_of_not_gt fun h => hab.not_lt <| one_lt_mul_of_lt_of_le' h hb
@@ -1753,24 +1123,12 @@ section Right
variable [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b : α}
-/- warning: eq_one_of_one_le_mul_right -> eq_one_of_one_le_mul_right is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b)) -> (Eq.{succ u1} α b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
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- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10333 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10335 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10333 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10335)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10348 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10350 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10348 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10350)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b)) -> (Eq.{succ u1} α b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
-Case conversion may be inaccurate. Consider using '#align eq_one_of_one_le_mul_right eq_one_of_one_le_mul_rightₓ'. -/
@[to_additive eq_zero_of_add_nonneg_right]
theorem eq_one_of_one_le_mul_right (ha : a ≤ 1) (hb : b ≤ 1) (hab : 1 ≤ a * b) : b = 1 :=
hb.eq_of_not_lt fun h => hab.not_lt <| Right.mul_lt_one_of_le_of_lt ha h
#align eq_one_of_one_le_mul_right eq_one_of_one_le_mul_right
#align eq_zero_of_add_nonneg_right eq_zero_of_add_nonneg_right
-/- warning: eq_one_of_mul_le_one_right -> eq_one_of_mul_le_one_right is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (Eq.{succ u1} α b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10415 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10417 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10415 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10417)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10430 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10432 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10430 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10432)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (Eq.{succ u1} α b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
-Case conversion may be inaccurate. Consider using '#align eq_one_of_mul_le_one_right eq_one_of_mul_le_one_rightₓ'. -/
@[to_additive]
theorem eq_one_of_mul_le_one_right (ha : 1 ≤ a) (hb : 1 ≤ b) (hab : a * b ≤ 1) : b = 1 :=
hb.eq_of_not_gt fun h => hab.not_lt <| Right.one_lt_mul_of_le_of_lt ha h
@@ -1785,12 +1143,6 @@ section LinearOrder
variable [LinearOrder α]
-/- warning: exists_square_le -> exists_square_le is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))))] (a : α), Exists.{succ u1} α (fun (b : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b b) a)
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10507 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10509 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10507 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10509) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10522 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10524 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10522 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10524)] (a : α), Exists.{succ u1} α (fun (b : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b b) a)
-Case conversion may be inaccurate. Consider using '#align exists_square_le exists_square_leₓ'. -/
theorem exists_square_le [CovariantClass α α (· * ·) (· < ·)] (a : α) : ∃ b : α, b * b ≤ a :=
by
by_cases h : a < 1
@@ -1815,12 +1167,6 @@ section PartialOrder
variable [PartialOrder α]
-/- warning: contravariant.to_left_cancel_semigroup -> Contravariant.toLeftCancelSemigroup is a dubious translation:
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- forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))], LeftCancelSemigroup.{u1} α
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10777 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10779 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10777 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10779) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10792 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10794 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10792 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10794)], LeftCancelSemigroup.{u1} α
-Case conversion may be inaccurate. Consider using '#align contravariant.to_left_cancel_semigroup Contravariant.toLeftCancelSemigroupₓ'. -/
/- This is not instance, since we want to have an instance from `left_cancel_semigroup`s
to the appropriate `covariant_class`. -/
/-- A semigroup with a partial order and satisfying `left_cancel_semigroup`
@@ -1833,12 +1179,6 @@ def Contravariant.toLeftCancelSemigroup [ContravariantClass α α (· * ·) (·
#align contravariant.to_left_cancel_semigroup Contravariant.toLeftCancelSemigroup
#align contravariant.to_left_cancel_add_semigroup Contravariant.toAddLeftCancelSemigroup
-/- warning: contravariant.to_right_cancel_semigroup -> Contravariant.toRightCancelSemigroup is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))], RightCancelSemigroup.{u1} α
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10860 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10862 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10860 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10862)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10875 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10877 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10875 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10877)], RightCancelSemigroup.{u1} α
-Case conversion may be inaccurate. Consider using '#align contravariant.to_right_cancel_semigroup Contravariant.toRightCancelSemigroupₓ'. -/
/- This is not instance, since we want to have an instance from `right_cancel_semigroup`s
to the appropriate `covariant_class`. -/
/-- A semigroup with a partial order and satisfying `right_cancel_semigroup`
@@ -1851,12 +1191,6 @@ def Contravariant.toRightCancelSemigroup [ContravariantClass α α (swap (· *
#align contravariant.to_right_cancel_semigroup Contravariant.toRightCancelSemigroup
#align contravariant.to_right_cancel_add_semigroup Contravariant.toAddRightCancelSemigroup
-/- warning: left.mul_eq_mul_iff_eq_and_eq -> Left.mul_eq_mul_iff_eq_and_eq is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_5 : ContravariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_6 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a c) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b d) -> (Iff (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)) c d)) (And (Eq.{succ u1} α a c) (Eq.{succ u1} α b d)))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10940 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10942 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10940 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10942) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10955 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10957 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10955 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10957)] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10977 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10979 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10977 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10979)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10992 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10994 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10992 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10994)] [_inst_5 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11011 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11013 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11011 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11013) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11026 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11028 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11026 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11028)] [_inst_6 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11048 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11050 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11048 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11050)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11063 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11065 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11063 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11065)] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b d) -> (Iff (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) c d)) (And (Eq.{succ u1} α a c) (Eq.{succ u1} α b d)))
-Case conversion may be inaccurate. Consider using '#align left.mul_eq_mul_iff_eq_and_eq Left.mul_eq_mul_iff_eq_and_eqₓ'. -/
@[to_additive]
theorem Left.mul_eq_mul_iff_eq_and_eq [CovariantClass α α (· * ·) (· < ·)]
[CovariantClass α α (swap (· * ·)) (· ≤ ·)] [ContravariantClass α α (· * ·) (· ≤ ·)]
@@ -1872,12 +1206,6 @@ theorem Left.mul_eq_mul_iff_eq_and_eq [CovariantClass α α (· * ·) (· < ·)]
#align left.mul_eq_mul_iff_eq_and_eq Left.mul_eq_mul_iff_eq_and_eq
#align left.add_eq_add_iff_eq_and_eq Left.add_eq_add_iff_eq_and_eq
-/- warning: right.mul_eq_mul_iff_eq_and_eq -> Right.mul_eq_mul_iff_eq_and_eq is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_4 : ContravariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_6 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a c) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b d) -> (Iff (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)) c d)) (And (Eq.{succ u1} α a c) (Eq.{succ u1} α b d)))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11203 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11205 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11203 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11205) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11218 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11220 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11218 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11220)] [_inst_4 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11237 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11239 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11237 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11239) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11252 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11254 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11252 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11254)] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11274 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11276 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11274 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11276)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11289 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11291 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11289 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11291)] [_inst_6 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11311 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11313 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11311 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11313)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11326 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11328 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11326 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11328)] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b d) -> (Iff (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) c d)) (And (Eq.{succ u1} α a c) (Eq.{succ u1} α b d)))
-Case conversion may be inaccurate. Consider using '#align right.mul_eq_mul_iff_eq_and_eq Right.mul_eq_mul_iff_eq_and_eqₓ'. -/
@[to_additive]
theorem Right.mul_eq_mul_iff_eq_and_eq [CovariantClass α α (· * ·) (· ≤ ·)]
[ContravariantClass α α (· * ·) (· ≤ ·)] [CovariantClass α α (swap (· * ·)) (· < ·)]
@@ -1893,12 +1221,6 @@ theorem Right.mul_eq_mul_iff_eq_and_eq [CovariantClass α α (· * ·) (· ≤
#align right.mul_eq_mul_iff_eq_and_eq Right.mul_eq_mul_iff_eq_and_eq
#align right.add_eq_add_iff_eq_and_eq Right.add_eq_add_iff_eq_and_eq
-/- warning: mul_eq_mul_iff_eq_and_eq -> mul_eq_mul_iff_eq_and_eq is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_5 : ContravariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_6 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a c) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b d) -> (Iff (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)) c d)) (And (Eq.{succ u1} α a c) (Eq.{succ u1} α b d)))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10940 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10942 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10940 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10942) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10955 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10957 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10955 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10957)] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10977 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10979 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10977 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10979)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10992 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10994 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10992 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10994)] [_inst_5 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11011 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11013 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11011 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11013) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11026 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11028 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11026 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11028)] [_inst_6 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11048 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11050 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11048 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11050)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11063 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11065 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11063 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11065)] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b d) -> (Iff (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) c d)) (And (Eq.{succ u1} α a c) (Eq.{succ u1} α b d)))
-Case conversion may be inaccurate. Consider using '#align mul_eq_mul_iff_eq_and_eq mul_eq_mul_iff_eq_and_eqₓ'. -/
alias Left.mul_eq_mul_iff_eq_and_eq ← mul_eq_mul_iff_eq_and_eq
#align mul_eq_mul_iff_eq_and_eq mul_eq_mul_iff_eq_and_eq
@@ -1912,108 +1234,54 @@ section Mono
variable [Mul α] [Preorder α] [Preorder β] {f g : β → α} {s : Set β}
-/- warning: monotone.const_mul' -> Monotone.const_mul' is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))], (Monotone.{u2, u1} β α _inst_3 _inst_2 f) -> (forall (a : α), Monotone.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a (f x)))
-but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11510 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11512 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11510 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11512) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11525 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11527 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11525 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11527)], (Monotone.{u1, u2} β α _inst_3 _inst_2 f) -> (forall (a : α), Monotone.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) a (f x)))
-Case conversion may be inaccurate. Consider using '#align monotone.const_mul' Monotone.const_mul'ₓ'. -/
@[to_additive const_add]
theorem Monotone.const_mul' [CovariantClass α α (· * ·) (· ≤ ·)] (hf : Monotone f) (a : α) :
Monotone fun x => a * f x := fun x y h => mul_le_mul_left' (hf h) a
#align monotone.const_mul' Monotone.const_mul'
#align monotone.const_add Monotone.const_add
-/- warning: monotone_on.const_mul' -> MonotoneOn.const_mul' is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))], (MonotoneOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (forall (a : α), MonotoneOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a (f x)) s)
-but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} {s : Set.{u1} β} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11596 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11598 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11596 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11598) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11611 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11613 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11611 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11613)], (MonotoneOn.{u1, u2} β α _inst_3 _inst_2 f s) -> (forall (a : α), MonotoneOn.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) a (f x)) s)
-Case conversion may be inaccurate. Consider using '#align monotone_on.const_mul' MonotoneOn.const_mul'ₓ'. -/
@[to_additive const_add]
theorem MonotoneOn.const_mul' [CovariantClass α α (· * ·) (· ≤ ·)] (hf : MonotoneOn f s) (a : α) :
MonotoneOn (fun x => a * f x) s := fun x hx y hy h => mul_le_mul_left' (hf hx hy h) a
#align monotone_on.const_mul' MonotoneOn.const_mul'
#align monotone_on.const_add MonotoneOn.const_add
-/- warning: antitone.const_mul' -> Antitone.const_mul' is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))], (Antitone.{u2, u1} β α _inst_3 _inst_2 f) -> (forall (a : α), Antitone.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a (f x)))
-but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11690 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11692 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11690 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11692) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11705 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11707 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11705 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11707)], (Antitone.{u1, u2} β α _inst_3 _inst_2 f) -> (forall (a : α), Antitone.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) a (f x)))
-Case conversion may be inaccurate. Consider using '#align antitone.const_mul' Antitone.const_mul'ₓ'. -/
@[to_additive const_add]
theorem Antitone.const_mul' [CovariantClass α α (· * ·) (· ≤ ·)] (hf : Antitone f) (a : α) :
Antitone fun x => a * f x := fun x y h => mul_le_mul_left' (hf h) a
#align antitone.const_mul' Antitone.const_mul'
#align antitone.const_add Antitone.const_add
-/- warning: antitone_on.const_mul' -> AntitoneOn.const_mul' is a dubious translation:
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@[to_additive const_add]
theorem AntitoneOn.const_mul' [CovariantClass α α (· * ·) (· ≤ ·)] (hf : AntitoneOn f s) (a : α) :
AntitoneOn (fun x => a * f x) s := fun x hx y hy h => mul_le_mul_left' (hf hx hy h) a
#align antitone_on.const_mul' AntitoneOn.const_mul'
#align antitone_on.const_add AntitoneOn.const_add
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@[to_additive add_const]
theorem Monotone.mul_const' [CovariantClass α α (swap (· * ·)) (· ≤ ·)] (hf : Monotone f) (a : α) :
Monotone fun x => f x * a := fun x y h => mul_le_mul_right' (hf h) a
#align monotone.mul_const' Monotone.mul_const'
#align monotone.add_const Monotone.add_const
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@[to_additive add_const]
theorem MonotoneOn.mul_const' [CovariantClass α α (swap (· * ·)) (· ≤ ·)] (hf : MonotoneOn f s)
(a : α) : MonotoneOn (fun x => f x * a) s := fun x hx y hy h => mul_le_mul_right' (hf hx hy h) a
#align monotone_on.mul_const' MonotoneOn.mul_const'
#align monotone_on.add_const MonotoneOn.add_const
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@[to_additive add_const]
theorem Antitone.mul_const' [CovariantClass α α (swap (· * ·)) (· ≤ ·)] (hf : Antitone f) (a : α) :
Antitone fun x => f x * a := fun x y h => mul_le_mul_right' (hf h) a
#align antitone.mul_const' Antitone.mul_const'
#align antitone.add_const Antitone.add_const
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@[to_additive add_const]
theorem AntitoneOn.mul_const' [CovariantClass α α (swap (· * ·)) (· ≤ ·)] (hf : AntitoneOn f s)
(a : α) : AntitoneOn (fun x => f x * a) s := fun x hx y hy h => mul_le_mul_right' (hf hx hy h) a
#align antitone_on.mul_const' AntitoneOn.mul_const'
#align antitone_on.add_const AntitoneOn.add_const
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/-- The product of two monotone functions is monotone. -/
@[to_additive add "The sum of two monotone functions is monotone."]
theorem Monotone.mul' [CovariantClass α α (· * ·) (· ≤ ·)]
@@ -2022,12 +1290,6 @@ theorem Monotone.mul' [CovariantClass α α (· * ·) (· ≤ ·)]
#align monotone.mul' Monotone.mul'
#align monotone.add Monotone.add
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/-- The product of two monotone functions is monotone. -/
@[to_additive add "The sum of two monotone functions is monotone."]
theorem MonotoneOn.mul' [CovariantClass α α (· * ·) (· ≤ ·)]
@@ -2036,12 +1298,6 @@ theorem MonotoneOn.mul' [CovariantClass α α (· * ·) (· ≤ ·)]
#align monotone_on.mul' MonotoneOn.mul'
#align monotone_on.add MonotoneOn.add
-/- warning: antitone.mul' -> Antitone.mul' is a dubious translation:
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/-- The product of two antitone functions is antitone. -/
@[to_additive add "The sum of two antitone functions is antitone."]
theorem Antitone.mul' [CovariantClass α α (· * ·) (· ≤ ·)]
@@ -2050,12 +1306,6 @@ theorem Antitone.mul' [CovariantClass α α (· * ·) (· ≤ ·)]
#align antitone.mul' Antitone.mul'
#align antitone.add Antitone.add
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/-- The product of two antitone functions is antitone. -/
@[to_additive add "The sum of two antitone functions is antitone."]
theorem AntitoneOn.mul' [CovariantClass α α (· * ·) (· ≤ ·)]
@@ -2068,48 +1318,24 @@ section Left
variable [CovariantClass α α (· * ·) (· < ·)]
-/- warning: strict_mono.const_mul' -> StrictMono.const_mul' is a dubious translation:
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@[to_additive const_add]
theorem StrictMono.const_mul' (hf : StrictMono f) (c : α) : StrictMono fun x => c * f x :=
fun a b ab => mul_lt_mul_left' (hf ab) c
#align strict_mono.const_mul' StrictMono.const_mul'
#align strict_mono.const_add StrictMono.const_add
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@[to_additive const_add]
theorem StrictMonoOn.const_mul' (hf : StrictMonoOn f s) (c : α) :
StrictMonoOn (fun x => c * f x) s := fun a ha b hb ab => mul_lt_mul_left' (hf ha hb ab) c
#align strict_mono_on.const_mul' StrictMonoOn.const_mul'
#align strict_mono_on.const_add StrictMonoOn.const_add
-/- warning: strict_anti.const_mul' -> StrictAnti.const_mul' is a dubious translation:
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@[to_additive const_add]
theorem StrictAnti.const_mul' (hf : StrictAnti f) (c : α) : StrictAnti fun x => c * f x :=
fun a b ab => mul_lt_mul_left' (hf ab) c
#align strict_anti.const_mul' StrictAnti.const_mul'
#align strict_anti.const_add StrictAnti.const_add
-/- warning: strict_anti_on.const_mul' -> StrictAntiOn.const_mul' is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align strict_anti_on.const_mul' StrictAntiOn.const_mul'ₓ'. -/
@[to_additive const_add]
theorem StrictAntiOn.const_mul' (hf : StrictAntiOn f s) (c : α) :
StrictAntiOn (fun x => c * f x) s := fun a ha b hb ab => mul_lt_mul_left' (hf ha hb ab) c
@@ -2122,48 +1348,24 @@ section Right
variable [CovariantClass α α (swap (· * ·)) (· < ·)]
-/- warning: strict_mono.mul_const' -> StrictMono.mul_const' is a dubious translation:
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@[to_additive add_const]
theorem StrictMono.mul_const' (hf : StrictMono f) (c : α) : StrictMono fun x => f x * c :=
fun a b ab => mul_lt_mul_right' (hf ab) c
#align strict_mono.mul_const' StrictMono.mul_const'
#align strict_mono.add_const StrictMono.add_const
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@[to_additive add_const]
theorem StrictMonoOn.mul_const' (hf : StrictMonoOn f s) (c : α) :
StrictMonoOn (fun x => f x * c) s := fun a ha b hb ab => mul_lt_mul_right' (hf ha hb ab) c
#align strict_mono_on.mul_const' StrictMonoOn.mul_const'
#align strict_mono_on.add_const StrictMonoOn.add_const
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@[to_additive add_const]
theorem StrictAnti.mul_const' (hf : StrictAnti f) (c : α) : StrictAnti fun x => f x * c :=
fun a b ab => mul_lt_mul_right' (hf ab) c
#align strict_anti.mul_const' StrictAnti.mul_const'
#align strict_anti.add_const StrictAnti.add_const
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@[to_additive add_const]
theorem StrictAntiOn.mul_const' (hf : StrictAntiOn f s) (c : α) :
StrictAntiOn (fun x => f x * c) s := fun a ha b hb ab => mul_lt_mul_right' (hf ha hb ab) c
@@ -2172,12 +1374,6 @@ theorem StrictAntiOn.mul_const' (hf : StrictAntiOn f s) (c : α) :
end Right
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/-- The product of two strictly monotone functions is strictly monotone. -/
@[to_additive add "The sum of two strictly monotone functions is strictly monotone."]
theorem StrictMono.mul' [CovariantClass α α (· * ·) (· < ·)]
@@ -2186,12 +1382,6 @@ theorem StrictMono.mul' [CovariantClass α α (· * ·) (· < ·)]
#align strict_mono.mul' StrictMono.mul'
#align strict_mono.add StrictMono.add
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/-- The product of two strictly monotone functions is strictly monotone. -/
@[to_additive add "The sum of two strictly monotone functions is strictly monotone."]
theorem StrictMonoOn.mul' [CovariantClass α α (· * ·) (· < ·)]
@@ -2201,12 +1391,6 @@ theorem StrictMonoOn.mul' [CovariantClass α α (· * ·) (· < ·)]
#align strict_mono_on.mul' StrictMonoOn.mul'
#align strict_mono_on.add StrictMonoOn.add
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/-- The product of two strictly antitone functions is strictly antitone. -/
@[to_additive add "The sum of two strictly antitone functions is strictly antitone."]
theorem StrictAnti.mul' [CovariantClass α α (· * ·) (· < ·)]
@@ -2215,12 +1399,6 @@ theorem StrictAnti.mul' [CovariantClass α α (· * ·) (· < ·)]
#align strict_anti.mul' StrictAnti.mul'
#align strict_anti.add StrictAnti.add
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-Case conversion may be inaccurate. Consider using '#align strict_anti_on.mul' StrictAntiOn.mul'ₓ'. -/
/-- The product of two strictly antitone functions is strictly antitone. -/
@[to_additive add "The sum of two strictly antitone functions is strictly antitone."]
theorem StrictAntiOn.mul' [CovariantClass α α (· * ·) (· < ·)]
@@ -2230,12 +1408,6 @@ theorem StrictAntiOn.mul' [CovariantClass α α (· * ·) (· < ·)]
#align strict_anti_on.mul' StrictAntiOn.mul'
#align strict_anti_on.add StrictAntiOn.add
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-Case conversion may be inaccurate. Consider using '#align monotone.mul_strict_mono' Monotone.mul_strictMono'ₓ'. -/
/-- The product of a monotone function and a strictly monotone function is strictly monotone. -/
@[to_additive add_strict_mono
"The sum of a monotone function and a strictly monotone function is strictly monotone."]
@@ -2246,12 +1418,6 @@ theorem Monotone.mul_strictMono' [CovariantClass α α (· * ·) (· < ·)]
#align monotone.mul_strict_mono' Monotone.mul_strictMono'
#align monotone.add_strict_mono Monotone.add_strictMono
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/-- The product of a monotone function and a strictly monotone function is strictly monotone. -/
@[to_additive add_strict_mono
"The sum of a monotone function and a strictly monotone function is strictly monotone."]
@@ -2262,12 +1428,6 @@ theorem MonotoneOn.mul_strictMono' [CovariantClass α α (· * ·) (· < ·)]
#align monotone_on.mul_strict_mono' MonotoneOn.mul_strictMono'
#align monotone_on.add_strict_mono MonotoneOn.add_strictMono
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/-- The product of a antitone function and a strictly antitone function is strictly antitone. -/
@[to_additive add_strict_anti
"The sum of a antitone function and a strictly antitone function is strictly antitone."]
@@ -2278,12 +1438,6 @@ theorem Antitone.mul_strictAnti' [CovariantClass α α (· * ·) (· < ·)]
#align antitone.mul_strict_anti' Antitone.mul_strictAnti'
#align antitone.add_strict_anti Antitone.add_strictAnti
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-Case conversion may be inaccurate. Consider using '#align antitone_on.mul_strict_anti' AntitoneOn.mul_strictAnti'ₓ'. -/
/-- The product of a antitone function and a strictly antitone function is strictly antitone. -/
@[to_additive add_strict_anti
"The sum of a antitone function and a strictly antitone function is strictly antitone."]
@@ -2296,12 +1450,6 @@ theorem AntitoneOn.mul_strictAnti' [CovariantClass α α (· * ·) (· < ·)]
variable [CovariantClass α α (· * ·) (· ≤ ·)] [CovariantClass α α (swap (· * ·)) (· < ·)]
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- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {g : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))], (StrictMono.{u2, u1} β α _inst_3 _inst_2 f) -> (Monotone.{u2, u1} β α _inst_3 _inst_2 g) -> (StrictMono.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)))
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-Case conversion may be inaccurate. Consider using '#align strict_mono.mul_monotone' StrictMono.mul_monotone'ₓ'. -/
/-- The product of a strictly monotone function and a monotone function is strictly monotone. -/
@[to_additive add_monotone
"The sum of a strictly monotone function and a monotone function is strictly monotone."]
@@ -2310,12 +1458,6 @@ theorem StrictMono.mul_monotone' (hf : StrictMono f) (hg : Monotone g) :
#align strict_mono.mul_monotone' StrictMono.mul_monotone'
#align strict_mono.add_monotone StrictMono.add_monotone
-/- warning: strict_mono_on.mul_monotone' -> StrictMonoOn.mul_monotone' is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {g : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))], (StrictMonoOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (MonotoneOn.{u2, u1} β α _inst_3 _inst_2 g s) -> (StrictMonoOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)) s)
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-Case conversion may be inaccurate. Consider using '#align strict_mono_on.mul_monotone' StrictMonoOn.mul_monotone'ₓ'. -/
/-- The product of a strictly monotone function and a monotone function is strictly monotone. -/
@[to_additive add_monotone
"The sum of a strictly monotone function and a monotone function is strictly monotone."]
@@ -2325,12 +1467,6 @@ theorem StrictMonoOn.mul_monotone' (hf : StrictMonoOn f s) (hg : MonotoneOn g s)
#align strict_mono_on.mul_monotone' StrictMonoOn.mul_monotone'
#align strict_mono_on.add_monotone StrictMonoOn.add_monotone
-/- warning: strict_anti.mul_antitone' -> StrictAnti.mul_antitone' is a dubious translation:
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- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {g : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15077 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15079 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15077 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15079) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15092 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15094 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15092 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15094)] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15114 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15116 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15114 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15116)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15129 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15131 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15129 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15131)], (StrictAnti.{u2, u1} β α _inst_3 _inst_2 f) -> (Antitone.{u2, u1} β α _inst_3 _inst_2 g) -> (StrictAnti.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)))
-Case conversion may be inaccurate. Consider using '#align strict_anti.mul_antitone' StrictAnti.mul_antitone'ₓ'. -/
/-- The product of a strictly antitone function and a antitone function is strictly antitone. -/
@[to_additive add_antitone
"The sum of a strictly antitone function and a antitone function is strictly antitone."]
@@ -2339,12 +1475,6 @@ theorem StrictAnti.mul_antitone' (hf : StrictAnti f) (hg : Antitone g) :
#align strict_anti.mul_antitone' StrictAnti.mul_antitone'
#align strict_anti.add_antitone StrictAnti.add_antitone
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- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {g : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15205 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15207 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15205 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15207) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15220 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15222 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15220 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15222)] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15242 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15244 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15242 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15244)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15257 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15259 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15257 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15259)], (StrictAntiOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (AntitoneOn.{u2, u1} β α _inst_3 _inst_2 g s) -> (StrictAntiOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)) s)
-Case conversion may be inaccurate. Consider using '#align strict_anti_on.mul_antitone' StrictAntiOn.mul_antitone'ₓ'. -/
/-- The product of a strictly antitone function and a antitone function is strictly antitone. -/
@[to_additive add_antitone
"The sum of a strictly antitone function and a antitone function is strictly antitone."]
@@ -2354,12 +1484,6 @@ theorem StrictAntiOn.mul_antitone' (hf : StrictAntiOn f s) (hg : AntitoneOn g s)
#align strict_anti_on.mul_antitone' StrictAntiOn.mul_antitone'
#align strict_anti_on.add_antitone StrictAntiOn.add_antitone
-/- warning: cmp_mul_left' -> cmp_mul_left' is a dubious translation:
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-but is expected to have type
- forall {α : Type.{u1}} [_inst_6 : Mul.{u1} α] [_inst_7 : LinearOrder.{u1} α] [_inst_8 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15419 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15421 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_6) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15419 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15421) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15434 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15436 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_7)))))) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15434 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15436)] (a : α) (b : α) (c : α), Eq.{1} Ordering (cmp.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_7)))))) (fun (a : α) (b : α) => instDecidableLtToLTToPreorderToPartialOrder.{u1} α _inst_7 a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_6) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_6) a c)) (cmp.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_7)))))) (fun (a : α) (b : α) => instDecidableLtToLTToPreorderToPartialOrder.{u1} α _inst_7 a b) b c)
-Case conversion may be inaccurate. Consider using '#align cmp_mul_left' cmp_mul_left'ₓ'. -/
@[simp, to_additive cmp_add_left]
theorem cmp_mul_left' {α : Type _} [Mul α] [LinearOrder α] [CovariantClass α α (· * ·) (· < ·)]
(a b c : α) : cmp (a * b) (a * c) = cmp b c :=
@@ -2367,12 +1491,6 @@ theorem cmp_mul_left' {α : Type _} [Mul α] [LinearOrder α] [CovariantClass α
#align cmp_mul_left' cmp_mul_left'
#align cmp_add_left cmp_add_left
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-Case conversion may be inaccurate. Consider using '#align cmp_mul_right' cmp_mul_right'ₓ'. -/
@[simp, to_additive cmp_add_right]
theorem cmp_mul_right' {α : Type _} [Mul α] [LinearOrder α]
[CovariantClass α α (swap (· * ·)) (· < ·)] (a b c : α) : cmp (a * c) (b * c) = cmp a b :=
@@ -2404,12 +1522,6 @@ theorem Contravariant.MulLECancellable [Mul α] [LE α] [ContravariantClass α
#align contravariant.add_le_cancellable Contravariant.AddLECancellable
-/
-/- warning: mul_le_cancellable_one -> mulLECancellable_one is a dubious translation:
-lean 3 declaration is
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@[to_additive]
theorem mulLECancellable_one [Monoid α] [LE α] : MulLECancellable (1 : α) := fun a b => by
simpa only [one_mul] using id
@@ -2418,24 +1530,12 @@ theorem mulLECancellable_one [Monoid α] [LE α] : MulLECancellable (1 : α) :=
namespace MulLECancellable
-/- warning: mul_le_cancellable.injective -> MulLECancellable.Injective is a dubious translation:
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-but is expected to have type
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@[to_additive]
protected theorem Injective [Mul α] [PartialOrder α] {a : α} (ha : MulLECancellable a) :
Injective ((· * ·) a) := fun b c h => le_antisymm (ha h.le) (ha h.ge)
#align mul_le_cancellable.injective MulLECancellable.Injective
#align add_le_cancellable.injective AddLECancellable.Injective
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@[to_additive]
protected theorem inj [Mul α] [PartialOrder α] {a b c : α} (ha : MulLECancellable a) :
a * b = a * c ↔ b = c :=
@@ -2443,12 +1543,6 @@ protected theorem inj [Mul α] [PartialOrder α] {a b c : α} (ha : MulLECancell
#align mul_le_cancellable.inj MulLECancellable.inj
#align add_le_cancellable.inj AddLECancellable.inj
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-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : CommSemigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] {a : α}, (MulLECancellable.{u1} α (Semigroup.toMul.{u1} α (CommSemigroup.toSemigroup.{u1} α _inst_1)) (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a) -> (Function.Injective.{succ u1, succ u1} α α (fun (_x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α (CommSemigroup.toSemigroup.{u1} α _inst_1))) _x a))
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@[to_additive]
protected theorem injective_left [CommSemigroup α] [PartialOrder α] {a : α}
(ha : MulLECancellable a) : Injective (· * a) := fun b c h =>
@@ -2456,12 +1550,6 @@ protected theorem injective_left [CommSemigroup α] [PartialOrder α] {a : α}
#align mul_le_cancellable.injective_left MulLECancellable.injective_left
#align add_le_cancellable.injective_left AddLECancellable.injective_left
-/- warning: mul_le_cancellable.inj_left -> MulLECancellable.inj_left is a dubious translation:
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@[to_additive]
protected theorem inj_left [CommSemigroup α] [PartialOrder α] {a b c : α}
(hc : MulLECancellable c) : a * c = b * c ↔ a = b :=
@@ -2480,12 +1568,6 @@ protected theorem mul_le_mul_iff_left [Mul α] [CovariantClass α α (· * ·) (
#align add_le_cancellable.add_le_add_iff_left AddLECancellable.add_le_add_iff_left
-/
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-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align mul_le_cancellable.mul_le_mul_iff_right MulLECancellable.mul_le_mul_iff_rightₓ'. -/
@[to_additive]
protected theorem mul_le_mul_iff_right [CommSemigroup α] [CovariantClass α α (· * ·) (· ≤ ·)]
{a b c : α} (ha : MulLECancellable a) : b * a ≤ c * a ↔ b ≤ c := by
@@ -2493,12 +1575,6 @@ protected theorem mul_le_mul_iff_right [CommSemigroup α] [CovariantClass α α
#align mul_le_cancellable.mul_le_mul_iff_right MulLECancellable.mul_le_mul_iff_right
#align add_le_cancellable.add_le_add_iff_right AddLECancellable.add_le_add_iff_right
-/- warning: mul_le_cancellable.le_mul_iff_one_le_right -> MulLECancellable.le_mul_iff_one_le_right is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] [_inst_2 : MulOneClass.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_2))) (LE.le.{u1} α _inst_1)] {a : α} {b : α}, (MulLECancellable.{u1} α (MulOneClass.toHasMul.{u1} α _inst_2) _inst_1 a) -> (Iff (LE.le.{u1} α _inst_1 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_2)) a b)) (LE.le.{u1} α _inst_1 (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_2)))) b))
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-Case conversion may be inaccurate. Consider using '#align mul_le_cancellable.le_mul_iff_one_le_right MulLECancellable.le_mul_iff_one_le_rightₓ'. -/
@[to_additive]
protected theorem le_mul_iff_one_le_right [MulOneClass α] [CovariantClass α α (· * ·) (· ≤ ·)]
{a b : α} (ha : MulLECancellable a) : a ≤ a * b ↔ 1 ≤ b :=
@@ -2506,12 +1582,6 @@ protected theorem le_mul_iff_one_le_right [MulOneClass α] [CovariantClass α α
#align mul_le_cancellable.le_mul_iff_one_le_right MulLECancellable.le_mul_iff_one_le_right
#align add_le_cancellable.le_add_iff_nonneg_right AddLECancellable.le_add_iff_nonneg_right
-/- warning: mul_le_cancellable.mul_le_iff_le_one_right -> MulLECancellable.mul_le_iff_le_one_right is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] [_inst_2 : MulOneClass.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16260 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16262 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16260 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16262) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16275 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16277 : α) => LE.le.{u1} α _inst_1 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16275 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16277)] {a : α} {b : α}, (MulLECancellable.{u1} α (MulOneClass.toMul.{u1} α _inst_2) _inst_1 a) -> (Iff (LE.le.{u1} α _inst_1 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_2)) a b) a) (LE.le.{u1} α _inst_1 b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_2)))))
-Case conversion may be inaccurate. Consider using '#align mul_le_cancellable.mul_le_iff_le_one_right MulLECancellable.mul_le_iff_le_one_rightₓ'. -/
@[to_additive]
protected theorem mul_le_iff_le_one_right [MulOneClass α] [CovariantClass α α (· * ·) (· ≤ ·)]
{a b : α} (ha : MulLECancellable a) : a * b ≤ a ↔ b ≤ 1 :=
@@ -2519,12 +1589,6 @@ protected theorem mul_le_iff_le_one_right [MulOneClass α] [CovariantClass α α
#align mul_le_cancellable.mul_le_iff_le_one_right MulLECancellable.mul_le_iff_le_one_right
#align add_le_cancellable.add_le_iff_nonpos_right AddLECancellable.add_le_iff_nonpos_right
-/- warning: mul_le_cancellable.le_mul_iff_one_le_left -> MulLECancellable.le_mul_iff_one_le_left is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] [_inst_2 : CommMonoid.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2))))) (LE.le.{u1} α _inst_1)] {a : α} {b : α}, (MulLECancellable.{u1} α (MulOneClass.toHasMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2))) _inst_1 a) -> (Iff (LE.le.{u1} α _inst_1 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2)))) b a)) (LE.le.{u1} α _inst_1 (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2)))))) b))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] [_inst_2 : CommMonoid.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16356 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16358 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2)))) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16356 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16358) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16371 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16373 : α) => LE.le.{u1} α _inst_1 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16371 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16373)] {a : α} {b : α}, (MulLECancellable.{u1} α (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2))) _inst_1 a) -> (Iff (LE.le.{u1} α _inst_1 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2)))) b a)) (LE.le.{u1} α _inst_1 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2)))) b))
-Case conversion may be inaccurate. Consider using '#align mul_le_cancellable.le_mul_iff_one_le_left MulLECancellable.le_mul_iff_one_le_leftₓ'. -/
@[to_additive]
protected theorem le_mul_iff_one_le_left [CommMonoid α] [CovariantClass α α (· * ·) (· ≤ ·)]
{a b : α} (ha : MulLECancellable a) : a ≤ b * a ↔ 1 ≤ b := by
@@ -2532,12 +1596,6 @@ protected theorem le_mul_iff_one_le_left [CommMonoid α] [CovariantClass α α (
#align mul_le_cancellable.le_mul_iff_one_le_left MulLECancellable.le_mul_iff_one_le_left
#align add_le_cancellable.le_add_iff_nonneg_left AddLECancellable.le_add_iff_nonneg_left
-/- warning: mul_le_cancellable.mul_le_iff_le_one_left -> MulLECancellable.mul_le_iff_le_one_left is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] [_inst_2 : CommMonoid.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2))))) (LE.le.{u1} α _inst_1)] {a : α} {b : α}, (MulLECancellable.{u1} α (MulOneClass.toHasMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2))) _inst_1 a) -> (Iff (LE.le.{u1} α _inst_1 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2)))) b a) a) (LE.le.{u1} α _inst_1 b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2))))))))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] [_inst_2 : CommMonoid.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16449 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16451 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2)))) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16449 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16451) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16464 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16466 : α) => LE.le.{u1} α _inst_1 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16464 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16466)] {a : α} {b : α}, (MulLECancellable.{u1} α (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2))) _inst_1 a) -> (Iff (LE.le.{u1} α _inst_1 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2)))) b a) a) (LE.le.{u1} α _inst_1 b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2))))))
-Case conversion may be inaccurate. Consider using '#align mul_le_cancellable.mul_le_iff_le_one_left MulLECancellable.mul_le_iff_le_one_leftₓ'. -/
@[to_additive]
protected theorem mul_le_iff_le_one_left [CommMonoid α] [CovariantClass α α (· * ·) (· ≤ ·)]
{a b : α} (ha : MulLECancellable a) : b * a ≤ a ↔ b ≤ 1 := by
@@ -2551,22 +1609,10 @@ section Bit
variable [Add α] [Preorder α]
-/- warning: bit0_mono -> bit0_mono is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Add.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))], Monotone.{u1, u1} α α _inst_2 _inst_2 (bit0.{u1} α _inst_1)
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Add.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16556 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16558 : α) => HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16556 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16558) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16571 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16573 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16571 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16573)] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16593 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16595 : α) => HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16593 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16595)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16608 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16610 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16608 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16610)], Monotone.{u1, u1} α α _inst_2 _inst_2 (bit0.{u1} α _inst_1)
-Case conversion may be inaccurate. Consider using '#align bit0_mono bit0_monoₓ'. -/
theorem bit0_mono [CovariantClass α α (· + ·) (· ≤ ·)] [CovariantClass α α (swap (· + ·)) (· ≤ ·)] :
Monotone (bit0 : α → α) := fun a b h => add_le_add h h
#align bit0_mono bit0_mono
-/- warning: bit0_strict_mono -> bit0_strictMono is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Add.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))], StrictMono.{u1, u1} α α _inst_2 _inst_2 (bit0.{u1} α _inst_1)
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Add.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16654 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16656 : α) => HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16654 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16656) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16669 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16671 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16669 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16671)] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16691 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16693 : α) => HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16691 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16693)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16706 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16708 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16706 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16708)], StrictMono.{u1, u1} α α _inst_2 _inst_2 (bit0.{u1} α _inst_1)
-Case conversion may be inaccurate. Consider using '#align bit0_strict_mono bit0_strictMonoₓ'. -/
theorem bit0_strictMono [CovariantClass α α (· + ·) (· < ·)]
[CovariantClass α α (swap (· + ·)) (· < ·)] : StrictMono (bit0 : α → α) := fun a b h =>
add_lt_add h h
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -433,11 +433,8 @@ but is expected to have type
forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : LinearOrder.{u1} α] {a : α} {b : α} {c : α} {d : α} [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2882 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2884 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2882 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2884) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2897 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2899 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2897 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2899)] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2919 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2921 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2919 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2921)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2934 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2936 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2934 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2936)], (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) c d)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (Min.min.{u1} α (LinearOrder.toMin.{u1} α _inst_2) a b) (Max.max.{u1} α (LinearOrder.toMax.{u1} α _inst_2) c d))
Case conversion may be inaccurate. Consider using '#align min_le_max_of_mul_le_mul min_le_max_of_mul_le_mulₓ'. -/
@[to_additive]
-theorem min_le_max_of_mul_le_mul (h : a * b ≤ c * d) : min a b ≤ max c d :=
- by
- simp_rw [min_le_iff, le_max_iff]
- contrapose! h
- exact mul_lt_mul_of_lt_of_lt h.1.1 h.2.2
+theorem min_le_max_of_mul_le_mul (h : a * b ≤ c * d) : min a b ≤ max c d := by
+ simp_rw [min_le_iff, le_max_iff]; contrapose! h; exact mul_lt_mul_of_lt_of_lt h.1.1 h.2.2
#align min_le_max_of_mul_le_mul min_le_max_of_mul_le_mul
#align min_le_max_of_add_le_add min_le_max_of_add_le_add
@@ -1714,10 +1711,7 @@ theorem mul_le_mul_iff_of_ge [CovariantClass α α (· * ·) (· ≤ ·)]
[CovariantClass α α (swap (· * ·)) (· < ·)] {a₁ a₂ b₁ b₂ : α} (ha : a₁ ≤ a₂) (hb : b₁ ≤ b₂) :
a₂ * b₂ ≤ a₁ * b₁ ↔ a₁ = a₂ ∧ b₁ = b₂ :=
by
- refine'
- ⟨fun h => _, by
- rintro ⟨rfl, rfl⟩
- rfl⟩
+ refine' ⟨fun h => _, by rintro ⟨rfl, rfl⟩; rfl⟩
simp only [eq_iff_le_not_lt, ha, hb, true_and_iff]
refine' ⟨fun ha => h.not_lt _, fun hb => h.not_lt _⟩
· exact mul_lt_mul_of_lt_of_le ha hb
mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
@@ -172,7 +172,12 @@ section Preorder
variable [Preorder α]
-#print mul_lt_mul_of_lt_of_lt /-
+/- warning: mul_lt_mul_of_lt_of_lt -> mul_lt_mul_of_lt_of_lt is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] {a : α} {b : α} {c : α} {d : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a b) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) c d) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b d))
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1146 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1148 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1146 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1148) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1161 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1163 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1161 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1163)] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1183 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1185 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1183 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1185)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1198 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1200 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1198 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1200)] {a : α} {b : α} {c : α} {d : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) c d) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b d))
+Case conversion may be inaccurate. Consider using '#align mul_lt_mul_of_lt_of_lt mul_lt_mul_of_lt_of_ltₓ'. -/
@[to_additive]
theorem mul_lt_mul_of_lt_of_lt [CovariantClass α α (· * ·) (· < ·)]
[CovariantClass α α (swap (· * ·)) (· < ·)] {a b c d : α} (h₁ : a < b) (h₂ : c < d) :
@@ -183,12 +188,22 @@ theorem mul_lt_mul_of_lt_of_lt [CovariantClass α α (· * ·) (· < ·)]
#align mul_lt_mul_of_lt_of_lt mul_lt_mul_of_lt_of_lt
#align add_lt_add_of_lt_of_lt add_lt_add_of_lt_of_lt
--/
+/- warning: add_lt_add -> add_lt_add is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : Add.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] {a : α} {b : α} {c : α} {d : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a b) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) c d) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α _inst_1) a c) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α _inst_1) b d))
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : Add.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1146 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1148 : α) => HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1146 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1148) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1161 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1163 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1161 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1163)] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1183 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1185 : α) => HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1183 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1185)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1198 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1200 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1198 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1200)] {a : α} {b : α} {c : α} {d : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) c d) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α _inst_1) a c) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α _inst_1) b d))
+Case conversion may be inaccurate. Consider using '#align add_lt_add add_lt_addₓ'. -/
alias add_lt_add_of_lt_of_lt ← add_lt_add
#align add_lt_add add_lt_add
-#print mul_lt_mul_of_le_of_lt /-
+/- warning: mul_lt_mul_of_le_of_lt -> mul_lt_mul_of_le_of_lt is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a b) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) c d) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b d))
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1286 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1288 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1286 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1288) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1301 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1303 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1301 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1303)] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1323 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1325 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1323 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1325)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1338 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1340 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1338 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1340)] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) c d) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b d))
+Case conversion may be inaccurate. Consider using '#align mul_lt_mul_of_le_of_lt mul_lt_mul_of_le_of_ltₓ'. -/
@[to_additive]
theorem mul_lt_mul_of_le_of_lt [CovariantClass α α (· * ·) (· < ·)]
[CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c d : α} (h₁ : a ≤ b) (h₂ : c < d) :
@@ -196,9 +211,13 @@ theorem mul_lt_mul_of_le_of_lt [CovariantClass α α (· * ·) (· < ·)]
(mul_le_mul_right' h₁ _).trans_lt (mul_lt_mul_left' h₂ b)
#align mul_lt_mul_of_le_of_lt mul_lt_mul_of_le_of_lt
#align add_lt_add_of_le_of_lt add_lt_add_of_le_of_lt
--/
-#print mul_lt_mul_of_lt_of_le /-
+/- warning: mul_lt_mul_of_lt_of_le -> mul_lt_mul_of_lt_of_le is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] {a : α} {b : α} {c : α} {d : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a b) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) c d) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b d))
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1402 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1404 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1402 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1404) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1417 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1419 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1417 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1419)] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1439 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1441 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1439 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1441)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1454 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1456 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1454 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1456)] {a : α} {b : α} {c : α} {d : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) c d) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b d))
+Case conversion may be inaccurate. Consider using '#align mul_lt_mul_of_lt_of_le mul_lt_mul_of_lt_of_leₓ'. -/
@[to_additive]
theorem mul_lt_mul_of_lt_of_le [CovariantClass α α (· * ·) (· ≤ ·)]
[CovariantClass α α (swap (· * ·)) (· < ·)] {a b c d : α} (h₁ : a < b) (h₂ : c ≤ d) :
@@ -206,9 +225,13 @@ theorem mul_lt_mul_of_lt_of_le [CovariantClass α α (· * ·) (· ≤ ·)]
(mul_le_mul_left' h₂ _).trans_lt (mul_lt_mul_right' h₁ d)
#align mul_lt_mul_of_lt_of_le mul_lt_mul_of_lt_of_le
#align add_lt_add_of_lt_of_le add_lt_add_of_lt_of_le
--/
-#print Left.mul_lt_mul /-
+/- warning: left.mul_lt_mul -> Left.mul_lt_mul is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α} {d : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a b) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) c d) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b d))
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1521 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1523 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1521 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1523) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1536 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1538 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1536 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1538)] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1558 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1560 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1558 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1560)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1573 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1575 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1573 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1575)] {a : α} {b : α} {c : α} {d : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) c d) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b d))
+Case conversion may be inaccurate. Consider using '#align left.mul_lt_mul Left.mul_lt_mulₓ'. -/
/-- Only assumes left strict covariance. -/
@[to_additive "Only assumes left strict covariance"]
theorem Left.mul_lt_mul [CovariantClass α α (· * ·) (· < ·)]
@@ -217,9 +240,13 @@ theorem Left.mul_lt_mul [CovariantClass α α (· * ·) (· < ·)]
mul_lt_mul_of_le_of_lt h₁.le h₂
#align left.mul_lt_mul Left.mul_lt_mul
#align left.add_lt_add Left.add_lt_add
--/
-#print Right.mul_lt_mul /-
+/- warning: right.mul_lt_mul -> Right.mul_lt_mul is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] {a : α} {b : α} {c : α} {d : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a b) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) c d) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b d))
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1633 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1635 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1633 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1635) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1648 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1650 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1648 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1650)] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1670 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1672 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1670 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1672)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1685 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1687 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1685 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1687)] {a : α} {b : α} {c : α} {d : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) c d) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b d))
+Case conversion may be inaccurate. Consider using '#align right.mul_lt_mul Right.mul_lt_mulₓ'. -/
/-- Only assumes right strict covariance. -/
@[to_additive "Only assumes right strict covariance"]
theorem Right.mul_lt_mul [CovariantClass α α (· * ·) (· ≤ ·)]
@@ -228,18 +255,26 @@ theorem Right.mul_lt_mul [CovariantClass α α (· * ·) (· ≤ ·)]
mul_lt_mul_of_lt_of_le h₁ h₂.le
#align right.mul_lt_mul Right.mul_lt_mul
#align right.add_lt_add Right.add_lt_add
--/
-#print mul_le_mul' /-
+/- warning: mul_le_mul' -> mul_le_mul' is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a b) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) c d) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b d))
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1742 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1744 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1742 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1744) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1757 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1759 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1757 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1759)] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1779 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1781 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1779 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1781)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1794 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1796 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1794 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1796)] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) c d) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b d))
+Case conversion may be inaccurate. Consider using '#align mul_le_mul' mul_le_mul'ₓ'. -/
@[to_additive add_le_add]
theorem mul_le_mul' [CovariantClass α α (· * ·) (· ≤ ·)] [CovariantClass α α (swap (· * ·)) (· ≤ ·)]
{a b c d : α} (h₁ : a ≤ b) (h₂ : c ≤ d) : a * c ≤ b * d :=
(mul_le_mul_left' h₂ _).trans (mul_le_mul_right' h₁ d)
#align mul_le_mul' mul_le_mul'
#align add_le_add add_le_add
--/
-#print mul_le_mul_three /-
+/- warning: mul_le_mul_three -> mul_le_mul_three is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α} {d : α} {e : α} {f : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a d) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) b e) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) c f) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a b) c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) d e) f))
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1858 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1860 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1858 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1860) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1873 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1875 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1873 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1875)] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1895 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1897 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1895 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1897)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1910 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1912 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1910 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1912)] {a : α} {b : α} {c : α} {d : α} {e : α} {f : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a d) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b e) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) c f) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a b) c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) d e) f))
+Case conversion may be inaccurate. Consider using '#align mul_le_mul_three mul_le_mul_threeₓ'. -/
@[to_additive]
theorem mul_le_mul_three [CovariantClass α α (· * ·) (· ≤ ·)]
[CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c d e f : α} (h₁ : a ≤ d) (h₂ : b ≤ e)
@@ -247,79 +282,110 @@ theorem mul_le_mul_three [CovariantClass α α (· * ·) (· ≤ ·)]
mul_le_mul' (mul_le_mul' h₁ h₂) h₃
#align mul_le_mul_three mul_le_mul_three
#align add_le_add_three add_le_add_three
--/
-#print mul_lt_of_mul_lt_left /-
+/- warning: mul_lt_of_mul_lt_left -> mul_lt_of_mul_lt_left is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α} {d : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a b) c) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) d b) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a d) c)
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1981 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1983 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1981 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1983) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1996 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1998 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1996 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.1998)] {a : α} {b : α} {c : α} {d : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a b) c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) d b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a d) c)
+Case conversion may be inaccurate. Consider using '#align mul_lt_of_mul_lt_left mul_lt_of_mul_lt_leftₓ'. -/
@[to_additive]
theorem mul_lt_of_mul_lt_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b c d : α} (h : a * b < c)
(hle : d ≤ b) : a * d < c :=
(mul_le_mul_left' hle a).trans_lt h
#align mul_lt_of_mul_lt_left mul_lt_of_mul_lt_left
#align add_lt_of_add_lt_left add_lt_of_add_lt_left
--/
-#print mul_le_of_mul_le_left /-
+/- warning: mul_le_of_mul_le_left -> mul_le_of_mul_le_left is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a b) c) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) d b) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a d) c)
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2056 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2058 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2056 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2058) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2071 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2073 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2071 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2073)] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a b) c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) d b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a d) c)
+Case conversion may be inaccurate. Consider using '#align mul_le_of_mul_le_left mul_le_of_mul_le_leftₓ'. -/
@[to_additive]
theorem mul_le_of_mul_le_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b c d : α} (h : a * b ≤ c)
(hle : d ≤ b) : a * d ≤ c :=
@act_rel_of_rel_of_act_rel _ _ _ (· ≤ ·) _ ⟨fun _ _ _ => le_trans⟩ a _ _ _ hle h
#align mul_le_of_mul_le_left mul_le_of_mul_le_left
#align add_le_of_add_le_left add_le_of_add_le_left
--/
-#print mul_lt_of_mul_lt_right /-
+/- warning: mul_lt_of_mul_lt_right -> mul_lt_of_mul_lt_right is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α} {d : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a b) c) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) d a) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) d b) c)
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2152 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2154 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2152 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2154)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2167 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2169 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2167 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2169)] {a : α} {b : α} {c : α} {d : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a b) c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) d a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) d b) c)
+Case conversion may be inaccurate. Consider using '#align mul_lt_of_mul_lt_right mul_lt_of_mul_lt_rightₓ'. -/
@[to_additive]
theorem mul_lt_of_mul_lt_right [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c d : α}
(h : a * b < c) (hle : d ≤ a) : d * b < c :=
(mul_le_mul_right' hle b).trans_lt h
#align mul_lt_of_mul_lt_right mul_lt_of_mul_lt_right
#align add_lt_of_add_lt_right add_lt_of_add_lt_right
--/
-#print mul_le_of_mul_le_right /-
+/- warning: mul_le_of_mul_le_right -> mul_le_of_mul_le_right is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a b) c) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) d a) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) d b) c)
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2230 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2232 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2230 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2232)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2245 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2247 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2245 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2247)] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a b) c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) d a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) d b) c)
+Case conversion may be inaccurate. Consider using '#align mul_le_of_mul_le_right mul_le_of_mul_le_rightₓ'. -/
@[to_additive]
theorem mul_le_of_mul_le_right [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c d : α}
(h : a * b ≤ c) (hle : d ≤ a) : d * b ≤ c :=
(mul_le_mul_right' hle b).trans h
#align mul_le_of_mul_le_right mul_le_of_mul_le_right
#align add_le_of_add_le_right add_le_of_add_le_right
--/
-#print lt_mul_of_lt_mul_left /-
+/- warning: lt_mul_of_lt_mul_left -> lt_mul_of_lt_mul_left is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α} {d : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b c)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) c d) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b d))
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2305 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2307 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2305 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2307) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2320 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2322 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2320 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2322)] {a : α} {b : α} {c : α} {d : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b c)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) c d) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b d))
+Case conversion may be inaccurate. Consider using '#align lt_mul_of_lt_mul_left lt_mul_of_lt_mul_leftₓ'. -/
@[to_additive]
theorem lt_mul_of_lt_mul_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b c d : α} (h : a < b * c)
(hle : c ≤ d) : a < b * d :=
h.trans_le (mul_le_mul_left' hle b)
#align lt_mul_of_lt_mul_left lt_mul_of_lt_mul_left
#align lt_add_of_lt_add_left lt_add_of_lt_add_left
--/
-#print le_mul_of_le_mul_left /-
+/- warning: le_mul_of_le_mul_left -> le_mul_of_le_mul_left is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b c)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) c d) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b d))
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2379 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2381 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2379 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2381) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2394 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2396 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2394 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2396)] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b c)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) c d) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b d))
+Case conversion may be inaccurate. Consider using '#align le_mul_of_le_mul_left le_mul_of_le_mul_leftₓ'. -/
@[to_additive]
theorem le_mul_of_le_mul_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b c d : α} (h : a ≤ b * c)
(hle : c ≤ d) : a ≤ b * d :=
@rel_act_of_rel_of_rel_act _ _ _ (· ≤ ·) _ ⟨fun _ _ _ => le_trans⟩ b _ _ _ hle h
#align le_mul_of_le_mul_left le_mul_of_le_mul_left
#align le_add_of_le_add_left le_add_of_le_add_left
--/
-#print lt_mul_of_lt_mul_right /-
+/- warning: lt_mul_of_lt_mul_right -> lt_mul_of_lt_mul_right is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α} {d : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b c)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) b d) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) d c))
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2475 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2477 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2475 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2477)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2490 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2492 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2490 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2492)] {a : α} {b : α} {c : α} {d : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b c)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b d) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) d c))
+Case conversion may be inaccurate. Consider using '#align lt_mul_of_lt_mul_right lt_mul_of_lt_mul_rightₓ'. -/
@[to_additive]
theorem lt_mul_of_lt_mul_right [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c d : α}
(h : a < b * c) (hle : b ≤ d) : a < d * c :=
h.trans_le (mul_le_mul_right' hle c)
#align lt_mul_of_lt_mul_right lt_mul_of_lt_mul_right
#align lt_add_of_lt_add_right lt_add_of_lt_add_right
--/
-#print le_mul_of_le_mul_right /-
+/- warning: le_mul_of_le_mul_right -> le_mul_of_le_mul_right is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b c)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) b d) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) d c))
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2552 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2554 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2552 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2554)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2567 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2569 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2567 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2569)] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) b c)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b d) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) d c))
+Case conversion may be inaccurate. Consider using '#align le_mul_of_le_mul_right le_mul_of_le_mul_rightₓ'. -/
@[to_additive]
theorem le_mul_of_le_mul_right [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c d : α}
(h : a ≤ b * c) (hle : b ≤ d) : a ≤ d * c :=
h.trans (mul_le_mul_right' hle c)
#align le_mul_of_le_mul_right le_mul_of_le_mul_right
#align le_add_of_le_add_right le_add_of_le_add_right
--/
end Preorder
@@ -327,23 +393,31 @@ section PartialOrder
variable [PartialOrder α]
-#print mul_left_cancel'' /-
+/- warning: mul_left_cancel'' -> mul_left_cancel'' is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a : α} {b : α} {c : α}, (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a c)) -> (Eq.{succ u1} α b c)
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2638 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2640 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2638 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2640) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2653 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2655 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2653 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2655)] {a : α} {b : α} {c : α}, (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a c)) -> (Eq.{succ u1} α b c)
+Case conversion may be inaccurate. Consider using '#align mul_left_cancel'' mul_left_cancel''ₓ'. -/
@[to_additive]
theorem mul_left_cancel'' [ContravariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (h : a * b = a * c) :
b = c :=
(le_of_mul_le_mul_left' h.le).antisymm (le_of_mul_le_mul_left' h.ge)
#align mul_left_cancel'' mul_left_cancel''
#align add_left_cancel'' add_left_cancel''
--/
-#print mul_right_cancel'' /-
+/- warning: mul_right_cancel'' -> mul_right_cancel'' is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a : α} {b : α} {c : α}, (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) c b)) -> (Eq.{succ u1} α a c)
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2712 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2714 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2712 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2714)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2727 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2729 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2727 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2729)] {a : α} {b : α} {c : α}, (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) c b)) -> (Eq.{succ u1} α a c)
+Case conversion may be inaccurate. Consider using '#align mul_right_cancel'' mul_right_cancel''ₓ'. -/
@[to_additive]
theorem mul_right_cancel'' [ContravariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α}
(h : a * b = c * b) : a = c :=
le_antisymm (le_of_mul_le_mul_right' h.le) (le_of_mul_le_mul_right' h.ge)
#align mul_right_cancel'' mul_right_cancel''
#align add_right_cancel'' add_right_cancel''
--/
end PartialOrder
@@ -354,7 +428,7 @@ variable [LinearOrder α] {a b c d : α} [CovariantClass α α (· * ·) (· <
/- warning: min_le_max_of_mul_le_mul -> min_le_max_of_mul_le_mul is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : LinearOrder.{u1} α] {a : α} {b : α} {c : α} {d : α} [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))))], (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) c d)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (LinearOrder.min.{u1} α _inst_2 a b) (LinearOrder.max.{u1} α _inst_2 c d))
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : LinearOrder.{u1} α] {a : α} {b : α} {c : α} {d : α} [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))))], (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) c d)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (LinearOrder.min.{u1} α _inst_2 a b) (LinearOrder.max.{u1} α _inst_2 c d))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : LinearOrder.{u1} α] {a : α} {b : α} {c : α} {d : α} [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2882 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2884 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2882 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2884) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2897 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2899 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2897 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2899)] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2919 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2921 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2919 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2921)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2934 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2936 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2934 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.2936)], (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) c d)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (Min.min.{u1} α (LinearOrder.toMin.{u1} α _inst_2) a b) (Max.max.{u1} α (LinearOrder.toMax.{u1} α _inst_2) c d))
Case conversion may be inaccurate. Consider using '#align min_le_max_of_mul_le_mul min_le_max_of_mul_le_mulₓ'. -/
@@ -734,7 +808,7 @@ which assume left covariance. -/
/- warning: mul_le_of_le_of_le_one -> mul_le_of_le_of_le_one is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b a) c)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b a) c)
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5405 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5407 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5405 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5407) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5420 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5422 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5420 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5422)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b a) c)
Case conversion may be inaccurate. Consider using '#align mul_le_of_le_of_le_one mul_le_of_le_of_le_oneₓ'. -/
@@ -751,7 +825,7 @@ theorem mul_le_of_le_of_le_one [CovariantClass α α (· * ·) (· ≤ ·)] {a b
/- warning: mul_lt_of_le_of_lt_one -> mul_lt_of_le_of_lt_one is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b a) c)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b a) c)
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5515 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5517 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5515 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5517) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5530 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5532 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5530 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5532)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b a) c)
Case conversion may be inaccurate. Consider using '#align mul_lt_of_le_of_lt_one mul_lt_of_le_of_lt_oneₓ'. -/
@@ -768,7 +842,7 @@ theorem mul_lt_of_le_of_lt_one [CovariantClass α α (· * ·) (· < ·)] {a b c
/- warning: mul_lt_of_lt_of_le_one -> mul_lt_of_lt_of_le_one is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b a) c)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b a) c)
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5625 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5627 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5625 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5627) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5640 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5642 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5640 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5642)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b a) c)
Case conversion may be inaccurate. Consider using '#align mul_lt_of_lt_of_le_one mul_lt_of_lt_of_le_oneₓ'. -/
@@ -785,7 +859,7 @@ theorem mul_lt_of_lt_of_le_one [CovariantClass α α (· * ·) (· ≤ ·)] {a b
/- warning: mul_lt_of_lt_of_lt_one -> mul_lt_of_lt_of_lt_one is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b a) c)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b a) c)
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5735 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5737 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5735 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5737) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5750 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5752 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5750 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5752)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b a) c)
Case conversion may be inaccurate. Consider using '#align mul_lt_of_lt_of_lt_one mul_lt_of_lt_of_lt_oneₓ'. -/
@@ -802,7 +876,7 @@ theorem mul_lt_of_lt_of_lt_one [CovariantClass α α (· * ·) (· < ·)] {a b c
/- warning: mul_lt_of_lt_of_lt_one' -> mul_lt_of_lt_of_lt_one' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b a) c)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b a) c)
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5845 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5847 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5845 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5847) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5860 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5862 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5860 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5862)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b a) c)
Case conversion may be inaccurate. Consider using '#align mul_lt_of_lt_of_lt_one' mul_lt_of_lt_of_lt_one'ₓ'. -/
@@ -815,7 +889,7 @@ theorem mul_lt_of_lt_of_lt_one' [CovariantClass α α (· * ·) (· ≤ ·)] {a
/- warning: left.mul_le_one -> Left.mul_le_one is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5916 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5918 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5916 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5918) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5931 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5933 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5931 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5933)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align left.mul_le_one Left.mul_le_oneₓ'. -/
@@ -831,7 +905,7 @@ theorem Left.mul_le_one [CovariantClass α α (· * ·) (· ≤ ·)] {a b : α}
/- warning: left.mul_lt_one_of_le_of_lt -> Left.mul_lt_one_of_le_of_lt is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5987 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5989 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5987 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5989) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6002 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6004 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6002 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6004)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align left.mul_lt_one_of_le_of_lt Left.mul_lt_one_of_le_of_ltₓ'. -/
@@ -847,7 +921,7 @@ theorem Left.mul_lt_one_of_le_of_lt [CovariantClass α α (· * ·) (· < ·)] {
/- warning: left.mul_lt_one_of_lt_of_le -> Left.mul_lt_one_of_lt_of_le is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6058 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6060 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6058 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6060) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6073 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6075 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6073 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6075)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align left.mul_lt_one_of_lt_of_le Left.mul_lt_one_of_lt_of_leₓ'. -/
@@ -863,7 +937,7 @@ theorem Left.mul_lt_one_of_lt_of_le [CovariantClass α α (· * ·) (· ≤ ·)]
/- warning: left.mul_lt_one -> Left.mul_lt_one is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6129 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6131 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6129 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6131) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6144 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6146 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6144 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6146)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align left.mul_lt_one Left.mul_lt_oneₓ'. -/
@@ -878,7 +952,7 @@ theorem Left.mul_lt_one [CovariantClass α α (· * ·) (· < ·)] {a b : α} (h
/- warning: left.mul_lt_one' -> Left.mul_lt_one' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6200 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6202 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6200 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6202) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6215 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6217 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6215 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6217)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align left.mul_lt_one' Left.mul_lt_one'ₓ'. -/
@@ -897,7 +971,7 @@ which assume left covariance. -/
/- warning: le_mul_of_le_of_one_le -> le_mul_of_le_of_one_le is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) c a))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) c a))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6269 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6271 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6269 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6271) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6284 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6286 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6284 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6286)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) c a))
Case conversion may be inaccurate. Consider using '#align le_mul_of_le_of_one_le le_mul_of_le_of_one_leₓ'. -/
@@ -914,7 +988,7 @@ theorem le_mul_of_le_of_one_le [CovariantClass α α (· * ·) (· ≤ ·)] {a b
/- warning: lt_mul_of_le_of_one_lt -> lt_mul_of_le_of_one_lt is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) c a))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) c a))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6382 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6384 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6382 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6384) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6397 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6399 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6397 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6399)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) c a))
Case conversion may be inaccurate. Consider using '#align lt_mul_of_le_of_one_lt lt_mul_of_le_of_one_ltₓ'. -/
@@ -931,7 +1005,7 @@ theorem lt_mul_of_le_of_one_lt [CovariantClass α α (· * ·) (· < ·)] {a b c
/- warning: lt_mul_of_lt_of_one_le -> lt_mul_of_lt_of_one_le is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) c a))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) c a))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6495 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6497 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6495 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6497) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6510 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6512 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6510 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6512)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) c a))
Case conversion may be inaccurate. Consider using '#align lt_mul_of_lt_of_one_le lt_mul_of_lt_of_one_leₓ'. -/
@@ -948,7 +1022,7 @@ theorem lt_mul_of_lt_of_one_le [CovariantClass α α (· * ·) (· ≤ ·)] {a b
/- warning: lt_mul_of_lt_of_one_lt -> lt_mul_of_lt_of_one_lt is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) c a))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) c a))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6608 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6610 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6608 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6610) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6623 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6625 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6623 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6625)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) c a))
Case conversion may be inaccurate. Consider using '#align lt_mul_of_lt_of_one_lt lt_mul_of_lt_of_one_ltₓ'. -/
@@ -965,7 +1039,7 @@ theorem lt_mul_of_lt_of_one_lt [CovariantClass α α (· * ·) (· < ·)] {a b c
/- warning: lt_mul_of_lt_of_one_lt' -> lt_mul_of_lt_of_one_lt' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) c a))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) c a))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6721 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6723 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6721 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6723) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6736 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6738 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6736 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6738)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) c a))
Case conversion may be inaccurate. Consider using '#align lt_mul_of_lt_of_one_lt' lt_mul_of_lt_of_one_lt'ₓ'. -/
@@ -978,7 +1052,7 @@ theorem lt_mul_of_lt_of_one_lt' [CovariantClass α α (· * ·) (· ≤ ·)] {a
/- warning: left.one_le_mul -> Left.one_le_mul is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6792 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6794 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6792 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6794) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6807 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6809 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6807 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6809)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
Case conversion may be inaccurate. Consider using '#align left.one_le_mul Left.one_le_mulₓ'. -/
@@ -994,7 +1068,7 @@ theorem Left.one_le_mul [CovariantClass α α (· * ·) (· ≤ ·)] {a b : α}
/- warning: left.one_lt_mul_of_le_of_lt -> Left.one_lt_mul_of_le_of_lt is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6863 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6865 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6863 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6865) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6878 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6880 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6878 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6880)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
Case conversion may be inaccurate. Consider using '#align left.one_lt_mul_of_le_of_lt Left.one_lt_mul_of_le_of_ltₓ'. -/
@@ -1010,7 +1084,7 @@ theorem Left.one_lt_mul_of_le_of_lt [CovariantClass α α (· * ·) (· < ·)] {
/- warning: left.one_lt_mul_of_lt_of_le -> Left.one_lt_mul_of_lt_of_le is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6934 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6936 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6934 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6936) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6949 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6951 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6949 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6951)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
Case conversion may be inaccurate. Consider using '#align left.one_lt_mul_of_lt_of_le Left.one_lt_mul_of_lt_of_leₓ'. -/
@@ -1026,7 +1100,7 @@ theorem Left.one_lt_mul_of_lt_of_le [CovariantClass α α (· * ·) (· ≤ ·)]
/- warning: left.one_lt_mul -> Left.one_lt_mul is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7005 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7007 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7005 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7007) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7020 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7022 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7020 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7022)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
Case conversion may be inaccurate. Consider using '#align left.one_lt_mul Left.one_lt_mulₓ'. -/
@@ -1042,7 +1116,7 @@ theorem Left.one_lt_mul [CovariantClass α α (· * ·) (· < ·)] {a b : α} (h
/- warning: left.one_lt_mul' -> Left.one_lt_mul' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7076 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7078 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7076 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7078) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7091 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7093 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7091 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7093)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
Case conversion may be inaccurate. Consider using '#align left.one_lt_mul' Left.one_lt_mul'ₓ'. -/
@@ -1062,7 +1136,7 @@ which assume right covariance. -/
/- warning: mul_le_of_le_one_of_le -> mul_le_of_le_one_of_le is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) c)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) c)
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7148 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7150 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7148 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7150)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7163 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7165 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7163 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7165)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) c)
Case conversion may be inaccurate. Consider using '#align mul_le_of_le_one_of_le mul_le_of_le_one_of_leₓ'. -/
@@ -1079,7 +1153,7 @@ theorem mul_le_of_le_one_of_le [CovariantClass α α (swap (· * ·)) (· ≤ ·
/- warning: mul_lt_of_lt_one_of_le -> mul_lt_of_lt_one_of_le is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) c)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) c)
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7261 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7263 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7261 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7263)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7276 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7278 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7276 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7278)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) c)
Case conversion may be inaccurate. Consider using '#align mul_lt_of_lt_one_of_le mul_lt_of_lt_one_of_leₓ'. -/
@@ -1096,7 +1170,7 @@ theorem mul_lt_of_lt_one_of_le [CovariantClass α α (swap (· * ·)) (· < ·)]
/- warning: mul_lt_of_le_one_of_lt -> mul_lt_of_le_one_of_lt is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) c)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) c)
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7374 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7376 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7374 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7376)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7389 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7391 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7389 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7391)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) c)
Case conversion may be inaccurate. Consider using '#align mul_lt_of_le_one_of_lt mul_lt_of_le_one_of_ltₓ'. -/
@@ -1113,7 +1187,7 @@ theorem mul_lt_of_le_one_of_lt [CovariantClass α α (swap (· * ·)) (· ≤ ·
/- warning: mul_lt_of_lt_one_of_lt -> mul_lt_of_lt_one_of_lt is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) c)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) c)
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7487 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7489 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7487 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7489)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7502 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7504 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7502 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7504)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) c)
Case conversion may be inaccurate. Consider using '#align mul_lt_of_lt_one_of_lt mul_lt_of_lt_one_of_ltₓ'. -/
@@ -1130,7 +1204,7 @@ theorem mul_lt_of_lt_one_of_lt [CovariantClass α α (swap (· * ·)) (· < ·)]
/- warning: mul_lt_of_lt_one_of_lt' -> mul_lt_of_lt_one_of_lt' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) c)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) c)
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7600 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7602 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7600 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7602)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7615 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7617 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7615 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7617)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) c)
Case conversion may be inaccurate. Consider using '#align mul_lt_of_lt_one_of_lt' mul_lt_of_lt_one_of_lt'ₓ'. -/
@@ -1143,7 +1217,7 @@ theorem mul_lt_of_lt_one_of_lt' [CovariantClass α α (swap (· * ·)) (· ≤
/- warning: right.mul_le_one -> Right.mul_le_one is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7674 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7676 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7674 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7676)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7689 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7691 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7689 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7691)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align right.mul_le_one Right.mul_le_oneₓ'. -/
@@ -1158,7 +1232,7 @@ theorem Right.mul_le_one [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a
/- warning: right.mul_lt_one_of_lt_of_le -> Right.mul_lt_one_of_lt_of_le is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7748 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7750 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7748 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7750)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7763 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7765 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7763 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7765)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align right.mul_lt_one_of_lt_of_le Right.mul_lt_one_of_lt_of_leₓ'. -/
@@ -1174,7 +1248,7 @@ theorem Right.mul_lt_one_of_lt_of_le [CovariantClass α α (swap (· * ·)) (·
/- warning: right.mul_lt_one_of_le_of_lt -> Right.mul_lt_one_of_le_of_lt is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7822 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7824 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7822 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7824)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7837 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7839 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7837 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7839)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align right.mul_lt_one_of_le_of_lt Right.mul_lt_one_of_le_of_ltₓ'. -/
@@ -1190,7 +1264,7 @@ theorem Right.mul_lt_one_of_le_of_lt [CovariantClass α α (swap (· * ·)) (·
/- warning: right.mul_lt_one -> Right.mul_lt_one is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7896 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7898 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7896 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7898)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7911 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7913 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7911 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7913)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align right.mul_lt_one Right.mul_lt_oneₓ'. -/
@@ -1205,7 +1279,7 @@ theorem Right.mul_lt_one [CovariantClass α α (swap (· * ·)) (· < ·)] {a b
/- warning: right.mul_lt_one' -> Right.mul_lt_one' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7970 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7972 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7970 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7972)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7985 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7987 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7985 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7987)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align right.mul_lt_one' Right.mul_lt_one'ₓ'. -/
@@ -1224,7 +1298,7 @@ which assume right covariance. -/
/- warning: le_mul_of_one_le_of_le -> le_mul_of_one_le_of_le is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a c))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a c))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8042 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8044 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8042 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8044)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8057 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8059 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8057 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8059)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a c))
Case conversion may be inaccurate. Consider using '#align le_mul_of_one_le_of_le le_mul_of_one_le_of_leₓ'. -/
@@ -1241,7 +1315,7 @@ theorem le_mul_of_one_le_of_le [CovariantClass α α (swap (· * ·)) (· ≤ ·
/- warning: lt_mul_of_one_lt_of_le -> lt_mul_of_one_lt_of_le is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a c))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a c))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8158 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8160 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8158 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8160)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8173 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8175 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8173 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8175)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a c))
Case conversion may be inaccurate. Consider using '#align lt_mul_of_one_lt_of_le lt_mul_of_one_lt_of_leₓ'. -/
@@ -1258,7 +1332,7 @@ theorem lt_mul_of_one_lt_of_le [CovariantClass α α (swap (· * ·)) (· < ·)]
/- warning: lt_mul_of_one_le_of_lt -> lt_mul_of_one_le_of_lt is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a c))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a c))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8274 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8276 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8274 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8276)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8289 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8291 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8289 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8291)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a c))
Case conversion may be inaccurate. Consider using '#align lt_mul_of_one_le_of_lt lt_mul_of_one_le_of_ltₓ'. -/
@@ -1275,7 +1349,7 @@ theorem lt_mul_of_one_le_of_lt [CovariantClass α α (swap (· * ·)) (· ≤ ·
/- warning: lt_mul_of_one_lt_of_lt -> lt_mul_of_one_lt_of_lt is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a c))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a c))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8390 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8392 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8390 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8392)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8405 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8407 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8405 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8407)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a c))
Case conversion may be inaccurate. Consider using '#align lt_mul_of_one_lt_of_lt lt_mul_of_one_lt_of_ltₓ'. -/
@@ -1292,7 +1366,7 @@ theorem lt_mul_of_one_lt_of_lt [CovariantClass α α (swap (· * ·)) (· < ·)]
/- warning: lt_mul_of_one_lt_of_lt' -> lt_mul_of_one_lt_of_lt' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a c))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a c))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8506 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8508 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8506 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8508)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8521 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8523 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8521 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8523)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a c))
Case conversion may be inaccurate. Consider using '#align lt_mul_of_one_lt_of_lt' lt_mul_of_one_lt_of_lt'ₓ'. -/
@@ -1305,7 +1379,7 @@ theorem lt_mul_of_one_lt_of_lt' [CovariantClass α α (swap (· * ·)) (· ≤
/- warning: right.one_le_mul -> Right.one_le_mul is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8580 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8582 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8580 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8582)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8595 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8597 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8595 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8597)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
Case conversion may be inaccurate. Consider using '#align right.one_le_mul Right.one_le_mulₓ'. -/
@@ -1321,7 +1395,7 @@ theorem Right.one_le_mul [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a
/- warning: right.one_lt_mul_of_lt_of_le -> Right.one_lt_mul_of_lt_of_le is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8654 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8656 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8654 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8656)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8669 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8671 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8669 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8671)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
Case conversion may be inaccurate. Consider using '#align right.one_lt_mul_of_lt_of_le Right.one_lt_mul_of_lt_of_leₓ'. -/
@@ -1337,7 +1411,7 @@ theorem Right.one_lt_mul_of_lt_of_le [CovariantClass α α (swap (· * ·)) (·
/- warning: right.one_lt_mul_of_le_of_lt -> Right.one_lt_mul_of_le_of_lt is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8728 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8730 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8728 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8730)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8743 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8745 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8743 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8745)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
Case conversion may be inaccurate. Consider using '#align right.one_lt_mul_of_le_of_lt Right.one_lt_mul_of_le_of_ltₓ'. -/
@@ -1353,7 +1427,7 @@ theorem Right.one_lt_mul_of_le_of_lt [CovariantClass α α (swap (· * ·)) (·
/- warning: right.one_lt_mul -> Right.one_lt_mul is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8802 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8804 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8802 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8804)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8817 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8819 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8817 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8819)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
Case conversion may be inaccurate. Consider using '#align right.one_lt_mul Right.one_lt_mulₓ'. -/
@@ -1369,7 +1443,7 @@ theorem Right.one_lt_mul [CovariantClass α α (swap (· * ·)) (· < ·)] {a b
/- warning: right.one_lt_mul' -> Right.one_lt_mul' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8876 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8878 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8876 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8878)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8891 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8893 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8891 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8893)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
Case conversion may be inaccurate. Consider using '#align right.one_lt_mul' Right.one_lt_mul'ₓ'. -/
@@ -1385,7 +1459,7 @@ theorem Right.one_lt_mul' [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a
/- warning: mul_le_one' -> mul_le_one' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5916 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5918 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5916 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5918) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5931 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5933 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5931 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5933)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align mul_le_one' mul_le_one'ₓ'. -/
@@ -1394,7 +1468,7 @@ alias Left.mul_le_one ← mul_le_one'
/- warning: mul_lt_one_of_le_of_lt -> mul_lt_one_of_le_of_lt is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5987 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5989 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5987 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5989) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6002 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6004 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6002 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6004)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align mul_lt_one_of_le_of_lt mul_lt_one_of_le_of_ltₓ'. -/
@@ -1403,7 +1477,7 @@ alias Left.mul_lt_one_of_le_of_lt ← mul_lt_one_of_le_of_lt
/- warning: mul_lt_one_of_lt_of_le -> mul_lt_one_of_lt_of_le is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6058 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6060 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6058 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6060) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6073 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6075 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6073 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6075)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align mul_lt_one_of_lt_of_le mul_lt_one_of_lt_of_leₓ'. -/
@@ -1412,7 +1486,7 @@ alias Left.mul_lt_one_of_lt_of_le ← mul_lt_one_of_lt_of_le
/- warning: mul_lt_one -> mul_lt_one is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6129 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6131 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6129 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6131) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6144 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6146 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6144 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6146)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align mul_lt_one mul_lt_oneₓ'. -/
@@ -1421,7 +1495,7 @@ alias Left.mul_lt_one ← mul_lt_one
/- warning: mul_lt_one' -> mul_lt_one' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6200 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6202 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6200 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6202) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6215 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6217 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6215 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6217)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align mul_lt_one' mul_lt_one'ₓ'. -/
@@ -1442,7 +1516,7 @@ attribute [to_additive "**Alias** of `left.add_neg'`."] mul_lt_one'
/- warning: one_le_mul -> one_le_mul is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6792 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6794 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6792 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6794) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6807 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6809 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6807 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6809)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
Case conversion may be inaccurate. Consider using '#align one_le_mul one_le_mulₓ'. -/
@@ -1451,7 +1525,7 @@ alias Left.one_le_mul ← one_le_mul
/- warning: one_lt_mul_of_le_of_lt' -> one_lt_mul_of_le_of_lt' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6863 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6865 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6863 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6865) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6878 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6880 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6878 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6880)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
Case conversion may be inaccurate. Consider using '#align one_lt_mul_of_le_of_lt' one_lt_mul_of_le_of_lt'ₓ'. -/
@@ -1460,7 +1534,7 @@ alias Left.one_lt_mul_of_le_of_lt ← one_lt_mul_of_le_of_lt'
/- warning: one_lt_mul_of_lt_of_le' -> one_lt_mul_of_lt_of_le' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6934 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6936 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6934 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6936) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6949 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6951 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6949 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6951)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
Case conversion may be inaccurate. Consider using '#align one_lt_mul_of_lt_of_le' one_lt_mul_of_lt_of_le'ₓ'. -/
@@ -1469,7 +1543,7 @@ alias Left.one_lt_mul_of_lt_of_le ← one_lt_mul_of_lt_of_le'
/- warning: one_lt_mul' -> one_lt_mul' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7005 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7007 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7005 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7007) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7020 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7022 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7020 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7022)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
Case conversion may be inaccurate. Consider using '#align one_lt_mul' one_lt_mul'ₓ'. -/
@@ -1478,7 +1552,7 @@ alias Left.one_lt_mul ← one_lt_mul'
/- warning: one_lt_mul'' -> one_lt_mul'' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7076 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7078 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7076 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7078) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7091 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7093 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7091 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7093)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
Case conversion may be inaccurate. Consider using '#align one_lt_mul'' one_lt_mul''ₓ'. -/
@@ -1499,7 +1573,7 @@ attribute [to_additive add_pos' "**Alias** of `left.add_pos'`."] one_lt_mul''
/- warning: lt_of_mul_lt_of_one_le_left -> lt_of_mul_lt_of_one_le_left is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a c)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) c) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a c)
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8984 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8986 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8984 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8986) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8999 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9001 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8999 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9001)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a c)
Case conversion may be inaccurate. Consider using '#align lt_of_mul_lt_of_one_le_left lt_of_mul_lt_of_one_le_leftₓ'. -/
@@ -1512,7 +1586,7 @@ theorem lt_of_mul_lt_of_one_le_left [CovariantClass α α (· * ·) (· ≤ ·)]
/- warning: le_of_mul_le_of_one_le_left -> le_of_mul_le_of_one_le_left is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a c)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) c) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a c)
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9055 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9057 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9055 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9057) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9070 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9072 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9070 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9072)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a c)
Case conversion may be inaccurate. Consider using '#align le_of_mul_le_of_one_le_left le_of_mul_le_of_one_le_leftₓ'. -/
@@ -1525,7 +1599,7 @@ theorem le_of_mul_le_of_one_le_left [CovariantClass α α (· * ·) (· ≤ ·)]
/- warning: lt_of_lt_mul_of_le_one_left -> lt_of_lt_mul_of_le_one_left is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b c)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) c (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a b)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b c)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) c (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a b)
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9126 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9128 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9126 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9128) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9141 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9143 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9141 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9143)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b c)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) c (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a b)
Case conversion may be inaccurate. Consider using '#align lt_of_lt_mul_of_le_one_left lt_of_lt_mul_of_le_one_leftₓ'. -/
@@ -1538,7 +1612,7 @@ theorem lt_of_lt_mul_of_le_one_left [CovariantClass α α (· * ·) (· ≤ ·)]
/- warning: le_of_le_mul_of_le_one_left -> le_of_le_mul_of_le_one_left is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b c)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) c (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a b)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b c)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) c (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a b)
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9196 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9198 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9196 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9198) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9211 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9213 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9211 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9213)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b c)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) c (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a b)
Case conversion may be inaccurate. Consider using '#align le_of_le_mul_of_le_one_left le_of_le_mul_of_le_one_leftₓ'. -/
@@ -1551,7 +1625,7 @@ theorem le_of_le_mul_of_le_one_left [CovariantClass α α (· * ·) (· ≤ ·)]
/- warning: lt_of_mul_lt_of_one_le_right -> lt_of_mul_lt_of_one_le_right is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) c) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) b c)
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9269 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9271 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9269 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9271)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9284 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9286 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9284 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9286)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c)
Case conversion may be inaccurate. Consider using '#align lt_of_mul_lt_of_one_le_right lt_of_mul_lt_of_one_le_rightₓ'. -/
@@ -1564,7 +1638,7 @@ theorem lt_of_mul_lt_of_one_le_right [CovariantClass α α (swap (· * ·)) (·
/- warning: le_of_mul_le_of_one_le_right -> le_of_mul_le_of_one_le_right is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) c) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) b c)
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9343 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9345 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9343 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9345)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9358 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9360 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9358 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9360)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c)
Case conversion may be inaccurate. Consider using '#align le_of_mul_le_of_one_le_right le_of_mul_le_of_one_le_rightₓ'. -/
@@ -1577,7 +1651,7 @@ theorem le_of_mul_le_of_one_le_right [CovariantClass α α (swap (· * ·)) (·
/- warning: lt_of_lt_mul_of_le_one_right -> lt_of_lt_mul_of_le_one_right is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b c)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a c)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b c)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a c)
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9417 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9419 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9417 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9419)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9432 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9434 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9432 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9434)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b c)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a c)
Case conversion may be inaccurate. Consider using '#align lt_of_lt_mul_of_le_one_right lt_of_lt_mul_of_le_one_rightₓ'. -/
@@ -1590,7 +1664,7 @@ theorem lt_of_lt_mul_of_le_one_right [CovariantClass α α (swap (· * ·)) (·
/- warning: le_of_le_mul_of_le_one_right -> le_of_le_mul_of_le_one_right is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b c)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a c)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b c)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a c)
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9490 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9492 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9490 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9492)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9505 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9507 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9505 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9507)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b c)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a c)
Case conversion may be inaccurate. Consider using '#align le_of_le_mul_of_le_one_right le_of_le_mul_of_le_one_rightₓ'. -/
@@ -1609,7 +1683,7 @@ variable [PartialOrder α]
/- warning: mul_eq_one_iff' -> mul_eq_one_iff' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (Iff (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) (And (Eq.{succ u1} α a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) (Eq.{succ u1} α b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (Iff (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) (And (Eq.{succ u1} α a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) (Eq.{succ u1} α b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9572 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9574 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9572 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9574) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9587 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9589 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9587 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9589)] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9609 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9611 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9609 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9611)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9624 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9626 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9624 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9626)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (Iff (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) (And (Eq.{succ u1} α a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) (Eq.{succ u1} α b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))))
Case conversion may be inaccurate. Consider using '#align mul_eq_one_iff' mul_eq_one_iff'ₓ'. -/
@@ -1630,7 +1704,7 @@ theorem mul_eq_one_iff' [CovariantClass α α (· * ·) (· ≤ ·)]
/- warning: mul_le_mul_iff_of_ge -> mul_le_mul_iff_of_ge is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_5 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_6 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a₁ : α} {a₂ : α} {b₁ : α} {b₂ : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a₁ a₂) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b₁ b₂) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a₂ b₂) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a₁ b₁)) (And (Eq.{succ u1} α a₁ a₂) (Eq.{succ u1} α b₁ b₂)))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_5 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_6 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a₁ : α} {a₂ : α} {b₁ : α} {b₂ : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a₁ a₂) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b₁ b₂) -> (Iff (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a₂ b₂) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a₁ b₁)) (And (Eq.{succ u1} α a₁ a₂) (Eq.{succ u1} α b₁ b₂)))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9831 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9833 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9831 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9833) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9846 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9848 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9846 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9848)] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9868 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9870 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9868 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9870)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9883 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9885 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9883 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9885)] [_inst_5 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9902 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9904 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9902 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9904) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9917 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9919 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9917 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9919)] [_inst_6 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9939 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9941 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9939 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9941)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9954 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9956 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9954 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9956)] {a₁ : α} {a₂ : α} {b₁ : α} {b₂ : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a₁ a₂) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b₁ b₂) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a₂ b₂) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a₁ b₁)) (And (Eq.{succ u1} α a₁ a₂) (Eq.{succ u1} α b₁ b₂)))
Case conversion may be inaccurate. Consider using '#align mul_le_mul_iff_of_ge mul_le_mul_iff_of_geₓ'. -/
@@ -1657,7 +1731,7 @@ variable [CovariantClass α α (· * ·) (· ≤ ·)] {a b : α}
/- warning: eq_one_of_one_le_mul_left -> eq_one_of_one_le_mul_left is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b)) -> (Eq.{succ u1} α a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b)) -> (Eq.{succ u1} α a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10119 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10121 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10119 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10121) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10134 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10136 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10134 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10136)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b)) -> (Eq.{succ u1} α a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align eq_one_of_one_le_mul_left eq_one_of_one_le_mul_leftₓ'. -/
@@ -1669,7 +1743,7 @@ theorem eq_one_of_one_le_mul_left (ha : a ≤ 1) (hb : b ≤ 1) (hab : 1 ≤ a *
/- warning: eq_one_of_mul_le_one_left -> eq_one_of_mul_le_one_left is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (Eq.{succ u1} α a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (Eq.{succ u1} α a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10198 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10200 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10198 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10200) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10213 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10215 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10213 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10215)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (Eq.{succ u1} α a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align eq_one_of_mul_le_one_left eq_one_of_mul_le_one_leftₓ'. -/
@@ -1687,7 +1761,7 @@ variable [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b : α}
/- warning: eq_one_of_one_le_mul_right -> eq_one_of_one_le_mul_right is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b)) -> (Eq.{succ u1} α b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b)) -> (Eq.{succ u1} α b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10333 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10335 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10333 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10335)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10348 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10350 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10348 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10350)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b)) -> (Eq.{succ u1} α b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align eq_one_of_one_le_mul_right eq_one_of_one_le_mul_rightₓ'. -/
@@ -1699,7 +1773,7 @@ theorem eq_one_of_one_le_mul_right (ha : a ≤ 1) (hb : b ≤ 1) (hab : 1 ≤ a
/- warning: eq_one_of_mul_le_one_right -> eq_one_of_mul_le_one_right is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (Eq.{succ u1} α b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (Eq.{succ u1} α b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10415 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10417 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10415 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10417)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10430 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10432 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10430 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10432)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (Eq.{succ u1} α b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align eq_one_of_mul_le_one_right eq_one_of_mul_le_one_rightₓ'. -/
@@ -1719,7 +1793,7 @@ variable [LinearOrder α]
/- warning: exists_square_le -> exists_square_le is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))))] (a : α), Exists.{succ u1} α (fun (b : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b b) a)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))))] (a : α), Exists.{succ u1} α (fun (b : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b b) a)
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10507 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10509 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10507 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10509) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10522 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10524 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10522 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10524)] (a : α), Exists.{succ u1} α (fun (b : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b b) a)
Case conversion may be inaccurate. Consider using '#align exists_square_le exists_square_leₓ'. -/
@@ -1749,7 +1823,7 @@ variable [PartialOrder α]
/- warning: contravariant.to_left_cancel_semigroup -> Contravariant.toLeftCancelSemigroup is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))], LeftCancelSemigroup.{u1} α
+ forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))], LeftCancelSemigroup.{u1} α
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10777 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10779 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10777 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10779) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10792 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10794 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10792 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10794)], LeftCancelSemigroup.{u1} α
Case conversion may be inaccurate. Consider using '#align contravariant.to_left_cancel_semigroup Contravariant.toLeftCancelSemigroupₓ'. -/
@@ -1767,7 +1841,7 @@ def Contravariant.toLeftCancelSemigroup [ContravariantClass α α (· * ·) (·
/- warning: contravariant.to_right_cancel_semigroup -> Contravariant.toRightCancelSemigroup is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))], RightCancelSemigroup.{u1} α
+ forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))], RightCancelSemigroup.{u1} α
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10860 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10862 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10860 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10862)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10875 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10877 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10875 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10877)], RightCancelSemigroup.{u1} α
Case conversion may be inaccurate. Consider using '#align contravariant.to_right_cancel_semigroup Contravariant.toRightCancelSemigroupₓ'. -/
@@ -1785,7 +1859,7 @@ def Contravariant.toRightCancelSemigroup [ContravariantClass α α (swap (· *
/- warning: left.mul_eq_mul_iff_eq_and_eq -> Left.mul_eq_mul_iff_eq_and_eq is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_5 : ContravariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_6 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b d) -> (Iff (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)) c d)) (And (Eq.{succ u1} α a c) (Eq.{succ u1} α b d)))
+ forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_5 : ContravariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_6 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a c) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b d) -> (Iff (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)) c d)) (And (Eq.{succ u1} α a c) (Eq.{succ u1} α b d)))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10940 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10942 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10940 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10942) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10955 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10957 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10955 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10957)] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10977 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10979 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10977 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10979)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10992 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10994 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10992 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10994)] [_inst_5 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11011 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11013 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11011 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11013) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11026 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11028 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11026 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11028)] [_inst_6 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11048 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11050 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11048 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11050)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11063 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11065 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11063 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11065)] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b d) -> (Iff (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) c d)) (And (Eq.{succ u1} α a c) (Eq.{succ u1} α b d)))
Case conversion may be inaccurate. Consider using '#align left.mul_eq_mul_iff_eq_and_eq Left.mul_eq_mul_iff_eq_and_eqₓ'. -/
@@ -1806,7 +1880,7 @@ theorem Left.mul_eq_mul_iff_eq_and_eq [CovariantClass α α (· * ·) (· < ·)]
/- warning: right.mul_eq_mul_iff_eq_and_eq -> Right.mul_eq_mul_iff_eq_and_eq is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_4 : ContravariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_6 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b d) -> (Iff (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)) c d)) (And (Eq.{succ u1} α a c) (Eq.{succ u1} α b d)))
+ forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_4 : ContravariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_6 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a c) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b d) -> (Iff (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)) c d)) (And (Eq.{succ u1} α a c) (Eq.{succ u1} α b d)))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11203 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11205 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11203 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11205) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11218 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11220 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11218 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11220)] [_inst_4 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11237 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11239 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11237 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11239) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11252 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11254 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11252 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11254)] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11274 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11276 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11274 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11276)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11289 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11291 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11289 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11291)] [_inst_6 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11311 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11313 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11311 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11313)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11326 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11328 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11326 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11328)] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b d) -> (Iff (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) c d)) (And (Eq.{succ u1} α a c) (Eq.{succ u1} α b d)))
Case conversion may be inaccurate. Consider using '#align right.mul_eq_mul_iff_eq_and_eq Right.mul_eq_mul_iff_eq_and_eqₓ'. -/
@@ -1827,7 +1901,7 @@ theorem Right.mul_eq_mul_iff_eq_and_eq [CovariantClass α α (· * ·) (· ≤
/- warning: mul_eq_mul_iff_eq_and_eq -> mul_eq_mul_iff_eq_and_eq is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_5 : ContravariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_6 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b d) -> (Iff (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)) c d)) (And (Eq.{succ u1} α a c) (Eq.{succ u1} α b d)))
+ forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_5 : ContravariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_6 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a c) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b d) -> (Iff (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)) c d)) (And (Eq.{succ u1} α a c) (Eq.{succ u1} α b d)))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10940 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10942 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10940 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10942) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10955 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10957 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10955 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10957)] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10977 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10979 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10977 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10979)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10992 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10994 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10992 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10994)] [_inst_5 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11011 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11013 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11011 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11013) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11026 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11028 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11026 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11028)] [_inst_6 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11048 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11050 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11048 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11050)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11063 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11065 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11063 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11065)] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b d) -> (Iff (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) c d)) (And (Eq.{succ u1} α a c) (Eq.{succ u1} α b d)))
Case conversion may be inaccurate. Consider using '#align mul_eq_mul_iff_eq_and_eq mul_eq_mul_iff_eq_and_eqₓ'. -/
@@ -1846,7 +1920,7 @@ variable [Mul α] [Preorder α] [Preorder β] {f g : β → α} {s : Set β}
/- warning: monotone.const_mul' -> Monotone.const_mul' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))], (Monotone.{u2, u1} β α _inst_3 _inst_2 f) -> (forall (a : α), Monotone.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a (f x)))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))], (Monotone.{u2, u1} β α _inst_3 _inst_2 f) -> (forall (a : α), Monotone.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a (f x)))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11510 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11512 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11510 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11512) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11525 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11527 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11525 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11527)], (Monotone.{u1, u2} β α _inst_3 _inst_2 f) -> (forall (a : α), Monotone.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) a (f x)))
Case conversion may be inaccurate. Consider using '#align monotone.const_mul' Monotone.const_mul'ₓ'. -/
@@ -1858,7 +1932,7 @@ theorem Monotone.const_mul' [CovariantClass α α (· * ·) (· ≤ ·)] (hf : M
/- warning: monotone_on.const_mul' -> MonotoneOn.const_mul' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))], (MonotoneOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (forall (a : α), MonotoneOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a (f x)) s)
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))], (MonotoneOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (forall (a : α), MonotoneOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a (f x)) s)
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} {s : Set.{u1} β} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11596 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11598 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11596 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11598) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11611 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11613 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11611 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11613)], (MonotoneOn.{u1, u2} β α _inst_3 _inst_2 f s) -> (forall (a : α), MonotoneOn.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) a (f x)) s)
Case conversion may be inaccurate. Consider using '#align monotone_on.const_mul' MonotoneOn.const_mul'ₓ'. -/
@@ -1870,7 +1944,7 @@ theorem MonotoneOn.const_mul' [CovariantClass α α (· * ·) (· ≤ ·)] (hf :
/- warning: antitone.const_mul' -> Antitone.const_mul' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))], (Antitone.{u2, u1} β α _inst_3 _inst_2 f) -> (forall (a : α), Antitone.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a (f x)))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))], (Antitone.{u2, u1} β α _inst_3 _inst_2 f) -> (forall (a : α), Antitone.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a (f x)))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11690 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11692 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11690 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11692) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11705 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11707 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11705 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11707)], (Antitone.{u1, u2} β α _inst_3 _inst_2 f) -> (forall (a : α), Antitone.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) a (f x)))
Case conversion may be inaccurate. Consider using '#align antitone.const_mul' Antitone.const_mul'ₓ'. -/
@@ -1882,7 +1956,7 @@ theorem Antitone.const_mul' [CovariantClass α α (· * ·) (· ≤ ·)] (hf : A
/- warning: antitone_on.const_mul' -> AntitoneOn.const_mul' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))], (AntitoneOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (forall (a : α), AntitoneOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a (f x)) s)
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))], (AntitoneOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (forall (a : α), AntitoneOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a (f x)) s)
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} {s : Set.{u1} β} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11776 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11778 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11776 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11778) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11791 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11793 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11791 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11793)], (AntitoneOn.{u1, u2} β α _inst_3 _inst_2 f s) -> (forall (a : α), AntitoneOn.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) a (f x)) s)
Case conversion may be inaccurate. Consider using '#align antitone_on.const_mul' AntitoneOn.const_mul'ₓ'. -/
@@ -1894,7 +1968,7 @@ theorem AntitoneOn.const_mul' [CovariantClass α α (· * ·) (· ≤ ·)] (hf :
/- warning: monotone.mul_const' -> Monotone.mul_const' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))], (Monotone.{u2, u1} β α _inst_3 _inst_2 f) -> (forall (a : α), Monotone.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) a))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))], (Monotone.{u2, u1} β α _inst_3 _inst_2 f) -> (forall (a : α), Monotone.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) a))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} [_inst_4 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11873 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11875 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11873 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11875)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11888 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11890 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11888 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11890)], (Monotone.{u1, u2} β α _inst_3 _inst_2 f) -> (forall (a : α), Monotone.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) a))
Case conversion may be inaccurate. Consider using '#align monotone.mul_const' Monotone.mul_const'ₓ'. -/
@@ -1906,7 +1980,7 @@ theorem Monotone.mul_const' [CovariantClass α α (swap (· * ·)) (· ≤ ·)]
/- warning: monotone_on.mul_const' -> MonotoneOn.mul_const' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))], (MonotoneOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (forall (a : α), MonotoneOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) a) s)
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))], (MonotoneOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (forall (a : α), MonotoneOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) a) s)
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} {s : Set.{u1} β} [_inst_4 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11962 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11964 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11962 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11964)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11977 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11979 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11977 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11979)], (MonotoneOn.{u1, u2} β α _inst_3 _inst_2 f s) -> (forall (a : α), MonotoneOn.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) a) s)
Case conversion may be inaccurate. Consider using '#align monotone_on.mul_const' MonotoneOn.mul_const'ₓ'. -/
@@ -1918,7 +1992,7 @@ theorem MonotoneOn.mul_const' [CovariantClass α α (swap (· * ·)) (· ≤ ·)
/- warning: antitone.mul_const' -> Antitone.mul_const' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))], (Antitone.{u2, u1} β α _inst_3 _inst_2 f) -> (forall (a : α), Antitone.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) a))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))], (Antitone.{u2, u1} β α _inst_3 _inst_2 f) -> (forall (a : α), Antitone.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) a))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} [_inst_4 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12059 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12061 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12059 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12061)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12074 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12076 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12074 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12076)], (Antitone.{u1, u2} β α _inst_3 _inst_2 f) -> (forall (a : α), Antitone.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) a))
Case conversion may be inaccurate. Consider using '#align antitone.mul_const' Antitone.mul_const'ₓ'. -/
@@ -1930,7 +2004,7 @@ theorem Antitone.mul_const' [CovariantClass α α (swap (· * ·)) (· ≤ ·)]
/- warning: antitone_on.mul_const' -> AntitoneOn.mul_const' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))], (AntitoneOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (forall (a : α), AntitoneOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) a) s)
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))], (AntitoneOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (forall (a : α), AntitoneOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) a) s)
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} {s : Set.{u1} β} [_inst_4 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12148 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12150 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12148 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12150)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12163 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12165 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12163 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12165)], (AntitoneOn.{u1, u2} β α _inst_3 _inst_2 f s) -> (forall (a : α), AntitoneOn.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) a) s)
Case conversion may be inaccurate. Consider using '#align antitone_on.mul_const' AntitoneOn.mul_const'ₓ'. -/
@@ -1942,7 +2016,7 @@ theorem AntitoneOn.mul_const' [CovariantClass α α (swap (· * ·)) (· ≤ ·)
/- warning: monotone.mul' -> Monotone.mul' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {g : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))], (Monotone.{u2, u1} β α _inst_3 _inst_2 f) -> (Monotone.{u2, u1} β α _inst_3 _inst_2 g) -> (Monotone.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {g : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))], (Monotone.{u2, u1} β α _inst_3 _inst_2 f) -> (Monotone.{u2, u1} β α _inst_3 _inst_2 g) -> (Monotone.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} {g : β -> α} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12242 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12244 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12242 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12244) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12257 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12259 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12257 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12259)] [_inst_5 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12279 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12281 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12279 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12281)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12294 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12296 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12294 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12296)], (Monotone.{u1, u2} β α _inst_3 _inst_2 f) -> (Monotone.{u1, u2} β α _inst_3 _inst_2 g) -> (Monotone.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) (g x)))
Case conversion may be inaccurate. Consider using '#align monotone.mul' Monotone.mul'ₓ'. -/
@@ -1956,7 +2030,7 @@ theorem Monotone.mul' [CovariantClass α α (· * ·) (· ≤ ·)]
/- warning: monotone_on.mul' -> MonotoneOn.mul' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {g : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))], (MonotoneOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (MonotoneOn.{u2, u1} β α _inst_3 _inst_2 g s) -> (MonotoneOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)) s)
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {g : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))], (MonotoneOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (MonotoneOn.{u2, u1} β α _inst_3 _inst_2 g s) -> (MonotoneOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)) s)
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} {g : β -> α} {s : Set.{u1} β} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12370 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12372 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12370 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12372) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12385 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12387 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12385 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12387)] [_inst_5 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12407 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12409 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12407 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12409)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12422 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12424 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12422 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12424)], (MonotoneOn.{u1, u2} β α _inst_3 _inst_2 f s) -> (MonotoneOn.{u1, u2} β α _inst_3 _inst_2 g s) -> (MonotoneOn.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) (g x)) s)
Case conversion may be inaccurate. Consider using '#align monotone_on.mul' MonotoneOn.mul'ₓ'. -/
@@ -1970,7 +2044,7 @@ theorem MonotoneOn.mul' [CovariantClass α α (· * ·) (· ≤ ·)]
/- warning: antitone.mul' -> Antitone.mul' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {g : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))], (Antitone.{u2, u1} β α _inst_3 _inst_2 f) -> (Antitone.{u2, u1} β α _inst_3 _inst_2 g) -> (Antitone.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {g : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))], (Antitone.{u2, u1} β α _inst_3 _inst_2 f) -> (Antitone.{u2, u1} β α _inst_3 _inst_2 g) -> (Antitone.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} {g : β -> α} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12509 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12511 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12509 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12511) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12524 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12526 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12524 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12526)] [_inst_5 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12546 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12548 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12546 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12548)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12561 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12563 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12561 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12563)], (Antitone.{u1, u2} β α _inst_3 _inst_2 f) -> (Antitone.{u1, u2} β α _inst_3 _inst_2 g) -> (Antitone.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) (g x)))
Case conversion may be inaccurate. Consider using '#align antitone.mul' Antitone.mul'ₓ'. -/
@@ -1984,7 +2058,7 @@ theorem Antitone.mul' [CovariantClass α α (· * ·) (· ≤ ·)]
/- warning: antitone_on.mul' -> AntitoneOn.mul' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {g : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))], (AntitoneOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (AntitoneOn.{u2, u1} β α _inst_3 _inst_2 g s) -> (AntitoneOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)) s)
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {g : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))], (AntitoneOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (AntitoneOn.{u2, u1} β α _inst_3 _inst_2 g s) -> (AntitoneOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)) s)
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} {g : β -> α} {s : Set.{u1} β} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12637 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12639 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12637 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12639) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12652 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12654 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12652 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12654)] [_inst_5 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12674 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12676 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12674 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12676)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12689 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12691 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12689 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12691)], (AntitoneOn.{u1, u2} β α _inst_3 _inst_2 f s) -> (AntitoneOn.{u1, u2} β α _inst_3 _inst_2 g s) -> (AntitoneOn.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) (g x)) s)
Case conversion may be inaccurate. Consider using '#align antitone_on.mul' AntitoneOn.mul'ₓ'. -/
@@ -2000,37 +2074,53 @@ section Left
variable [CovariantClass α α (· * ·) (· < ·)]
-#print StrictMono.const_mul' /-
+/- warning: strict_mono.const_mul' -> StrictMono.const_mul' is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))], (StrictMono.{u2, u1} β α _inst_3 _inst_2 f) -> (forall (c : α), StrictMono.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) c (f x)))
+but is expected to have type
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12832 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12834 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12832 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12834) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12847 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12849 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12847 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12849)], (StrictMono.{u2, u1} β α _inst_3 _inst_2 f) -> (forall (c : α), StrictMono.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) c (f x)))
+Case conversion may be inaccurate. Consider using '#align strict_mono.const_mul' StrictMono.const_mul'ₓ'. -/
@[to_additive const_add]
theorem StrictMono.const_mul' (hf : StrictMono f) (c : α) : StrictMono fun x => c * f x :=
fun a b ab => mul_lt_mul_left' (hf ab) c
#align strict_mono.const_mul' StrictMono.const_mul'
#align strict_mono.const_add StrictMono.const_add
--/
-#print StrictMonoOn.const_mul' /-
+/- warning: strict_mono_on.const_mul' -> StrictMonoOn.const_mul' is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))], (StrictMonoOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (forall (c : α), StrictMonoOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) c (f x)) s)
+but is expected to have type
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12918 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12920 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12918 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12920) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12933 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12935 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12933 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12935)], (StrictMonoOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (forall (c : α), StrictMonoOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) c (f x)) s)
+Case conversion may be inaccurate. Consider using '#align strict_mono_on.const_mul' StrictMonoOn.const_mul'ₓ'. -/
@[to_additive const_add]
theorem StrictMonoOn.const_mul' (hf : StrictMonoOn f s) (c : α) :
StrictMonoOn (fun x => c * f x) s := fun a ha b hb ab => mul_lt_mul_left' (hf ha hb ab) c
#align strict_mono_on.const_mul' StrictMonoOn.const_mul'
#align strict_mono_on.const_add StrictMonoOn.const_add
--/
-#print StrictAnti.const_mul' /-
+/- warning: strict_anti.const_mul' -> StrictAnti.const_mul' is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))], (StrictAnti.{u2, u1} β α _inst_3 _inst_2 f) -> (forall (c : α), StrictAnti.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) c (f x)))
+but is expected to have type
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13012 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13014 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13012 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13014) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13027 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13029 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13027 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13029)], (StrictAnti.{u2, u1} β α _inst_3 _inst_2 f) -> (forall (c : α), StrictAnti.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) c (f x)))
+Case conversion may be inaccurate. Consider using '#align strict_anti.const_mul' StrictAnti.const_mul'ₓ'. -/
@[to_additive const_add]
theorem StrictAnti.const_mul' (hf : StrictAnti f) (c : α) : StrictAnti fun x => c * f x :=
fun a b ab => mul_lt_mul_left' (hf ab) c
#align strict_anti.const_mul' StrictAnti.const_mul'
#align strict_anti.const_add StrictAnti.const_add
--/
-#print StrictAntiOn.const_mul' /-
+/- warning: strict_anti_on.const_mul' -> StrictAntiOn.const_mul' is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))], (StrictAntiOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (forall (c : α), StrictAntiOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) c (f x)) s)
+but is expected to have type
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13098 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13100 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13098 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13100) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13113 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13115 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13113 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13115)], (StrictAntiOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (forall (c : α), StrictAntiOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) c (f x)) s)
+Case conversion may be inaccurate. Consider using '#align strict_anti_on.const_mul' StrictAntiOn.const_mul'ₓ'. -/
@[to_additive const_add]
theorem StrictAntiOn.const_mul' (hf : StrictAntiOn f s) (c : α) :
StrictAntiOn (fun x => c * f x) s := fun a ha b hb ab => mul_lt_mul_left' (hf ha hb ab) c
#align strict_anti_on.const_mul' StrictAntiOn.const_mul'
#align strict_anti_on.const_add StrictAntiOn.const_add
--/
end Left
@@ -2038,43 +2128,59 @@ section Right
variable [CovariantClass α α (swap (· * ·)) (· < ·)]
-#print StrictMono.mul_const' /-
+/- warning: strict_mono.mul_const' -> StrictMono.mul_const' is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))], (StrictMono.{u2, u1} β α _inst_3 _inst_2 f) -> (forall (c : α), StrictMono.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) c))
+but is expected to have type
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13255 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13257 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13255 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13257)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13270 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13272 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13270 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13272)], (StrictMono.{u2, u1} β α _inst_3 _inst_2 f) -> (forall (c : α), StrictMono.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) c))
+Case conversion may be inaccurate. Consider using '#align strict_mono.mul_const' StrictMono.mul_const'ₓ'. -/
@[to_additive add_const]
theorem StrictMono.mul_const' (hf : StrictMono f) (c : α) : StrictMono fun x => f x * c :=
fun a b ab => mul_lt_mul_right' (hf ab) c
#align strict_mono.mul_const' StrictMono.mul_const'
#align strict_mono.add_const StrictMono.add_const
--/
-#print StrictMonoOn.mul_const' /-
+/- warning: strict_mono_on.mul_const' -> StrictMonoOn.mul_const' is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))], (StrictMonoOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (forall (c : α), StrictMonoOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) c) s)
+but is expected to have type
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13344 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13346 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13344 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13346)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13359 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13361 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13359 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13361)], (StrictMonoOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (forall (c : α), StrictMonoOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) c) s)
+Case conversion may be inaccurate. Consider using '#align strict_mono_on.mul_const' StrictMonoOn.mul_const'ₓ'. -/
@[to_additive add_const]
theorem StrictMonoOn.mul_const' (hf : StrictMonoOn f s) (c : α) :
StrictMonoOn (fun x => f x * c) s := fun a ha b hb ab => mul_lt_mul_right' (hf ha hb ab) c
#align strict_mono_on.mul_const' StrictMonoOn.mul_const'
#align strict_mono_on.add_const StrictMonoOn.add_const
--/
-#print StrictAnti.mul_const' /-
+/- warning: strict_anti.mul_const' -> StrictAnti.mul_const' is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))], (StrictAnti.{u2, u1} β α _inst_3 _inst_2 f) -> (forall (c : α), StrictAnti.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) c))
+but is expected to have type
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13441 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13443 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13441 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13443)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13456 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13458 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13456 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13458)], (StrictAnti.{u2, u1} β α _inst_3 _inst_2 f) -> (forall (c : α), StrictAnti.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) c))
+Case conversion may be inaccurate. Consider using '#align strict_anti.mul_const' StrictAnti.mul_const'ₓ'. -/
@[to_additive add_const]
theorem StrictAnti.mul_const' (hf : StrictAnti f) (c : α) : StrictAnti fun x => f x * c :=
fun a b ab => mul_lt_mul_right' (hf ab) c
#align strict_anti.mul_const' StrictAnti.mul_const'
#align strict_anti.add_const StrictAnti.add_const
--/
-#print StrictAntiOn.mul_const' /-
+/- warning: strict_anti_on.mul_const' -> StrictAntiOn.mul_const' is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))], (StrictAntiOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (forall (c : α), StrictAntiOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) c) s)
+but is expected to have type
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13530 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13532 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13530 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13532)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13545 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13547 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13545 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13547)], (StrictAntiOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (forall (c : α), StrictAntiOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) c) s)
+Case conversion may be inaccurate. Consider using '#align strict_anti_on.mul_const' StrictAntiOn.mul_const'ₓ'. -/
@[to_additive add_const]
theorem StrictAntiOn.mul_const' (hf : StrictAntiOn f s) (c : α) :
StrictAntiOn (fun x => f x * c) s := fun a ha b hb ab => mul_lt_mul_right' (hf ha hb ab) c
#align strict_anti_on.mul_const' StrictAntiOn.mul_const'
#align strict_anti_on.add_const StrictAntiOn.add_const
--/
end Right
/- warning: strict_mono.mul' -> StrictMono.mul' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {g : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))], (StrictMono.{u2, u1} β α _inst_3 _inst_2 f) -> (StrictMono.{u2, u1} β α _inst_3 _inst_2 g) -> (StrictMono.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {g : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))], (StrictMono.{u2, u1} β α _inst_3 _inst_2 f) -> (StrictMono.{u2, u1} β α _inst_3 _inst_2 g) -> (StrictMono.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} {g : β -> α} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13625 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13627 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13625 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13627) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13640 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13642 : α) => LT.lt.{u2} α (Preorder.toLT.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13640 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13642)] [_inst_5 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13662 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13664 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13662 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13664)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13677 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13679 : α) => LT.lt.{u2} α (Preorder.toLT.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13677 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13679)], (StrictMono.{u1, u2} β α _inst_3 _inst_2 f) -> (StrictMono.{u1, u2} β α _inst_3 _inst_2 g) -> (StrictMono.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) (g x)))
Case conversion may be inaccurate. Consider using '#align strict_mono.mul' StrictMono.mul'ₓ'. -/
@@ -2088,7 +2194,7 @@ theorem StrictMono.mul' [CovariantClass α α (· * ·) (· < ·)]
/- warning: strict_mono_on.mul' -> StrictMonoOn.mul' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {g : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))], (StrictMonoOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (StrictMonoOn.{u2, u1} β α _inst_3 _inst_2 g s) -> (StrictMonoOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)) s)
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {g : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))], (StrictMonoOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (StrictMonoOn.{u2, u1} β α _inst_3 _inst_2 g s) -> (StrictMonoOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)) s)
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} {g : β -> α} {s : Set.{u1} β} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13753 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13755 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13753 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13755) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13768 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13770 : α) => LT.lt.{u2} α (Preorder.toLT.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13768 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13770)] [_inst_5 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13790 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13792 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13790 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13792)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13805 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13807 : α) => LT.lt.{u2} α (Preorder.toLT.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13805 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13807)], (StrictMonoOn.{u1, u2} β α _inst_3 _inst_2 f s) -> (StrictMonoOn.{u1, u2} β α _inst_3 _inst_2 g s) -> (StrictMonoOn.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) (g x)) s)
Case conversion may be inaccurate. Consider using '#align strict_mono_on.mul' StrictMonoOn.mul'ₓ'. -/
@@ -2103,7 +2209,7 @@ theorem StrictMonoOn.mul' [CovariantClass α α (· * ·) (· < ·)]
/- warning: strict_anti.mul' -> StrictAnti.mul' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {g : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))], (StrictAnti.{u2, u1} β α _inst_3 _inst_2 f) -> (StrictAnti.{u2, u1} β α _inst_3 _inst_2 g) -> (StrictAnti.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {g : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))], (StrictAnti.{u2, u1} β α _inst_3 _inst_2 f) -> (StrictAnti.{u2, u1} β α _inst_3 _inst_2 g) -> (StrictAnti.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} {g : β -> α} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13892 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13894 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13892 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13894) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13907 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13909 : α) => LT.lt.{u2} α (Preorder.toLT.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13907 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13909)] [_inst_5 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13929 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13931 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13929 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13931)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13944 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13946 : α) => LT.lt.{u2} α (Preorder.toLT.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13944 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13946)], (StrictAnti.{u1, u2} β α _inst_3 _inst_2 f) -> (StrictAnti.{u1, u2} β α _inst_3 _inst_2 g) -> (StrictAnti.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) (g x)))
Case conversion may be inaccurate. Consider using '#align strict_anti.mul' StrictAnti.mul'ₓ'. -/
@@ -2117,7 +2223,7 @@ theorem StrictAnti.mul' [CovariantClass α α (· * ·) (· < ·)]
/- warning: strict_anti_on.mul' -> StrictAntiOn.mul' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {g : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))], (StrictAntiOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (StrictAntiOn.{u2, u1} β α _inst_3 _inst_2 g s) -> (StrictAntiOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)) s)
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {g : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))], (StrictAntiOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (StrictAntiOn.{u2, u1} β α _inst_3 _inst_2 g s) -> (StrictAntiOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)) s)
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} {g : β -> α} {s : Set.{u1} β} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14020 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14022 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14020 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14022) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14035 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14037 : α) => LT.lt.{u2} α (Preorder.toLT.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14035 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14037)] [_inst_5 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14057 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14059 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14057 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14059)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14072 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14074 : α) => LT.lt.{u2} α (Preorder.toLT.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14072 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14074)], (StrictAntiOn.{u1, u2} β α _inst_3 _inst_2 f s) -> (StrictAntiOn.{u1, u2} β α _inst_3 _inst_2 g s) -> (StrictAntiOn.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) (g x)) s)
Case conversion may be inaccurate. Consider using '#align strict_anti_on.mul' StrictAntiOn.mul'ₓ'. -/
@@ -2132,7 +2238,7 @@ theorem StrictAntiOn.mul' [CovariantClass α α (· * ·) (· < ·)]
/- warning: monotone.mul_strict_mono' -> Monotone.mul_strictMono' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {f : β -> α} {g : β -> α}, (Monotone.{u2, u1} β α _inst_3 _inst_2 f) -> (StrictMono.{u2, u1} β α _inst_3 _inst_2 g) -> (StrictMono.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {f : β -> α} {g : β -> α}, (Monotone.{u2, u1} β α _inst_3 _inst_2 f) -> (StrictMono.{u2, u1} β α _inst_3 _inst_2 g) -> (StrictMono.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14159 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14161 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14159 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14161) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14174 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14176 : α) => LT.lt.{u2} α (Preorder.toLT.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14174 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14176)] [_inst_5 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14196 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14198 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14196 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14198)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14211 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14213 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14211 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14213)] {f : β -> α} {g : β -> α}, (Monotone.{u1, u2} β α _inst_3 _inst_2 f) -> (StrictMono.{u1, u2} β α _inst_3 _inst_2 g) -> (StrictMono.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) (g x)))
Case conversion may be inaccurate. Consider using '#align monotone.mul_strict_mono' Monotone.mul_strictMono'ₓ'. -/
@@ -2148,7 +2254,7 @@ theorem Monotone.mul_strictMono' [CovariantClass α α (· * ·) (· < ·)]
/- warning: monotone_on.mul_strict_mono' -> MonotoneOn.mul_strictMono' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {f : β -> α} {g : β -> α}, (MonotoneOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (StrictMonoOn.{u2, u1} β α _inst_3 _inst_2 g s) -> (StrictMonoOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)) s)
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {f : β -> α} {g : β -> α}, (MonotoneOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (StrictMonoOn.{u2, u1} β α _inst_3 _inst_2 g s) -> (StrictMonoOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)) s)
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {s : Set.{u1} β} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14293 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14295 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14293 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14295) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14308 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14310 : α) => LT.lt.{u2} α (Preorder.toLT.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14308 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14310)] [_inst_5 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14330 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14332 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14330 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14332)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14345 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14347 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14345 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14347)] {f : β -> α} {g : β -> α}, (MonotoneOn.{u1, u2} β α _inst_3 _inst_2 f s) -> (StrictMonoOn.{u1, u2} β α _inst_3 _inst_2 g s) -> (StrictMonoOn.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) (g x)) s)
Case conversion may be inaccurate. Consider using '#align monotone_on.mul_strict_mono' MonotoneOn.mul_strictMono'ₓ'. -/
@@ -2164,7 +2270,7 @@ theorem MonotoneOn.mul_strictMono' [CovariantClass α α (· * ·) (· < ·)]
/- warning: antitone.mul_strict_anti' -> Antitone.mul_strictAnti' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {f : β -> α} {g : β -> α}, (Antitone.{u2, u1} β α _inst_3 _inst_2 f) -> (StrictAnti.{u2, u1} β α _inst_3 _inst_2 g) -> (StrictAnti.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)))
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {f : β -> α} {g : β -> α}, (Antitone.{u2, u1} β α _inst_3 _inst_2 f) -> (StrictAnti.{u2, u1} β α _inst_3 _inst_2 g) -> (StrictAnti.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)))
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14438 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14440 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14438 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14440) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14453 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14455 : α) => LT.lt.{u2} α (Preorder.toLT.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14453 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14455)] [_inst_5 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14475 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14477 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14475 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14477)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14490 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14492 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14490 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14492)] {f : β -> α} {g : β -> α}, (Antitone.{u1, u2} β α _inst_3 _inst_2 f) -> (StrictAnti.{u1, u2} β α _inst_3 _inst_2 g) -> (StrictAnti.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) (g x)))
Case conversion may be inaccurate. Consider using '#align antitone.mul_strict_anti' Antitone.mul_strictAnti'ₓ'. -/
@@ -2180,7 +2286,7 @@ theorem Antitone.mul_strictAnti' [CovariantClass α α (· * ·) (· < ·)]
/- warning: antitone_on.mul_strict_anti' -> AntitoneOn.mul_strictAnti' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {f : β -> α} {g : β -> α}, (AntitoneOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (StrictAntiOn.{u2, u1} β α _inst_3 _inst_2 g s) -> (StrictAntiOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)) s)
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] {f : β -> α} {g : β -> α}, (AntitoneOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (StrictAntiOn.{u2, u1} β α _inst_3 _inst_2 g s) -> (StrictAntiOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)) s)
but is expected to have type
forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {s : Set.{u1} β} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14572 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14574 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14572 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14574) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14587 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14589 : α) => LT.lt.{u2} α (Preorder.toLT.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14587 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14589)] [_inst_5 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14609 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14611 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14609 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14611)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14624 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14626 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14624 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14626)] {f : β -> α} {g : β -> α}, (AntitoneOn.{u1, u2} β α _inst_3 _inst_2 f s) -> (StrictAntiOn.{u1, u2} β α _inst_3 _inst_2 g s) -> (StrictAntiOn.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) (g x)) s)
Case conversion may be inaccurate. Consider using '#align antitone_on.mul_strict_anti' AntitoneOn.mul_strictAnti'ₓ'. -/
@@ -2196,7 +2302,12 @@ theorem AntitoneOn.mul_strictAnti' [CovariantClass α α (· * ·) (· < ·)]
variable [CovariantClass α α (· * ·) (· ≤ ·)] [CovariantClass α α (swap (· * ·)) (· < ·)]
-#print StrictMono.mul_monotone' /-
+/- warning: strict_mono.mul_monotone' -> StrictMono.mul_monotone' is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {g : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))], (StrictMono.{u2, u1} β α _inst_3 _inst_2 f) -> (Monotone.{u2, u1} β α _inst_3 _inst_2 g) -> (StrictMono.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)))
+but is expected to have type
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {g : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14810 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14812 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14810 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14812) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14825 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14827 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14825 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14827)] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14847 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14849 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14847 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14849)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14862 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14864 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14862 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14864)], (StrictMono.{u2, u1} β α _inst_3 _inst_2 f) -> (Monotone.{u2, u1} β α _inst_3 _inst_2 g) -> (StrictMono.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)))
+Case conversion may be inaccurate. Consider using '#align strict_mono.mul_monotone' StrictMono.mul_monotone'ₓ'. -/
/-- The product of a strictly monotone function and a monotone function is strictly monotone. -/
@[to_additive add_monotone
"The sum of a strictly monotone function and a monotone function is strictly monotone."]
@@ -2204,9 +2315,13 @@ theorem StrictMono.mul_monotone' (hf : StrictMono f) (hg : Monotone g) :
StrictMono fun x => f x * g x := fun x y h => mul_lt_mul_of_lt_of_le (hf h) (hg h.le)
#align strict_mono.mul_monotone' StrictMono.mul_monotone'
#align strict_mono.add_monotone StrictMono.add_monotone
--/
-#print StrictMonoOn.mul_monotone' /-
+/- warning: strict_mono_on.mul_monotone' -> StrictMonoOn.mul_monotone' is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {g : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))], (StrictMonoOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (MonotoneOn.{u2, u1} β α _inst_3 _inst_2 g s) -> (StrictMonoOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)) s)
+but is expected to have type
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {g : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14938 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14940 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14938 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14940) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14953 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14955 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14953 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14955)] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14975 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14977 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14975 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14977)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14990 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14992 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14990 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14992)], (StrictMonoOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (MonotoneOn.{u2, u1} β α _inst_3 _inst_2 g s) -> (StrictMonoOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)) s)
+Case conversion may be inaccurate. Consider using '#align strict_mono_on.mul_monotone' StrictMonoOn.mul_monotone'ₓ'. -/
/-- The product of a strictly monotone function and a monotone function is strictly monotone. -/
@[to_additive add_monotone
"The sum of a strictly monotone function and a monotone function is strictly monotone."]
@@ -2215,9 +2330,13 @@ theorem StrictMonoOn.mul_monotone' (hf : StrictMonoOn f s) (hg : MonotoneOn g s)
mul_lt_mul_of_lt_of_le (hf hx hy h) (hg hx hy h.le)
#align strict_mono_on.mul_monotone' StrictMonoOn.mul_monotone'
#align strict_mono_on.add_monotone StrictMonoOn.add_monotone
--/
-#print StrictAnti.mul_antitone' /-
+/- warning: strict_anti.mul_antitone' -> StrictAnti.mul_antitone' is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {g : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))], (StrictAnti.{u2, u1} β α _inst_3 _inst_2 f) -> (Antitone.{u2, u1} β α _inst_3 _inst_2 g) -> (StrictAnti.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)))
+but is expected to have type
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {g : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15077 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15079 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15077 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15079) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15092 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15094 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15092 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15094)] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15114 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15116 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15114 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15116)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15129 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15131 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15129 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15131)], (StrictAnti.{u2, u1} β α _inst_3 _inst_2 f) -> (Antitone.{u2, u1} β α _inst_3 _inst_2 g) -> (StrictAnti.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)))
+Case conversion may be inaccurate. Consider using '#align strict_anti.mul_antitone' StrictAnti.mul_antitone'ₓ'. -/
/-- The product of a strictly antitone function and a antitone function is strictly antitone. -/
@[to_additive add_antitone
"The sum of a strictly antitone function and a antitone function is strictly antitone."]
@@ -2225,9 +2344,13 @@ theorem StrictAnti.mul_antitone' (hf : StrictAnti f) (hg : Antitone g) :
StrictAnti fun x => f x * g x := fun x y h => mul_lt_mul_of_lt_of_le (hf h) (hg h.le)
#align strict_anti.mul_antitone' StrictAnti.mul_antitone'
#align strict_anti.add_antitone StrictAnti.add_antitone
--/
-#print StrictAntiOn.mul_antitone' /-
+/- warning: strict_anti_on.mul_antitone' -> StrictAntiOn.mul_antitone' is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {g : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))], (StrictAntiOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (AntitoneOn.{u2, u1} β α _inst_3 _inst_2 g s) -> (StrictAntiOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)) s)
+but is expected to have type
+ forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {g : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15205 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15207 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15205 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15207) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15220 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15222 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15220 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15222)] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15242 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15244 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15242 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15244)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15257 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15259 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15257 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15259)], (StrictAntiOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (AntitoneOn.{u2, u1} β α _inst_3 _inst_2 g s) -> (StrictAntiOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)) s)
+Case conversion may be inaccurate. Consider using '#align strict_anti_on.mul_antitone' StrictAntiOn.mul_antitone'ₓ'. -/
/-- The product of a strictly antitone function and a antitone function is strictly antitone. -/
@[to_additive add_antitone
"The sum of a strictly antitone function and a antitone function is strictly antitone."]
@@ -2236,25 +2359,32 @@ theorem StrictAntiOn.mul_antitone' (hf : StrictAntiOn f s) (hg : AntitoneOn g s)
mul_lt_mul_of_lt_of_le (hf hx hy h) (hg hx hy h.le)
#align strict_anti_on.mul_antitone' StrictAntiOn.mul_antitone'
#align strict_anti_on.add_antitone StrictAntiOn.add_antitone
--/
-#print cmp_mul_left' /-
+/- warning: cmp_mul_left' -> cmp_mul_left' is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_6 : Mul.{u1} α] [_inst_7 : LinearOrder.{u1} α] [_inst_8 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_6)) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_7))))))] (a : α) (b : α) (c : α), Eq.{1} Ordering (cmp.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_7))))) (fun (a : α) (b : α) => LT.lt.decidable.{u1} α _inst_7 a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_6) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_6) a c)) (cmp.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_7))))) (fun (a : α) (b : α) => LT.lt.decidable.{u1} α _inst_7 a b) b c)
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_6 : Mul.{u1} α] [_inst_7 : LinearOrder.{u1} α] [_inst_8 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15419 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15421 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_6) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15419 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15421) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15434 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15436 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_7)))))) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15434 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15436)] (a : α) (b : α) (c : α), Eq.{1} Ordering (cmp.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_7)))))) (fun (a : α) (b : α) => instDecidableLtToLTToPreorderToPartialOrder.{u1} α _inst_7 a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_6) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_6) a c)) (cmp.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_7)))))) (fun (a : α) (b : α) => instDecidableLtToLTToPreorderToPartialOrder.{u1} α _inst_7 a b) b c)
+Case conversion may be inaccurate. Consider using '#align cmp_mul_left' cmp_mul_left'ₓ'. -/
@[simp, to_additive cmp_add_left]
theorem cmp_mul_left' {α : Type _} [Mul α] [LinearOrder α] [CovariantClass α α (· * ·) (· < ·)]
(a b c : α) : cmp (a * b) (a * c) = cmp b c :=
(strictMono_id.const_mul' a).cmp_map_eq b c
#align cmp_mul_left' cmp_mul_left'
#align cmp_add_left cmp_add_left
--/
-#print cmp_mul_right' /-
+/- warning: cmp_mul_right' -> cmp_mul_right' is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_6 : Mul.{u1} α] [_inst_7 : LinearOrder.{u1} α] [_inst_8 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_6))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_7))))))] (a : α) (b : α) (c : α), Eq.{1} Ordering (cmp.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_7))))) (fun (a : α) (b : α) => LT.lt.decidable.{u1} α _inst_7 a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_6) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_6) b c)) (cmp.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_7))))) (fun (a : α) (b : α) => LT.lt.decidable.{u1} α _inst_7 a b) a b)
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_6 : Mul.{u1} α] [_inst_7 : LinearOrder.{u1} α] [_inst_8 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15587 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15589 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_6) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15587 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15589)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15602 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15604 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_7)))))) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15602 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15604)] (a : α) (b : α) (c : α), Eq.{1} Ordering (cmp.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_7)))))) (fun (a : α) (b : α) => instDecidableLtToLTToPreorderToPartialOrder.{u1} α _inst_7 a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_6) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_6) b c)) (cmp.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_7)))))) (fun (a : α) (b : α) => instDecidableLtToLTToPreorderToPartialOrder.{u1} α _inst_7 a b) a b)
+Case conversion may be inaccurate. Consider using '#align cmp_mul_right' cmp_mul_right'ₓ'. -/
@[simp, to_additive cmp_add_right]
theorem cmp_mul_right' {α : Type _} [Mul α] [LinearOrder α]
[CovariantClass α α (swap (· * ·)) (· < ·)] (a b c : α) : cmp (a * c) (b * c) = cmp a b :=
(strictMono_id.mul_const' c).cmp_map_eq a b
#align cmp_mul_right' cmp_mul_right'
#align cmp_add_right cmp_add_right
--/
end Mono
@@ -2294,26 +2424,34 @@ theorem mulLECancellable_one [Monoid α] [LE α] : MulLECancellable (1 : α) :=
namespace MulLECancellable
-#print MulLECancellable.Injective /-
+/- warning: mul_le_cancellable.injective -> MulLECancellable.Injective is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : PartialOrder.{u1} α] {a : α}, (MulLECancellable.{u1} α _inst_1 (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a) -> (Function.Injective.{succ u1, succ u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a))
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : PartialOrder.{u1} α] {a : α}, (MulLECancellable.{u1} α _inst_1 (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a) -> (Function.Injective.{succ u1, succ u1} α α ((fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15787 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15789 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15787 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.15789) a))
+Case conversion may be inaccurate. Consider using '#align mul_le_cancellable.injective MulLECancellable.Injectiveₓ'. -/
@[to_additive]
protected theorem Injective [Mul α] [PartialOrder α] {a : α} (ha : MulLECancellable a) :
Injective ((· * ·) a) := fun b c h => le_antisymm (ha h.le) (ha h.ge)
#align mul_le_cancellable.injective MulLECancellable.Injective
#align add_le_cancellable.injective AddLECancellable.Injective
--/
-#print MulLECancellable.inj /-
+/- warning: mul_le_cancellable.inj -> MulLECancellable.inj is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : PartialOrder.{u1} α] {a : α} {b : α} {c : α}, (MulLECancellable.{u1} α _inst_1 (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a) -> (Iff (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a c)) (Eq.{succ u1} α b c))
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : Mul.{u1} α] [_inst_2 : PartialOrder.{u1} α] {a : α} {b : α} {c : α}, (MulLECancellable.{u1} α _inst_1 (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a) -> (Iff (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a c)) (Eq.{succ u1} α b c))
+Case conversion may be inaccurate. Consider using '#align mul_le_cancellable.inj MulLECancellable.injₓ'. -/
@[to_additive]
protected theorem inj [Mul α] [PartialOrder α] {a b c : α} (ha : MulLECancellable a) :
a * b = a * c ↔ b = c :=
ha.Injective.eq_iff
#align mul_le_cancellable.inj MulLECancellable.inj
#align add_le_cancellable.inj AddLECancellable.inj
--/
/- warning: mul_le_cancellable.injective_left -> MulLECancellable.injective_left is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : CommSemigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] {a : α}, (MulLECancellable.{u1} α (Semigroup.toHasMul.{u1} α (CommSemigroup.toSemigroup.{u1} α _inst_1)) (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a) -> (Function.Injective.{succ u1, succ u1} α α (fun (_x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α (CommSemigroup.toSemigroup.{u1} α _inst_1))) _x a))
+ forall {α : Type.{u1}} [_inst_1 : CommSemigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] {a : α}, (MulLECancellable.{u1} α (Semigroup.toHasMul.{u1} α (CommSemigroup.toSemigroup.{u1} α _inst_1)) (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a) -> (Function.Injective.{succ u1, succ u1} α α (fun (_x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α (CommSemigroup.toSemigroup.{u1} α _inst_1))) _x a))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : CommSemigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] {a : α}, (MulLECancellable.{u1} α (Semigroup.toMul.{u1} α (CommSemigroup.toSemigroup.{u1} α _inst_1)) (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a) -> (Function.Injective.{succ u1, succ u1} α α (fun (_x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α (CommSemigroup.toSemigroup.{u1} α _inst_1))) _x a))
Case conversion may be inaccurate. Consider using '#align mul_le_cancellable.injective_left MulLECancellable.injective_leftₓ'. -/
@@ -2326,7 +2464,7 @@ protected theorem injective_left [CommSemigroup α] [PartialOrder α] {a : α}
/- warning: mul_le_cancellable.inj_left -> MulLECancellable.inj_left is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : CommSemigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] {a : α} {b : α} {c : α}, (MulLECancellable.{u1} α (Semigroup.toHasMul.{u1} α (CommSemigroup.toSemigroup.{u1} α _inst_1)) (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) c) -> (Iff (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α (CommSemigroup.toSemigroup.{u1} α _inst_1))) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α (CommSemigroup.toSemigroup.{u1} α _inst_1))) b c)) (Eq.{succ u1} α a b))
+ forall {α : Type.{u1}} [_inst_1 : CommSemigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] {a : α} {b : α} {c : α}, (MulLECancellable.{u1} α (Semigroup.toHasMul.{u1} α (CommSemigroup.toSemigroup.{u1} α _inst_1)) (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) c) -> (Iff (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α (CommSemigroup.toSemigroup.{u1} α _inst_1))) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α (CommSemigroup.toSemigroup.{u1} α _inst_1))) b c)) (Eq.{succ u1} α a b))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : CommSemigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] {a : α} {b : α} {c : α}, (MulLECancellable.{u1} α (Semigroup.toMul.{u1} α (CommSemigroup.toSemigroup.{u1} α _inst_1)) (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) c) -> (Iff (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α (CommSemigroup.toSemigroup.{u1} α _inst_1))) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α (CommSemigroup.toSemigroup.{u1} α _inst_1))) b c)) (Eq.{succ u1} α a b))
Case conversion may be inaccurate. Consider using '#align mul_le_cancellable.inj_left MulLECancellable.inj_leftₓ'. -/
@@ -2419,18 +2557,26 @@ section Bit
variable [Add α] [Preorder α]
-#print bit0_mono /-
+/- warning: bit0_mono -> bit0_mono is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : Add.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2))], Monotone.{u1, u1} α α _inst_2 _inst_2 (bit0.{u1} α _inst_1)
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : Add.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16556 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16558 : α) => HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16556 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16558) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16571 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16573 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16571 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16573)] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16593 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16595 : α) => HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16593 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16595)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16608 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16610 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16608 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16610)], Monotone.{u1, u1} α α _inst_2 _inst_2 (bit0.{u1} α _inst_1)
+Case conversion may be inaccurate. Consider using '#align bit0_mono bit0_monoₓ'. -/
theorem bit0_mono [CovariantClass α α (· + ·) (· ≤ ·)] [CovariantClass α α (swap (· + ·)) (· ≤ ·)] :
Monotone (bit0 : α → α) := fun a b h => add_le_add h h
#align bit0_mono bit0_mono
--/
-#print bit0_strictMono /-
+/- warning: bit0_strict_mono -> bit0_strictMono is a dubious translation:
+lean 3 declaration is
+ forall {α : Type.{u1}} [_inst_1 : Add.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2))], StrictMono.{u1, u1} α α _inst_2 _inst_2 (bit0.{u1} α _inst_1)
+but is expected to have type
+ forall {α : Type.{u1}} [_inst_1 : Add.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16654 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16656 : α) => HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16654 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16656) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16669 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16671 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16669 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16671)] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16691 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16693 : α) => HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16691 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16693)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16706 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16708 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16706 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16708)], StrictMono.{u1, u1} α α _inst_2 _inst_2 (bit0.{u1} α _inst_1)
+Case conversion may be inaccurate. Consider using '#align bit0_strict_mono bit0_strictMonoₓ'. -/
theorem bit0_strictMono [CovariantClass α α (· + ·) (· < ·)]
[CovariantClass α α (swap (· + ·)) (· < ·)] : StrictMono (bit0 : α → α) := fun a b h =>
add_lt_add h h
#align bit0_strict_mono bit0_strictMono
--/
end Bit
mathlib commit https://github.com/leanprover-community/mathlib/commit/36b8aa61ea7c05727161f96a0532897bd72aedab
@@ -384,7 +384,7 @@ variable [LE α]
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α _inst_2)] {a : α} {b : α}, (LE.le.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LE.le.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3034 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3036 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3034 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3036) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3049 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3051 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3049 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3051)] {a : α} {b : α}, (LE.le.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LE.le.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3032 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3034 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3032 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3034) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3047 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3049 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3047 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3049)] {a : α} {b : α}, (LE.le.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LE.le.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
Case conversion may be inaccurate. Consider using '#align le_mul_of_one_le_right' le_mul_of_one_le_right'ₓ'. -/
@[to_additive le_add_of_nonneg_right]
theorem le_mul_of_one_le_right' [CovariantClass α α (· * ·) (· ≤ ·)] {a b : α} (h : 1 ≤ b) :
@@ -400,7 +400,7 @@ theorem le_mul_of_one_le_right' [CovariantClass α α (· * ·) (· ≤ ·)] {a
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α _inst_2)] {a : α} {b : α}, (LE.le.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) a)
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3126 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3128 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3126 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3128) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3141 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3143 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3141 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3143)] {a : α} {b : α}, (LE.le.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) a)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3124 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3126 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3124 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3126) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3139 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3141 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3139 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3141)] {a : α} {b : α}, (LE.le.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) a)
Case conversion may be inaccurate. Consider using '#align mul_le_of_le_one_right' mul_le_of_le_one_right'ₓ'. -/
@[to_additive add_le_of_nonpos_right]
theorem mul_le_of_le_one_right' [CovariantClass α α (· * ·) (· ≤ ·)] {a b : α} (h : b ≤ 1) :
@@ -416,7 +416,7 @@ theorem mul_le_of_le_one_right' [CovariantClass α α (· * ·) (· ≤ ·)] {a
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α _inst_2)] {a : α} {b : α}, (LE.le.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LE.le.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b a))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3218 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3220 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3218 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3220)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3233 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3235 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3233 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3235)] {a : α} {b : α}, (LE.le.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LE.le.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b a))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3216 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3218 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3216 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3218)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3231 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3233 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3231 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3233)] {a : α} {b : α}, (LE.le.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LE.le.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b a))
Case conversion may be inaccurate. Consider using '#align le_mul_of_one_le_left' le_mul_of_one_le_left'ₓ'. -/
@[to_additive le_add_of_nonneg_left]
theorem le_mul_of_one_le_left' [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b : α} (h : 1 ≤ b) :
@@ -432,7 +432,7 @@ theorem le_mul_of_one_le_left' [CovariantClass α α (swap (· * ·)) (· ≤ ·
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α _inst_2)] {a : α} {b : α}, (LE.le.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b a) a)
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3313 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3315 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3313 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3315)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3328 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3330 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3328 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3330)] {a : α} {b : α}, (LE.le.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b a) a)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3311 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3313 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3311 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3313)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3326 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3328 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3326 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3328)] {a : α} {b : α}, (LE.le.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b a) a)
Case conversion may be inaccurate. Consider using '#align mul_le_of_le_one_left' mul_le_of_le_one_left'ₓ'. -/
@[to_additive add_le_of_nonpos_left]
theorem mul_le_of_le_one_left' [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b : α} (h : b ≤ 1) :
@@ -448,7 +448,7 @@ theorem mul_le_of_le_one_left' [CovariantClass α α (swap (· * ·)) (· ≤ ·
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α _inst_2)] {a : α} {b : α}, (LE.le.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b)) -> (LE.le.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b)
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3402 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3404 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3402 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3404) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3417 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3419 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3417 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3419)] {a : α} {b : α}, (LE.le.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b)) -> (LE.le.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3400 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3402 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3400 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3402) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3415 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3417 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3415 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3417)] {a : α} {b : α}, (LE.le.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b)) -> (LE.le.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b)
Case conversion may be inaccurate. Consider using '#align one_le_of_le_mul_right one_le_of_le_mul_rightₓ'. -/
@[to_additive]
theorem one_le_of_le_mul_right [ContravariantClass α α (· * ·) (· ≤ ·)] {a b : α} (h : a ≤ a * b) :
@@ -461,7 +461,7 @@ theorem one_le_of_le_mul_right [ContravariantClass α α (· * ·) (· ≤ ·)]
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α _inst_2)] {a : α} {b : α}, (LE.le.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) a) -> (LE.le.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3468 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3470 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3468 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3470) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3483 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3485 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3483 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3485)] {a : α} {b : α}, (LE.le.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) a) -> (LE.le.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3466 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3468 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3466 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3468) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3481 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3483 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3481 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3483)] {a : α} {b : α}, (LE.le.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) a) -> (LE.le.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align le_one_of_mul_le_right le_one_of_mul_le_rightₓ'. -/
@[to_additive]
theorem le_one_of_mul_le_right [ContravariantClass α α (· * ·) (· ≤ ·)] {a b : α} (h : a * b ≤ a) :
@@ -474,7 +474,7 @@ theorem le_one_of_mul_le_right [ContravariantClass α α (· * ·) (· ≤ ·)]
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α _inst_2)] {a : α} {b : α}, (LE.le.{u1} α _inst_2 b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b)) -> (LE.le.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a)
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3537 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3539 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3537 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3539)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3552 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3554 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3552 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3554)] {a : α} {b : α}, (LE.le.{u1} α _inst_2 b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b)) -> (LE.le.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3535 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3537 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3535 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3537)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3550 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3552 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3550 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3552)] {a : α} {b : α}, (LE.le.{u1} α _inst_2 b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b)) -> (LE.le.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a)
Case conversion may be inaccurate. Consider using '#align one_le_of_le_mul_left one_le_of_le_mul_leftₓ'. -/
@[to_additive]
theorem one_le_of_le_mul_left [ContravariantClass α α (swap (· * ·)) (· ≤ ·)] {a b : α}
@@ -487,7 +487,7 @@ theorem one_le_of_le_mul_left [ContravariantClass α α (swap (· * ·)) (· ≤
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α _inst_2)] {a : α} {b : α}, (LE.le.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) b) -> (LE.le.{u1} α _inst_2 a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3606 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3608 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3606 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3608)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3621 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3623 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3621 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3623)] {a : α} {b : α}, (LE.le.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) b) -> (LE.le.{u1} α _inst_2 a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3604 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3606 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3604 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3606)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3619 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3621 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3619 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3621)] {a : α} {b : α}, (LE.le.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) b) -> (LE.le.{u1} α _inst_2 a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align le_one_of_mul_le_left le_one_of_mul_le_leftₓ'. -/
@[to_additive]
theorem le_one_of_mul_le_left [ContravariantClass α α (swap (· * ·)) (· ≤ ·)] {a b : α}
@@ -500,7 +500,7 @@ theorem le_one_of_mul_le_left [ContravariantClass α α (swap (· * ·)) (· ≤
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α _inst_2)] [_inst_4 : ContravariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α _inst_2)] (a : α) {b : α}, Iff (LE.le.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b)) (LE.le.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b)
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3672 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3674 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3672 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3674) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3687 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3689 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3687 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3689)] [_inst_4 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3706 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3708 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3706 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3708) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3721 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3723 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3721 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3723)] (a : α) {b : α}, Iff (LE.le.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b)) (LE.le.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3670 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3672 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3670 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3672) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3685 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3687 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3685 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3687)] [_inst_4 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3704 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3706 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3704 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3706) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3719 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3721 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3719 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3721)] (a : α) {b : α}, Iff (LE.le.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b)) (LE.le.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b)
Case conversion may be inaccurate. Consider using '#align le_mul_iff_one_le_right' le_mul_iff_one_le_right'ₓ'. -/
@[simp, to_additive le_add_iff_nonneg_right]
theorem le_mul_iff_one_le_right' [CovariantClass α α (· * ·) (· ≤ ·)]
@@ -513,7 +513,7 @@ theorem le_mul_iff_one_le_right' [CovariantClass α α (· * ·) (· ≤ ·)]
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α _inst_2)] [_inst_4 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α _inst_2)] (a : α) {b : α}, Iff (LE.le.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b a)) (LE.le.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b)
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3806 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3808 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3806 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3808)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3821 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3823 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3821 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3823)] [_inst_4 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3843 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3845 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3843 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3845)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3858 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3860 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3858 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3860)] (a : α) {b : α}, Iff (LE.le.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b a)) (LE.le.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3804 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3806 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3804 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3806)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3819 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3821 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3819 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3821)] [_inst_4 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3841 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3843 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3841 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3843)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3856 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3858 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3856 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3858)] (a : α) {b : α}, Iff (LE.le.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b a)) (LE.le.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b)
Case conversion may be inaccurate. Consider using '#align le_mul_iff_one_le_left' le_mul_iff_one_le_left'ₓ'. -/
@[simp, to_additive le_add_iff_nonneg_left]
theorem le_mul_iff_one_le_left' [CovariantClass α α (swap (· * ·)) (· ≤ ·)]
@@ -526,7 +526,7 @@ theorem le_mul_iff_one_le_left' [CovariantClass α α (swap (· * ·)) (· ≤
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α _inst_2)] [_inst_4 : ContravariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α _inst_2)] (a : α) {b : α}, Iff (LE.le.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) a) (LE.le.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3940 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3942 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3940 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3942) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3955 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3957 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3955 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3957)] [_inst_4 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3974 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3976 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3974 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3976) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3989 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3991 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3989 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3991)] (a : α) {b : α}, Iff (LE.le.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) a) (LE.le.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3938 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3940 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3938 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3940) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3953 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3955 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3953 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3955)] [_inst_4 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3972 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3974 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3972 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3974) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3987 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3989 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3987 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.3989)] (a : α) {b : α}, Iff (LE.le.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) a) (LE.le.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align mul_le_iff_le_one_right' mul_le_iff_le_one_right'ₓ'. -/
@[simp, to_additive add_le_iff_nonpos_right]
theorem mul_le_iff_le_one_right' [CovariantClass α α (· * ·) (· ≤ ·)]
@@ -539,7 +539,7 @@ theorem mul_le_iff_le_one_right' [CovariantClass α α (· * ·) (· ≤ ·)]
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α _inst_2)] [_inst_4 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α _inst_2)] {a : α} {b : α}, Iff (LE.le.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) b) (LE.le.{u1} α _inst_2 a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4074 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4076 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4074 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4076)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4089 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4091 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4089 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4091)] [_inst_4 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4111 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4113 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4111 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4113)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4126 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4128 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4126 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4128)] {a : α} {b : α}, Iff (LE.le.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) b) (LE.le.{u1} α _inst_2 a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LE.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4072 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4074 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4072 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4074)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4087 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4089 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4087 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4089)] [_inst_4 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4109 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4111 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4109 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4111)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4124 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4126 : α) => LE.le.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4124 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4126)] {a : α} {b : α}, Iff (LE.le.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) b) (LE.le.{u1} α _inst_2 a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align mul_le_iff_le_one_left' mul_le_iff_le_one_left'ₓ'. -/
@[simp, to_additive add_le_iff_nonpos_left]
theorem mul_le_iff_le_one_left' [CovariantClass α α (swap (· * ·)) (· ≤ ·)]
@@ -558,7 +558,7 @@ variable [LT α]
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α _inst_2)] (a : α) {b : α}, (LT.lt.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4220 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4222 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4220 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4222) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4235 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4237 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4235 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4237)] (a : α) {b : α}, (LT.lt.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4218 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4220 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4218 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4220) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4233 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4235 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4233 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4235)] (a : α) {b : α}, (LT.lt.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
Case conversion may be inaccurate. Consider using '#align lt_mul_of_one_lt_right' lt_mul_of_one_lt_right'ₓ'. -/
@[to_additive lt_add_of_pos_right]
theorem lt_mul_of_one_lt_right' [CovariantClass α α (· * ·) (· < ·)] (a : α) {b : α} (h : 1 < b) :
@@ -574,7 +574,7 @@ theorem lt_mul_of_one_lt_right' [CovariantClass α α (· * ·) (· < ·)] (a :
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α _inst_2)] (a : α) {b : α}, (LT.lt.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) a)
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4312 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4314 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4312 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4314) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4327 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4329 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4327 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4329)] (a : α) {b : α}, (LT.lt.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) a)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4310 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4312 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4310 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4312) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4325 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4327 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4325 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4327)] (a : α) {b : α}, (LT.lt.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) a)
Case conversion may be inaccurate. Consider using '#align mul_lt_of_lt_one_right' mul_lt_of_lt_one_right'ₓ'. -/
@[to_additive add_lt_of_neg_right]
theorem mul_lt_of_lt_one_right' [CovariantClass α α (· * ·) (· < ·)] (a : α) {b : α} (h : b < 1) :
@@ -590,7 +590,7 @@ theorem mul_lt_of_lt_one_right' [CovariantClass α α (· * ·) (· < ·)] (a :
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α _inst_2)] (a : α) {b : α}, (LT.lt.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b a))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4404 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4406 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4404 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4406)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4419 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4421 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4419 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4421)] (a : α) {b : α}, (LT.lt.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b a))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4402 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4404 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4402 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4404)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4417 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4419 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4417 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4419)] (a : α) {b : α}, (LT.lt.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b a))
Case conversion may be inaccurate. Consider using '#align lt_mul_of_one_lt_left' lt_mul_of_one_lt_left'ₓ'. -/
@[to_additive lt_add_of_pos_left]
theorem lt_mul_of_one_lt_left' [CovariantClass α α (swap (· * ·)) (· < ·)] (a : α) {b : α}
@@ -606,7 +606,7 @@ theorem lt_mul_of_one_lt_left' [CovariantClass α α (swap (· * ·)) (· < ·)]
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α _inst_2)] (a : α) {b : α}, (LT.lt.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b a) a)
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4499 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4501 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4499 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4501)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4514 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4516 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4514 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4516)] (a : α) {b : α}, (LT.lt.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b a) a)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4497 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4499 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4497 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4499)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4512 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4514 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4512 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4514)] (a : α) {b : α}, (LT.lt.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b a) a)
Case conversion may be inaccurate. Consider using '#align mul_lt_of_lt_one_left' mul_lt_of_lt_one_left'ₓ'. -/
@[to_additive add_lt_of_neg_left]
theorem mul_lt_of_lt_one_left' [CovariantClass α α (swap (· * ·)) (· < ·)] (a : α) {b : α}
@@ -622,7 +622,7 @@ theorem mul_lt_of_lt_one_left' [CovariantClass α α (swap (· * ·)) (· < ·)]
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α _inst_2)] {a : α} {b : α}, (LT.lt.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b)) -> (LT.lt.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b)
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4588 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4590 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4588 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4590) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4603 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4605 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4603 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4605)] {a : α} {b : α}, (LT.lt.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b)) -> (LT.lt.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4586 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4588 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4586 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4588) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4601 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4603 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4601 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4603)] {a : α} {b : α}, (LT.lt.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b)) -> (LT.lt.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b)
Case conversion may be inaccurate. Consider using '#align one_lt_of_lt_mul_right one_lt_of_lt_mul_rightₓ'. -/
@[to_additive]
theorem one_lt_of_lt_mul_right [ContravariantClass α α (· * ·) (· < ·)] {a b : α} (h : a < a * b) :
@@ -635,7 +635,7 @@ theorem one_lt_of_lt_mul_right [ContravariantClass α α (· * ·) (· < ·)] {a
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α _inst_2)] {a : α} {b : α}, (LT.lt.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) a) -> (LT.lt.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4654 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4656 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4654 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4656) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4669 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4671 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4669 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4671)] {a : α} {b : α}, (LT.lt.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) a) -> (LT.lt.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4652 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4654 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4652 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4654) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4667 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4669 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4667 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4669)] {a : α} {b : α}, (LT.lt.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) a) -> (LT.lt.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align lt_one_of_mul_lt_right lt_one_of_mul_lt_rightₓ'. -/
@[to_additive]
theorem lt_one_of_mul_lt_right [ContravariantClass α α (· * ·) (· < ·)] {a b : α} (h : a * b < a) :
@@ -648,7 +648,7 @@ theorem lt_one_of_mul_lt_right [ContravariantClass α α (· * ·) (· < ·)] {a
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α _inst_2)] {a : α} {b : α}, (LT.lt.{u1} α _inst_2 b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b)) -> (LT.lt.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a)
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4723 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4725 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4723 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4725)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4738 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4740 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4738 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4740)] {a : α} {b : α}, (LT.lt.{u1} α _inst_2 b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b)) -> (LT.lt.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4721 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4723 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4721 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4723)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4736 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4738 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4736 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4738)] {a : α} {b : α}, (LT.lt.{u1} α _inst_2 b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b)) -> (LT.lt.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a)
Case conversion may be inaccurate. Consider using '#align one_lt_of_lt_mul_left one_lt_of_lt_mul_leftₓ'. -/
@[to_additive]
theorem one_lt_of_lt_mul_left [ContravariantClass α α (swap (· * ·)) (· < ·)] {a b : α}
@@ -661,7 +661,7 @@ theorem one_lt_of_lt_mul_left [ContravariantClass α α (swap (· * ·)) (· <
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α _inst_2)] {a : α} {b : α}, (LT.lt.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) b) -> (LT.lt.{u1} α _inst_2 a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4792 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4794 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4792 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4794)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4807 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4809 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4807 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4809)] {a : α} {b : α}, (LT.lt.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) b) -> (LT.lt.{u1} α _inst_2 a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4790 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4792 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4790 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4792)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4805 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4807 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4805 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4807)] {a : α} {b : α}, (LT.lt.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) b) -> (LT.lt.{u1} α _inst_2 a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align lt_one_of_mul_lt_left lt_one_of_mul_lt_leftₓ'. -/
@[to_additive]
theorem lt_one_of_mul_lt_left [ContravariantClass α α (swap (· * ·)) (· < ·)] {a b : α}
@@ -674,7 +674,7 @@ theorem lt_one_of_mul_lt_left [ContravariantClass α α (swap (· * ·)) (· <
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α _inst_2)] [_inst_4 : ContravariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α _inst_2)] (a : α) {b : α}, Iff (LT.lt.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b)) (LT.lt.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b)
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4858 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4860 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4858 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4860) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4873 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4875 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4873 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4875)] [_inst_4 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4892 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4894 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4892 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4894) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4907 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4909 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4907 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4909)] (a : α) {b : α}, Iff (LT.lt.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b)) (LT.lt.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4856 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4858 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4856 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4858) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4871 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4873 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4871 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4873)] [_inst_4 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4890 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4892 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4890 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4892) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4905 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4907 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4905 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4907)] (a : α) {b : α}, Iff (LT.lt.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b)) (LT.lt.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b)
Case conversion may be inaccurate. Consider using '#align lt_mul_iff_one_lt_right' lt_mul_iff_one_lt_right'ₓ'. -/
@[simp, to_additive lt_add_iff_pos_right]
theorem lt_mul_iff_one_lt_right' [CovariantClass α α (· * ·) (· < ·)]
@@ -687,7 +687,7 @@ theorem lt_mul_iff_one_lt_right' [CovariantClass α α (· * ·) (· < ·)]
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α _inst_2)] [_inst_4 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α _inst_2)] (a : α) {b : α}, Iff (LT.lt.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b a)) (LT.lt.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b)
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4992 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4994 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4992 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4994)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5007 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5009 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5007 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5009)] [_inst_4 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5029 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5031 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5029 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5031)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5044 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5046 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5044 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5046)] (a : α) {b : α}, Iff (LT.lt.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b a)) (LT.lt.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4990 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4992 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4990 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.4992)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5005 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5007 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5005 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5007)] [_inst_4 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5027 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5029 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5027 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5029)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5042 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5044 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5042 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5044)] (a : α) {b : α}, Iff (LT.lt.{u1} α _inst_2 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b a)) (LT.lt.{u1} α _inst_2 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b)
Case conversion may be inaccurate. Consider using '#align lt_mul_iff_one_lt_left' lt_mul_iff_one_lt_left'ₓ'. -/
@[simp, to_additive lt_add_iff_pos_left]
theorem lt_mul_iff_one_lt_left' [CovariantClass α α (swap (· * ·)) (· < ·)]
@@ -700,7 +700,7 @@ theorem lt_mul_iff_one_lt_left' [CovariantClass α α (swap (· * ·)) (· < ·)
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α _inst_2)] [_inst_4 : ContravariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α _inst_2)] {a : α} {b : α}, Iff (LT.lt.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) a) (LT.lt.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5126 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5128 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5126 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5128) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5141 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5143 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5141 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5143)] [_inst_4 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5160 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5162 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5160 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5162) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5175 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5177 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5175 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5177)] {a : α} {b : α}, Iff (LT.lt.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) a) (LT.lt.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5124 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5126 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5124 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5126) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5139 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5141 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5139 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5141)] [_inst_4 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5158 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5160 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5158 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5160) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5173 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5175 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5173 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5175)] {a : α} {b : α}, Iff (LT.lt.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) a) (LT.lt.{u1} α _inst_2 b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align mul_lt_iff_lt_one_left' mul_lt_iff_lt_one_left'ₓ'. -/
@[simp, to_additive add_lt_iff_neg_left]
theorem mul_lt_iff_lt_one_left' [CovariantClass α α (· * ·) (· < ·)]
@@ -713,7 +713,7 @@ theorem mul_lt_iff_lt_one_left' [CovariantClass α α (· * ·) (· < ·)]
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α _inst_2)] [_inst_4 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α _inst_2)] {a : α} (b : α), Iff (LT.lt.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) b) (LT.lt.{u1} α _inst_2 a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5260 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5262 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5260 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5262)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5275 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5277 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5275 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5277)] [_inst_4 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5297 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5299 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5297 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5299)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5312 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5314 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5312 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5314)] {a : α} (b : α), Iff (LT.lt.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) b) (LT.lt.{u1} α _inst_2 a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LT.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5258 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5260 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5258 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5260)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5273 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5275 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5273 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5275)] [_inst_4 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5295 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5297 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5295 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5297)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5310 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5312 : α) => LT.lt.{u1} α _inst_2 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5310 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5312)] {a : α} (b : α), Iff (LT.lt.{u1} α _inst_2 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) b) (LT.lt.{u1} α _inst_2 a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align mul_lt_iff_lt_one_right' mul_lt_iff_lt_one_right'ₓ'. -/
@[simp, to_additive add_lt_iff_neg_right]
theorem mul_lt_iff_lt_one_right' [CovariantClass α α (swap (· * ·)) (· < ·)]
@@ -736,7 +736,7 @@ which assume left covariance. -/
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b a) c)
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5407 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5409 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5407 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5409) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5422 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5424 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5422 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5424)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b a) c)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5405 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5407 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5405 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5407) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5420 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5422 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5420 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5422)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b a) c)
Case conversion may be inaccurate. Consider using '#align mul_le_of_le_of_le_one mul_le_of_le_of_le_oneₓ'. -/
@[to_additive]
theorem mul_le_of_le_of_le_one [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (hbc : b ≤ c)
@@ -753,7 +753,7 @@ theorem mul_le_of_le_of_le_one [CovariantClass α α (· * ·) (· ≤ ·)] {a b
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b a) c)
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5517 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5519 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5517 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5519) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5532 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5534 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5532 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5534)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b a) c)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5515 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5517 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5515 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5517) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5530 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5532 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5530 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5532)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b a) c)
Case conversion may be inaccurate. Consider using '#align mul_lt_of_le_of_lt_one mul_lt_of_le_of_lt_oneₓ'. -/
@[to_additive]
theorem mul_lt_of_le_of_lt_one [CovariantClass α α (· * ·) (· < ·)] {a b c : α} (hbc : b ≤ c)
@@ -770,7 +770,7 @@ theorem mul_lt_of_le_of_lt_one [CovariantClass α α (· * ·) (· < ·)] {a b c
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b a) c)
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5627 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5629 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5627 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5629) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5642 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5644 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5642 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5644)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b a) c)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5625 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5627 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5625 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5627) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5640 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5642 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5640 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5642)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b a) c)
Case conversion may be inaccurate. Consider using '#align mul_lt_of_lt_of_le_one mul_lt_of_lt_of_le_oneₓ'. -/
@[to_additive]
theorem mul_lt_of_lt_of_le_one [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (hbc : b < c)
@@ -787,7 +787,7 @@ theorem mul_lt_of_lt_of_le_one [CovariantClass α α (· * ·) (· ≤ ·)] {a b
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b a) c)
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5737 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5739 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5737 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5739) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5752 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5754 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5752 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5754)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b a) c)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5735 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5737 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5735 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5737) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5750 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5752 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5750 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5752)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b a) c)
Case conversion may be inaccurate. Consider using '#align mul_lt_of_lt_of_lt_one mul_lt_of_lt_of_lt_oneₓ'. -/
@[to_additive]
theorem mul_lt_of_lt_of_lt_one [CovariantClass α α (· * ·) (· < ·)] {a b c : α} (hbc : b < c)
@@ -804,7 +804,7 @@ theorem mul_lt_of_lt_of_lt_one [CovariantClass α α (· * ·) (· < ·)] {a b c
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b a) c)
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5847 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5849 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5847 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5849) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5862 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5864 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5862 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5864)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b a) c)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5845 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5847 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5845 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5847) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5860 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5862 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5860 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5862)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b a) c)
Case conversion may be inaccurate. Consider using '#align mul_lt_of_lt_of_lt_one' mul_lt_of_lt_of_lt_one'ₓ'. -/
@[to_additive]
theorem mul_lt_of_lt_of_lt_one' [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (hbc : b < c)
@@ -817,7 +817,7 @@ theorem mul_lt_of_lt_of_lt_one' [CovariantClass α α (· * ·) (· ≤ ·)] {a
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5918 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5920 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5918 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5920) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5933 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5935 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5933 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5935)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5916 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5918 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5916 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5918) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5931 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5933 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5931 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5933)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align left.mul_le_one Left.mul_le_oneₓ'. -/
/-- Assumes left covariance.
The lemma assuming right covariance is `right.mul_le_one`. -/
@@ -833,7 +833,7 @@ theorem Left.mul_le_one [CovariantClass α α (· * ·) (· ≤ ·)] {a b : α}
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5989 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5991 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5989 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5991) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6004 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6006 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6004 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6006)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5987 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5989 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5987 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5989) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6002 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6004 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6002 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6004)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align left.mul_lt_one_of_le_of_lt Left.mul_lt_one_of_le_of_ltₓ'. -/
/-- Assumes left covariance.
The lemma assuming right covariance is `right.mul_lt_one_of_le_of_lt`. -/
@@ -849,7 +849,7 @@ theorem Left.mul_lt_one_of_le_of_lt [CovariantClass α α (· * ·) (· < ·)] {
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6060 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6062 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6060 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6062) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6075 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6077 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6075 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6077)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6058 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6060 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6058 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6060) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6073 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6075 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6073 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6075)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align left.mul_lt_one_of_lt_of_le Left.mul_lt_one_of_lt_of_leₓ'. -/
/-- Assumes left covariance.
The lemma assuming right covariance is `right.mul_lt_one_of_lt_of_le`. -/
@@ -865,7 +865,7 @@ theorem Left.mul_lt_one_of_lt_of_le [CovariantClass α α (· * ·) (· ≤ ·)]
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6131 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6133 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6131 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6133) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6146 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6148 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6146 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6148)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6129 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6131 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6129 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6131) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6144 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6146 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6144 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6146)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align left.mul_lt_one Left.mul_lt_oneₓ'. -/
/-- Assumes left covariance.
The lemma assuming right covariance is `right.mul_lt_one`. -/
@@ -880,7 +880,7 @@ theorem Left.mul_lt_one [CovariantClass α α (· * ·) (· < ·)] {a b : α} (h
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6202 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6204 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6202 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6204) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6217 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6219 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6217 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6219)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6200 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6202 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6200 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6202) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6215 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6217 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6215 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6217)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align left.mul_lt_one' Left.mul_lt_one'ₓ'. -/
/-- Assumes left covariance.
The lemma assuming right covariance is `right.mul_lt_one'`. -/
@@ -899,7 +899,7 @@ which assume left covariance. -/
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) c a))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6271 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6273 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6271 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6273) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6286 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6288 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6286 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6288)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) c a))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6269 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6271 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6269 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6271) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6284 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6286 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6284 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6286)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) c a))
Case conversion may be inaccurate. Consider using '#align le_mul_of_le_of_one_le le_mul_of_le_of_one_leₓ'. -/
@[to_additive]
theorem le_mul_of_le_of_one_le [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (hbc : b ≤ c)
@@ -916,7 +916,7 @@ theorem le_mul_of_le_of_one_le [CovariantClass α α (· * ·) (· ≤ ·)] {a b
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) c a))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6384 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6386 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6384 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6386) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6399 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6401 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6399 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6401)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) c a))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6382 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6384 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6382 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6384) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6397 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6399 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6397 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6399)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) c a))
Case conversion may be inaccurate. Consider using '#align lt_mul_of_le_of_one_lt lt_mul_of_le_of_one_ltₓ'. -/
@[to_additive]
theorem lt_mul_of_le_of_one_lt [CovariantClass α α (· * ·) (· < ·)] {a b c : α} (hbc : b ≤ c)
@@ -933,7 +933,7 @@ theorem lt_mul_of_le_of_one_lt [CovariantClass α α (· * ·) (· < ·)] {a b c
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) c a))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6497 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6499 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6497 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6499) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6512 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6514 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6512 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6514)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) c a))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6495 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6497 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6495 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6497) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6510 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6512 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6510 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6512)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) c a))
Case conversion may be inaccurate. Consider using '#align lt_mul_of_lt_of_one_le lt_mul_of_lt_of_one_leₓ'. -/
@[to_additive]
theorem lt_mul_of_lt_of_one_le [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (hbc : b < c)
@@ -950,7 +950,7 @@ theorem lt_mul_of_lt_of_one_le [CovariantClass α α (· * ·) (· ≤ ·)] {a b
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) c a))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6610 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6612 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6610 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6612) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6625 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6627 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6625 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6627)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) c a))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6608 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6610 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6608 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6610) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6623 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6625 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6623 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6625)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) c a))
Case conversion may be inaccurate. Consider using '#align lt_mul_of_lt_of_one_lt lt_mul_of_lt_of_one_ltₓ'. -/
@[to_additive]
theorem lt_mul_of_lt_of_one_lt [CovariantClass α α (· * ·) (· < ·)] {a b c : α} (hbc : b < c)
@@ -967,7 +967,7 @@ theorem lt_mul_of_lt_of_one_lt [CovariantClass α α (· * ·) (· < ·)] {a b c
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) c a))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6723 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6725 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6723 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6725) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6738 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6740 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6738 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6740)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) c a))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6721 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6723 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6721 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6723) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6736 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6738 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6736 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6738)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) c a))
Case conversion may be inaccurate. Consider using '#align lt_mul_of_lt_of_one_lt' lt_mul_of_lt_of_one_lt'ₓ'. -/
@[to_additive]
theorem lt_mul_of_lt_of_one_lt' [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (hbc : b < c)
@@ -980,7 +980,7 @@ theorem lt_mul_of_lt_of_one_lt' [CovariantClass α α (· * ·) (· ≤ ·)] {a
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6794 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6796 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6794 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6796) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6809 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6811 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6809 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6811)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6792 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6794 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6792 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6794) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6807 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6809 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6807 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6809)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
Case conversion may be inaccurate. Consider using '#align left.one_le_mul Left.one_le_mulₓ'. -/
/-- Assumes left covariance.
The lemma assuming right covariance is `right.one_le_mul`. -/
@@ -996,7 +996,7 @@ theorem Left.one_le_mul [CovariantClass α α (· * ·) (· ≤ ·)] {a b : α}
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6865 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6867 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6865 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6867) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6880 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6882 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6880 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6882)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6863 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6865 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6863 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6865) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6878 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6880 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6878 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6880)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
Case conversion may be inaccurate. Consider using '#align left.one_lt_mul_of_le_of_lt Left.one_lt_mul_of_le_of_ltₓ'. -/
/-- Assumes left covariance.
The lemma assuming right covariance is `right.one_lt_mul_of_le_of_lt`. -/
@@ -1012,7 +1012,7 @@ theorem Left.one_lt_mul_of_le_of_lt [CovariantClass α α (· * ·) (· < ·)] {
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6936 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6938 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6936 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6938) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6951 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6953 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6951 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6953)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6934 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6936 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6934 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6936) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6949 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6951 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6949 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6951)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
Case conversion may be inaccurate. Consider using '#align left.one_lt_mul_of_lt_of_le Left.one_lt_mul_of_lt_of_leₓ'. -/
/-- Assumes left covariance.
The lemma assuming right covariance is `right.one_lt_mul_of_lt_of_le`. -/
@@ -1028,7 +1028,7 @@ theorem Left.one_lt_mul_of_lt_of_le [CovariantClass α α (· * ·) (· ≤ ·)]
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7007 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7009 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7007 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7009) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7022 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7024 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7022 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7024)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7005 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7007 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7005 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7007) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7020 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7022 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7020 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7022)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
Case conversion may be inaccurate. Consider using '#align left.one_lt_mul Left.one_lt_mulₓ'. -/
/-- Assumes left covariance.
The lemma assuming right covariance is `right.one_lt_mul`. -/
@@ -1044,7 +1044,7 @@ theorem Left.one_lt_mul [CovariantClass α α (· * ·) (· < ·)] {a b : α} (h
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7078 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7080 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7078 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7080) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7093 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7095 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7093 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7095)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7076 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7078 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7076 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7078) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7091 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7093 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7091 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7093)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
Case conversion may be inaccurate. Consider using '#align left.one_lt_mul' Left.one_lt_mul'ₓ'. -/
/-- Assumes left covariance.
The lemma assuming right covariance is `right.one_lt_mul'`. -/
@@ -1064,7 +1064,7 @@ which assume right covariance. -/
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) c)
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7150 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7152 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7150 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7152)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7165 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7167 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7165 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7167)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) c)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7148 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7150 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7148 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7150)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7163 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7165 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7163 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7165)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) c)
Case conversion may be inaccurate. Consider using '#align mul_le_of_le_one_of_le mul_le_of_le_one_of_leₓ'. -/
@[to_additive]
theorem mul_le_of_le_one_of_le [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α} (ha : a ≤ 1)
@@ -1081,7 +1081,7 @@ theorem mul_le_of_le_one_of_le [CovariantClass α α (swap (· * ·)) (· ≤ ·
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) c)
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7263 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7265 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7263 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7265)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7278 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7280 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7278 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7280)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) c)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7261 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7263 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7261 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7263)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7276 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7278 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7276 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7278)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) c)
Case conversion may be inaccurate. Consider using '#align mul_lt_of_lt_one_of_le mul_lt_of_lt_one_of_leₓ'. -/
@[to_additive]
theorem mul_lt_of_lt_one_of_le [CovariantClass α α (swap (· * ·)) (· < ·)] {a b c : α} (ha : a < 1)
@@ -1098,7 +1098,7 @@ theorem mul_lt_of_lt_one_of_le [CovariantClass α α (swap (· * ·)) (· < ·)]
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) c)
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7376 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7378 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7376 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7378)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7391 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7393 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7391 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7393)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) c)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7374 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7376 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7374 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7376)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7389 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7391 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7389 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7391)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) c)
Case conversion may be inaccurate. Consider using '#align mul_lt_of_le_one_of_lt mul_lt_of_le_one_of_ltₓ'. -/
@[to_additive]
theorem mul_lt_of_le_one_of_lt [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α} (ha : a ≤ 1)
@@ -1115,7 +1115,7 @@ theorem mul_lt_of_le_one_of_lt [CovariantClass α α (swap (· * ·)) (· ≤ ·
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) c)
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7489 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7491 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7489 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7491)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7504 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7506 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7504 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7506)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) c)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7487 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7489 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7487 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7489)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7502 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7504 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7502 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7504)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) c)
Case conversion may be inaccurate. Consider using '#align mul_lt_of_lt_one_of_lt mul_lt_of_lt_one_of_ltₓ'. -/
@[to_additive]
theorem mul_lt_of_lt_one_of_lt [CovariantClass α α (swap (· * ·)) (· < ·)] {a b c : α} (ha : a < 1)
@@ -1132,7 +1132,7 @@ theorem mul_lt_of_lt_one_of_lt [CovariantClass α α (swap (· * ·)) (· < ·)]
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) c)
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7602 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7604 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7602 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7604)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7617 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7619 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7617 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7619)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) c)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7600 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7602 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7600 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7602)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7615 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7617 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7615 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7617)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) c)
Case conversion may be inaccurate. Consider using '#align mul_lt_of_lt_one_of_lt' mul_lt_of_lt_one_of_lt'ₓ'. -/
@[to_additive]
theorem mul_lt_of_lt_one_of_lt' [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α} (ha : a < 1)
@@ -1145,7 +1145,7 @@ theorem mul_lt_of_lt_one_of_lt' [CovariantClass α α (swap (· * ·)) (· ≤
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7676 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7678 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7676 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7678)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7691 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7693 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7691 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7693)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7674 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7676 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7674 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7676)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7689 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7691 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7689 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7691)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align right.mul_le_one Right.mul_le_oneₓ'. -/
/-- Assumes right covariance.
The lemma assuming left covariance is `left.mul_le_one`. -/
@@ -1160,7 +1160,7 @@ theorem Right.mul_le_one [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7750 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7752 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7750 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7752)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7765 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7767 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7765 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7767)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7748 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7750 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7748 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7750)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7763 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7765 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7763 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7765)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align right.mul_lt_one_of_lt_of_le Right.mul_lt_one_of_lt_of_leₓ'. -/
/-- Assumes right covariance.
The lemma assuming left covariance is `left.mul_lt_one_of_lt_of_le`. -/
@@ -1176,7 +1176,7 @@ theorem Right.mul_lt_one_of_lt_of_le [CovariantClass α α (swap (· * ·)) (·
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7824 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7826 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7824 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7826)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7839 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7841 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7839 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7841)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7822 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7824 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7822 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7824)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7837 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7839 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7837 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7839)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align right.mul_lt_one_of_le_of_lt Right.mul_lt_one_of_le_of_ltₓ'. -/
/-- Assumes right covariance.
The lemma assuming left covariance is `left.mul_lt_one_of_le_of_lt`. -/
@@ -1192,7 +1192,7 @@ theorem Right.mul_lt_one_of_le_of_lt [CovariantClass α α (swap (· * ·)) (·
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7898 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7900 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7898 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7900)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7913 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7915 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7913 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7915)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7896 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7898 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7896 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7898)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7911 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7913 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7911 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7913)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align right.mul_lt_one Right.mul_lt_oneₓ'. -/
/-- Assumes right covariance.
The lemma assuming left covariance is `left.mul_lt_one`. -/
@@ -1207,7 +1207,7 @@ theorem Right.mul_lt_one [CovariantClass α α (swap (· * ·)) (· < ·)] {a b
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7972 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7974 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7972 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7974)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7987 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7989 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7987 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7989)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7970 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7972 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7970 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7972)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7985 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7987 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7985 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7987)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align right.mul_lt_one' Right.mul_lt_one'ₓ'. -/
/-- Assumes right covariance.
The lemma assuming left covariance is `left.mul_lt_one'`. -/
@@ -1226,7 +1226,7 @@ which assume right covariance. -/
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a c))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8044 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8046 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8044 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8046)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8059 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8061 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8059 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8061)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a c))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8042 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8044 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8042 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8044)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8057 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8059 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8057 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8059)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a c))
Case conversion may be inaccurate. Consider using '#align le_mul_of_one_le_of_le le_mul_of_one_le_of_leₓ'. -/
@[to_additive]
theorem le_mul_of_one_le_of_le [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α} (ha : 1 ≤ a)
@@ -1243,7 +1243,7 @@ theorem le_mul_of_one_le_of_le [CovariantClass α α (swap (· * ·)) (· ≤ ·
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a c))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8160 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8162 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8160 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8162)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8175 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8177 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8175 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8177)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a c))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8158 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8160 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8158 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8160)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8173 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8175 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8173 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8175)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a c))
Case conversion may be inaccurate. Consider using '#align lt_mul_of_one_lt_of_le lt_mul_of_one_lt_of_leₓ'. -/
@[to_additive]
theorem lt_mul_of_one_lt_of_le [CovariantClass α α (swap (· * ·)) (· < ·)] {a b c : α} (ha : 1 < a)
@@ -1260,7 +1260,7 @@ theorem lt_mul_of_one_lt_of_le [CovariantClass α α (swap (· * ·)) (· < ·)]
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a c))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8276 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8278 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8276 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8278)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8291 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8293 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8291 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8293)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a c))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8274 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8276 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8274 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8276)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8289 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8291 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8289 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8291)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a c))
Case conversion may be inaccurate. Consider using '#align lt_mul_of_one_le_of_lt lt_mul_of_one_le_of_ltₓ'. -/
@[to_additive]
theorem lt_mul_of_one_le_of_lt [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α} (ha : 1 ≤ a)
@@ -1277,7 +1277,7 @@ theorem lt_mul_of_one_le_of_lt [CovariantClass α α (swap (· * ·)) (· ≤ ·
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a c))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8392 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8394 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8392 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8394)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8407 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8409 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8407 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8409)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a c))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8390 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8392 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8390 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8392)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8405 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8407 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8405 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8407)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a c))
Case conversion may be inaccurate. Consider using '#align lt_mul_of_one_lt_of_lt lt_mul_of_one_lt_of_ltₓ'. -/
@[to_additive]
theorem lt_mul_of_one_lt_of_lt [CovariantClass α α (swap (· * ·)) (· < ·)] {a b c : α} (ha : 1 < a)
@@ -1294,7 +1294,7 @@ theorem lt_mul_of_one_lt_of_lt [CovariantClass α α (swap (· * ·)) (· < ·)]
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a c))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8508 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8510 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8508 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8510)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8523 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8525 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8523 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8525)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a c))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8506 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8508 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8506 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8508)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8521 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8523 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8521 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8523)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a c))
Case conversion may be inaccurate. Consider using '#align lt_mul_of_one_lt_of_lt' lt_mul_of_one_lt_of_lt'ₓ'. -/
@[to_additive]
theorem lt_mul_of_one_lt_of_lt' [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α} (ha : 1 < a)
@@ -1307,7 +1307,7 @@ theorem lt_mul_of_one_lt_of_lt' [CovariantClass α α (swap (· * ·)) (· ≤
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8582 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8584 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8582 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8584)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8597 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8599 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8597 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8599)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8580 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8582 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8580 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8582)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8595 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8597 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8595 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8597)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
Case conversion may be inaccurate. Consider using '#align right.one_le_mul Right.one_le_mulₓ'. -/
/-- Assumes right covariance.
The lemma assuming left covariance is `left.one_le_mul`. -/
@@ -1323,7 +1323,7 @@ theorem Right.one_le_mul [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8656 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8658 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8656 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8658)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8671 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8673 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8671 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8673)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8654 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8656 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8654 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8656)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8669 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8671 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8669 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8671)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
Case conversion may be inaccurate. Consider using '#align right.one_lt_mul_of_lt_of_le Right.one_lt_mul_of_lt_of_leₓ'. -/
/-- Assumes right covariance.
The lemma assuming left covariance is `left.one_lt_mul_of_lt_of_le`. -/
@@ -1339,7 +1339,7 @@ theorem Right.one_lt_mul_of_lt_of_le [CovariantClass α α (swap (· * ·)) (·
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8730 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8732 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8730 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8732)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8745 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8747 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8745 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8747)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8728 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8730 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8728 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8730)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8743 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8745 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8743 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8745)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
Case conversion may be inaccurate. Consider using '#align right.one_lt_mul_of_le_of_lt Right.one_lt_mul_of_le_of_ltₓ'. -/
/-- Assumes right covariance.
The lemma assuming left covariance is `left.one_lt_mul_of_le_of_lt`. -/
@@ -1355,7 +1355,7 @@ theorem Right.one_lt_mul_of_le_of_lt [CovariantClass α α (swap (· * ·)) (·
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8804 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8806 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8804 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8806)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8819 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8821 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8819 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8821)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8802 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8804 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8802 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8804)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8817 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8819 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8817 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8819)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
Case conversion may be inaccurate. Consider using '#align right.one_lt_mul Right.one_lt_mulₓ'. -/
/-- Assumes right covariance.
The lemma assuming left covariance is `left.one_lt_mul`. -/
@@ -1371,7 +1371,7 @@ theorem Right.one_lt_mul [CovariantClass α α (swap (· * ·)) (· < ·)] {a b
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8878 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8880 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8878 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8880)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8893 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8895 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8893 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8895)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8876 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8878 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8876 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8878)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8891 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8893 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8891 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8893)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
Case conversion may be inaccurate. Consider using '#align right.one_lt_mul' Right.one_lt_mul'ₓ'. -/
/-- Assumes right covariance.
The lemma assuming left covariance is `left.one_lt_mul'`. -/
@@ -1387,7 +1387,7 @@ theorem Right.one_lt_mul' [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5918 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5920 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5918 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5920) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5933 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5935 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5933 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5935)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5916 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5918 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5916 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5918) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5931 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5933 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5931 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5933)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align mul_le_one' mul_le_one'ₓ'. -/
alias Left.mul_le_one ← mul_le_one'
#align mul_le_one' mul_le_one'
@@ -1396,7 +1396,7 @@ alias Left.mul_le_one ← mul_le_one'
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5989 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5991 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5989 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5991) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6004 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6006 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6004 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6006)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5987 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5989 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5987 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.5989) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6002 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6004 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6002 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6004)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align mul_lt_one_of_le_of_lt mul_lt_one_of_le_of_ltₓ'. -/
alias Left.mul_lt_one_of_le_of_lt ← mul_lt_one_of_le_of_lt
#align mul_lt_one_of_le_of_lt mul_lt_one_of_le_of_lt
@@ -1405,7 +1405,7 @@ alias Left.mul_lt_one_of_le_of_lt ← mul_lt_one_of_le_of_lt
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6060 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6062 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6060 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6062) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6075 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6077 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6075 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6077)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6058 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6060 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6058 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6060) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6073 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6075 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6073 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6075)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align mul_lt_one_of_lt_of_le mul_lt_one_of_lt_of_leₓ'. -/
alias Left.mul_lt_one_of_lt_of_le ← mul_lt_one_of_lt_of_le
#align mul_lt_one_of_lt_of_le mul_lt_one_of_lt_of_le
@@ -1414,7 +1414,7 @@ alias Left.mul_lt_one_of_lt_of_le ← mul_lt_one_of_lt_of_le
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6131 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6133 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6131 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6133) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6146 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6148 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6146 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6148)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6129 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6131 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6129 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6131) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6144 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6146 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6144 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6146)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align mul_lt_one mul_lt_oneₓ'. -/
alias Left.mul_lt_one ← mul_lt_one
#align mul_lt_one mul_lt_one
@@ -1423,7 +1423,7 @@ alias Left.mul_lt_one ← mul_lt_one
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6202 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6204 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6202 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6204) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6217 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6219 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6217 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6219)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6200 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6202 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6200 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6202) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6215 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6217 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6215 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6217)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align mul_lt_one' mul_lt_one'ₓ'. -/
alias Left.mul_lt_one' ← mul_lt_one'
#align mul_lt_one' mul_lt_one'
@@ -1444,7 +1444,7 @@ attribute [to_additive "**Alias** of `left.add_neg'`."] mul_lt_one'
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6794 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6796 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6794 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6796) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6809 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6811 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6809 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6811)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6792 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6794 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6792 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6794) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6807 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6809 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6807 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6809)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
Case conversion may be inaccurate. Consider using '#align one_le_mul one_le_mulₓ'. -/
alias Left.one_le_mul ← one_le_mul
#align one_le_mul one_le_mul
@@ -1453,7 +1453,7 @@ alias Left.one_le_mul ← one_le_mul
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6865 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6867 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6865 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6867) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6880 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6882 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6880 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6882)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6863 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6865 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6863 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6865) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6878 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6880 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6878 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6880)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
Case conversion may be inaccurate. Consider using '#align one_lt_mul_of_le_of_lt' one_lt_mul_of_le_of_lt'ₓ'. -/
alias Left.one_lt_mul_of_le_of_lt ← one_lt_mul_of_le_of_lt'
#align one_lt_mul_of_le_of_lt' one_lt_mul_of_le_of_lt'
@@ -1462,7 +1462,7 @@ alias Left.one_lt_mul_of_le_of_lt ← one_lt_mul_of_le_of_lt'
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6936 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6938 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6936 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6938) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6951 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6953 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6951 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6953)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6934 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6936 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6934 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6936) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6949 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6951 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6949 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.6951)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
Case conversion may be inaccurate. Consider using '#align one_lt_mul_of_lt_of_le' one_lt_mul_of_lt_of_le'ₓ'. -/
alias Left.one_lt_mul_of_lt_of_le ← one_lt_mul_of_lt_of_le'
#align one_lt_mul_of_lt_of_le' one_lt_mul_of_lt_of_le'
@@ -1471,7 +1471,7 @@ alias Left.one_lt_mul_of_lt_of_le ← one_lt_mul_of_lt_of_le'
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7007 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7009 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7007 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7009) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7022 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7024 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7022 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7024)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7005 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7007 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7005 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7007) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7020 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7022 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7020 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7022)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
Case conversion may be inaccurate. Consider using '#align one_lt_mul' one_lt_mul'ₓ'. -/
alias Left.one_lt_mul ← one_lt_mul'
#align one_lt_mul' one_lt_mul'
@@ -1480,7 +1480,7 @@ alias Left.one_lt_mul ← one_lt_mul'
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7078 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7080 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7078 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7080) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7093 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7095 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7093 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7095)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7076 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7078 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7076 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7078) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7091 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7093 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7091 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.7093)] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b))
Case conversion may be inaccurate. Consider using '#align one_lt_mul'' one_lt_mul''ₓ'. -/
alias Left.one_lt_mul' ← one_lt_mul''
#align one_lt_mul'' one_lt_mul''
@@ -1501,7 +1501,7 @@ attribute [to_additive add_pos' "**Alias** of `left.add_pos'`."] one_lt_mul''
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a c)
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8986 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8988 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8986 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8988) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9001 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9003 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9001 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9003)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a c)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8984 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8986 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8984 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8986) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8999 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9001 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.8999 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9001)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a c)
Case conversion may be inaccurate. Consider using '#align lt_of_mul_lt_of_one_le_left lt_of_mul_lt_of_one_le_leftₓ'. -/
@[to_additive]
theorem lt_of_mul_lt_of_one_le_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (h : a * b < c)
@@ -1514,7 +1514,7 @@ theorem lt_of_mul_lt_of_one_le_left [CovariantClass α α (· * ·) (· ≤ ·)]
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a c)
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9057 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9059 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9057 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9059) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9072 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9074 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9072 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9074)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a c)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9055 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9057 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9055 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9057) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9070 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9072 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9070 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9072)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a c)
Case conversion may be inaccurate. Consider using '#align le_of_mul_le_of_one_le_left le_of_mul_le_of_one_le_leftₓ'. -/
@[to_additive]
theorem le_of_mul_le_of_one_le_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (h : a * b ≤ c)
@@ -1527,7 +1527,7 @@ theorem le_of_mul_le_of_one_le_left [CovariantClass α α (· * ·) (· ≤ ·)]
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b c)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) c (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a b)
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9128 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9130 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9128 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9130) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9143 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9145 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9143 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9145)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b c)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) c (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a b)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9126 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9128 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9126 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9128) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9141 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9143 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9141 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9143)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b c)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) c (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a b)
Case conversion may be inaccurate. Consider using '#align lt_of_lt_mul_of_le_one_left lt_of_lt_mul_of_le_one_leftₓ'. -/
@[to_additive]
theorem lt_of_lt_mul_of_le_one_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (h : a < b * c)
@@ -1540,7 +1540,7 @@ theorem lt_of_lt_mul_of_le_one_left [CovariantClass α α (· * ·) (· ≤ ·)]
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b c)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) c (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a b)
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9198 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9200 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9198 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9200) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9213 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9215 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9213 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9215)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b c)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) c (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a b)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9196 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9198 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9196 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9198) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9211 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9213 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9211 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9213)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b c)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) c (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a b)
Case conversion may be inaccurate. Consider using '#align le_of_le_mul_of_le_one_left le_of_le_mul_of_le_one_leftₓ'. -/
@[to_additive]
theorem le_of_le_mul_of_le_one_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (h : a ≤ b * c)
@@ -1553,7 +1553,7 @@ theorem le_of_le_mul_of_le_one_left [CovariantClass α α (· * ·) (· ≤ ·)]
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c)
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9271 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9273 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9271 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9273)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9286 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9288 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9286 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9288)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9269 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9271 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9269 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9271)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9284 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9286 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9284 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9286)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b c)
Case conversion may be inaccurate. Consider using '#align lt_of_mul_lt_of_one_le_right lt_of_mul_lt_of_one_le_rightₓ'. -/
@[to_additive]
theorem lt_of_mul_lt_of_one_le_right [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α}
@@ -1566,7 +1566,7 @@ theorem lt_of_mul_lt_of_one_le_right [CovariantClass α α (swap (· * ·)) (·
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c)
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9345 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9347 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9345 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9347)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9360 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9362 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9360 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9362)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9343 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9345 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9343 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9345)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9358 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9360 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9358 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9360)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b c)
Case conversion may be inaccurate. Consider using '#align le_of_mul_le_of_one_le_right le_of_mul_le_of_one_le_rightₓ'. -/
@[to_additive]
theorem le_of_mul_le_of_one_le_right [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α}
@@ -1579,7 +1579,7 @@ theorem le_of_mul_le_of_one_le_right [CovariantClass α α (swap (· * ·)) (·
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b c)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a c)
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9419 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9421 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9419 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9421)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9434 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9436 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9434 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9436)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b c)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a c)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9417 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9419 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9417 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9419)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9432 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9434 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9432 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9434)] {a : α} {b : α} {c : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b c)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a c)
Case conversion may be inaccurate. Consider using '#align lt_of_lt_mul_of_le_one_right lt_of_lt_mul_of_le_one_rightₓ'. -/
@[to_additive]
theorem lt_of_lt_mul_of_le_one_right [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α}
@@ -1592,7 +1592,7 @@ theorem lt_of_lt_mul_of_le_one_right [CovariantClass α α (swap (· * ·)) (·
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b c)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a c)
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9492 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9494 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9492 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9494)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9507 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9509 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9507 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9509)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b c)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a c)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9490 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9492 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9490 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9492)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9505 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9507 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9505 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9507)] {a : α} {b : α} {c : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b c)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a c)
Case conversion may be inaccurate. Consider using '#align le_of_le_mul_of_le_one_right le_of_le_mul_of_le_one_rightₓ'. -/
@[to_additive]
theorem le_of_le_mul_of_le_one_right [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α}
@@ -1611,7 +1611,7 @@ variable [PartialOrder α]
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (Iff (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) (And (Eq.{succ u1} α a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) (Eq.{succ u1} α b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9574 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9576 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9574 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9576) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9589 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9591 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9589 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9591)] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9611 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9613 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9611 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9613)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9626 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9628 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9626 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9628)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (Iff (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) (And (Eq.{succ u1} α a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) (Eq.{succ u1} α b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9572 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9574 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9572 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9574) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9587 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9589 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9587 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9589)] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9609 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9611 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9609 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9611)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9624 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9626 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9624 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9626)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (Iff (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) (And (Eq.{succ u1} α a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) (Eq.{succ u1} α b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))))
Case conversion may be inaccurate. Consider using '#align mul_eq_one_iff' mul_eq_one_iff'ₓ'. -/
@[to_additive]
theorem mul_eq_one_iff' [CovariantClass α α (· * ·) (· ≤ ·)]
@@ -1632,7 +1632,7 @@ theorem mul_eq_one_iff' [CovariantClass α α (· * ·) (· ≤ ·)]
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_5 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_6 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a₁ : α} {a₂ : α} {b₁ : α} {b₂ : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a₁ a₂) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b₁ b₂) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a₂ b₂) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a₁ b₁)) (And (Eq.{succ u1} α a₁ a₂) (Eq.{succ u1} α b₁ b₂)))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9833 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9835 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9833 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9835) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9848 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9850 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9848 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9850)] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9870 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9872 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9870 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9872)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9885 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9887 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9885 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9887)] [_inst_5 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9904 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9906 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9904 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9906) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9919 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9921 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9919 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9921)] [_inst_6 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9941 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9943 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9941 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9943)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9956 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9958 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9956 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9958)] {a₁ : α} {a₂ : α} {b₁ : α} {b₂ : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a₁ a₂) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b₁ b₂) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a₂ b₂) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a₁ b₁)) (And (Eq.{succ u1} α a₁ a₂) (Eq.{succ u1} α b₁ b₂)))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9831 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9833 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9831 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9833) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9846 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9848 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9846 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9848)] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9868 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9870 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9868 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9870)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9883 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9885 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9883 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9885)] [_inst_5 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9902 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9904 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9902 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9904) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9917 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9919 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9917 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9919)] [_inst_6 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9939 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9941 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9939 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9941)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9954 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9956 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9954 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.9956)] {a₁ : α} {a₂ : α} {b₁ : α} {b₂ : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a₁ a₂) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b₁ b₂) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a₂ b₂) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a₁ b₁)) (And (Eq.{succ u1} α a₁ a₂) (Eq.{succ u1} α b₁ b₂)))
Case conversion may be inaccurate. Consider using '#align mul_le_mul_iff_of_ge mul_le_mul_iff_of_geₓ'. -/
@[to_additive]
theorem mul_le_mul_iff_of_ge [CovariantClass α α (· * ·) (· ≤ ·)]
@@ -1659,7 +1659,7 @@ variable [CovariantClass α α (· * ·) (· ≤ ·)] {a b : α}
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b)) -> (Eq.{succ u1} α a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10121 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10123 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10121 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10123) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10136 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10138 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10136 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10138)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b)) -> (Eq.{succ u1} α a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10119 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10121 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10119 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10121) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10134 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10136 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10134 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10136)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b)) -> (Eq.{succ u1} α a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align eq_one_of_one_le_mul_left eq_one_of_one_le_mul_leftₓ'. -/
@[to_additive eq_zero_of_add_nonneg_left]
theorem eq_one_of_one_le_mul_left (ha : a ≤ 1) (hb : b ≤ 1) (hab : 1 ≤ a * b) : a = 1 :=
@@ -1671,7 +1671,7 @@ theorem eq_one_of_one_le_mul_left (ha : a ≤ 1) (hb : b ≤ 1) (hab : 1 ≤ a *
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (Eq.{succ u1} α a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10200 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10202 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10200 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10202) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10215 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10217 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10215 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10217)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (Eq.{succ u1} α a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10198 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10200 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10198 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10200) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10213 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10215 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10213 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10215)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (Eq.{succ u1} α a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align eq_one_of_mul_le_one_left eq_one_of_mul_le_one_leftₓ'. -/
@[to_additive]
theorem eq_one_of_mul_le_one_left (ha : 1 ≤ a) (hb : 1 ≤ b) (hab : a * b ≤ 1) : a = 1 :=
@@ -1689,7 +1689,7 @@ variable [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b : α}
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b)) -> (Eq.{succ u1} α b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10335 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10337 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10335 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10337)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10350 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10352 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10350 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10352)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b)) -> (Eq.{succ u1} α b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10333 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10335 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10333 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10335)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10348 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10350 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10348 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10350)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b)) -> (Eq.{succ u1} α b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align eq_one_of_one_le_mul_right eq_one_of_one_le_mul_rightₓ'. -/
@[to_additive eq_zero_of_add_nonneg_right]
theorem eq_one_of_one_le_mul_right (ha : a ≤ 1) (hb : b ≤ 1) (hab : 1 ≤ a * b) : b = 1 :=
@@ -1701,7 +1701,7 @@ theorem eq_one_of_one_le_mul_right (ha : a ≤ 1) (hb : b ≤ 1) (hab : 1 ≤ a
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1))))) -> (Eq.{succ u1} α b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_1)))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10417 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10419 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10417 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10419)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10432 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10434 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10432 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10434)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (Eq.{succ u1} α b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10415 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10417 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10415 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10417)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10430 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10432 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10430 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10432)] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) a b) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1)))) -> (Eq.{succ u1} α b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_1))))
Case conversion may be inaccurate. Consider using '#align eq_one_of_mul_le_one_right eq_one_of_mul_le_one_rightₓ'. -/
@[to_additive]
theorem eq_one_of_mul_le_one_right (ha : 1 ≤ a) (hb : 1 ≤ b) (hab : a * b ≤ 1) : b = 1 :=
@@ -1721,7 +1721,7 @@ variable [LinearOrder α]
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))))] (a : α), Exists.{succ u1} α (fun (b : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_1)) b b) a)
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10509 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10511 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10509 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10511) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10524 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10526 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10524 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10526)] (a : α), Exists.{succ u1} α (fun (b : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b b) a)
+ forall {α : Type.{u1}} [_inst_1 : MulOneClass.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10507 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10509 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10507 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10509) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10522 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10524 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10522 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10524)] (a : α), Exists.{succ u1} α (fun (b : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_1)) b b) a)
Case conversion may be inaccurate. Consider using '#align exists_square_le exists_square_leₓ'. -/
theorem exists_square_le [CovariantClass α α (· * ·) (· < ·)] (a : α) : ∃ b : α, b * b ≤ a :=
by
@@ -1751,7 +1751,7 @@ variable [PartialOrder α]
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))], LeftCancelSemigroup.{u1} α
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10779 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10781 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10779 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10781) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10794 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10796 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10794 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10796)], LeftCancelSemigroup.{u1} α
+ forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10777 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10779 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10777 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10779) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10792 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10794 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10792 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10794)], LeftCancelSemigroup.{u1} α
Case conversion may be inaccurate. Consider using '#align contravariant.to_left_cancel_semigroup Contravariant.toLeftCancelSemigroupₓ'. -/
/- This is not instance, since we want to have an instance from `left_cancel_semigroup`s
to the appropriate `covariant_class`. -/
@@ -1769,7 +1769,7 @@ def Contravariant.toLeftCancelSemigroup [ContravariantClass α α (· * ·) (·
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))], RightCancelSemigroup.{u1} α
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10862 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10864 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10862 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10864)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10877 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10879 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10877 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10879)], RightCancelSemigroup.{u1} α
+ forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10860 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10862 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10860 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10862)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10875 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10877 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10875 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10877)], RightCancelSemigroup.{u1} α
Case conversion may be inaccurate. Consider using '#align contravariant.to_right_cancel_semigroup Contravariant.toRightCancelSemigroupₓ'. -/
/- This is not instance, since we want to have an instance from `right_cancel_semigroup`s
to the appropriate `covariant_class`. -/
@@ -1787,7 +1787,7 @@ def Contravariant.toRightCancelSemigroup [ContravariantClass α α (swap (· *
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_5 : ContravariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_6 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b d) -> (Iff (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)) c d)) (And (Eq.{succ u1} α a c) (Eq.{succ u1} α b d)))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10942 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10944 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10942 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10944) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10957 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10959 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10957 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10959)] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10979 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10981 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10979 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10981)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10994 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10996 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10994 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10996)] [_inst_5 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11013 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11015 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11013 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11015) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11028 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11030 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11028 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11030)] [_inst_6 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11050 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11052 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11050 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11052)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11065 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11067 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11065 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11067)] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b d) -> (Iff (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) c d)) (And (Eq.{succ u1} α a c) (Eq.{succ u1} α b d)))
+ forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10940 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10942 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10940 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10942) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10955 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10957 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10955 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10957)] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10977 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10979 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10977 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10979)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10992 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10994 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10992 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10994)] [_inst_5 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11011 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11013 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11011 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11013) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11026 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11028 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11026 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11028)] [_inst_6 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11048 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11050 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11048 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11050)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11063 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11065 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11063 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11065)] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b d) -> (Iff (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) c d)) (And (Eq.{succ u1} α a c) (Eq.{succ u1} α b d)))
Case conversion may be inaccurate. Consider using '#align left.mul_eq_mul_iff_eq_and_eq Left.mul_eq_mul_iff_eq_and_eqₓ'. -/
@[to_additive]
theorem Left.mul_eq_mul_iff_eq_and_eq [CovariantClass α α (· * ·) (· < ·)]
@@ -1808,7 +1808,7 @@ theorem Left.mul_eq_mul_iff_eq_and_eq [CovariantClass α α (· * ·) (· < ·)]
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_4 : ContravariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)))) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_6 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b d) -> (Iff (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)) c d)) (And (Eq.{succ u1} α a c) (Eq.{succ u1} α b d)))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11205 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11207 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11205 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11207) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11220 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11222 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11220 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11222)] [_inst_4 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11239 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11241 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11239 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11241) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11254 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11256 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11254 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11256)] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11276 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11278 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11276 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11278)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11291 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11293 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11291 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11293)] [_inst_6 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11313 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11315 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11313 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11315)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11328 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11330 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11328 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11330)] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b d) -> (Iff (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) c d)) (And (Eq.{succ u1} α a c) (Eq.{succ u1} α b d)))
+ forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11203 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11205 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11203 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11205) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11218 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11220 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11218 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11220)] [_inst_4 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11237 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11239 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11237 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11239) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11252 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11254 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11252 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11254)] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11274 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11276 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11274 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11276)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11289 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11291 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11289 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11291)] [_inst_6 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11311 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11313 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11311 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11313)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11326 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11328 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11326 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11328)] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b d) -> (Iff (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) c d)) (And (Eq.{succ u1} α a c) (Eq.{succ u1} α b d)))
Case conversion may be inaccurate. Consider using '#align right.mul_eq_mul_iff_eq_and_eq Right.mul_eq_mul_iff_eq_and_eqₓ'. -/
@[to_additive]
theorem Right.mul_eq_mul_iff_eq_and_eq [CovariantClass α α (· * ·) (· ≤ ·)]
@@ -1829,7 +1829,7 @@ theorem Right.mul_eq_mul_iff_eq_and_eq [CovariantClass α α (· * ·) (· ≤
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_5 : ContravariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] [_inst_6 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)))) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)))] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b d) -> (Iff (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α _inst_1)) c d)) (And (Eq.{succ u1} α a c) (Eq.{succ u1} α b d)))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10942 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10944 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10942 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10944) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10957 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10959 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10957 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10959)] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10979 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10981 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10979 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10981)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10994 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10996 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10994 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10996)] [_inst_5 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11013 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11015 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11013 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11015) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11028 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11030 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11028 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11030)] [_inst_6 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11050 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11052 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11050 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11052)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11065 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11067 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11065 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11067)] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b d) -> (Iff (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) c d)) (And (Eq.{succ u1} α a c) (Eq.{succ u1} α b d)))
+ forall {α : Type.{u1}} [_inst_1 : Semigroup.{u1} α] [_inst_2 : PartialOrder.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10940 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10942 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10940 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10942) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10955 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10957 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10955 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10957)] [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10977 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10979 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10977 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10979)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10992 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10994 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10992 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.10994)] [_inst_5 : ContravariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11011 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11013 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11011 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11013) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11026 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11028 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11026 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11028)] [_inst_6 : ContravariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11048 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11050 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11048 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11050)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11063 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11065 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11063 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11065)] {a : α} {b : α} {c : α} {d : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) a c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_2)) b d) -> (Iff (Eq.{succ u1} α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α _inst_1)) c d)) (And (Eq.{succ u1} α a c) (Eq.{succ u1} α b d)))
Case conversion may be inaccurate. Consider using '#align mul_eq_mul_iff_eq_and_eq mul_eq_mul_iff_eq_and_eqₓ'. -/
alias Left.mul_eq_mul_iff_eq_and_eq ← mul_eq_mul_iff_eq_and_eq
#align mul_eq_mul_iff_eq_and_eq mul_eq_mul_iff_eq_and_eq
@@ -1848,7 +1848,7 @@ variable [Mul α] [Preorder α] [Preorder β] {f g : β → α} {s : Set β}
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))], (Monotone.{u2, u1} β α _inst_3 _inst_2 f) -> (forall (a : α), Monotone.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a (f x)))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11512 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11514 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11512 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11514) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11527 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11529 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11527 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11529)], (Monotone.{u1, u2} β α _inst_3 _inst_2 f) -> (forall (a : α), Monotone.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) a (f x)))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11510 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11512 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11510 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11512) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11525 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11527 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11525 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11527)], (Monotone.{u1, u2} β α _inst_3 _inst_2 f) -> (forall (a : α), Monotone.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) a (f x)))
Case conversion may be inaccurate. Consider using '#align monotone.const_mul' Monotone.const_mul'ₓ'. -/
@[to_additive const_add]
theorem Monotone.const_mul' [CovariantClass α α (· * ·) (· ≤ ·)] (hf : Monotone f) (a : α) :
@@ -1860,7 +1860,7 @@ theorem Monotone.const_mul' [CovariantClass α α (· * ·) (· ≤ ·)] (hf : M
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))], (MonotoneOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (forall (a : α), MonotoneOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a (f x)) s)
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} {s : Set.{u1} β} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11598 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11600 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11598 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11600) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11613 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11615 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11613 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11615)], (MonotoneOn.{u1, u2} β α _inst_3 _inst_2 f s) -> (forall (a : α), MonotoneOn.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) a (f x)) s)
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} {s : Set.{u1} β} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11596 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11598 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11596 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11598) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11611 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11613 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11611 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11613)], (MonotoneOn.{u1, u2} β α _inst_3 _inst_2 f s) -> (forall (a : α), MonotoneOn.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) a (f x)) s)
Case conversion may be inaccurate. Consider using '#align monotone_on.const_mul' MonotoneOn.const_mul'ₓ'. -/
@[to_additive const_add]
theorem MonotoneOn.const_mul' [CovariantClass α α (· * ·) (· ≤ ·)] (hf : MonotoneOn f s) (a : α) :
@@ -1872,7 +1872,7 @@ theorem MonotoneOn.const_mul' [CovariantClass α α (· * ·) (· ≤ ·)] (hf :
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))], (Antitone.{u2, u1} β α _inst_3 _inst_2 f) -> (forall (a : α), Antitone.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a (f x)))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11692 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11694 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11692 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11694) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11707 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11709 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11707 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11709)], (Antitone.{u1, u2} β α _inst_3 _inst_2 f) -> (forall (a : α), Antitone.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) a (f x)))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11690 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11692 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11690 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11692) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11705 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11707 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11705 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11707)], (Antitone.{u1, u2} β α _inst_3 _inst_2 f) -> (forall (a : α), Antitone.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) a (f x)))
Case conversion may be inaccurate. Consider using '#align antitone.const_mul' Antitone.const_mul'ₓ'. -/
@[to_additive const_add]
theorem Antitone.const_mul' [CovariantClass α α (· * ·) (· ≤ ·)] (hf : Antitone f) (a : α) :
@@ -1884,7 +1884,7 @@ theorem Antitone.const_mul' [CovariantClass α α (· * ·) (· ≤ ·)] (hf : A
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))], (AntitoneOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (forall (a : α), AntitoneOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) a (f x)) s)
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} {s : Set.{u1} β} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11778 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11780 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11778 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11780) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11793 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11795 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11793 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11795)], (AntitoneOn.{u1, u2} β α _inst_3 _inst_2 f s) -> (forall (a : α), AntitoneOn.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) a (f x)) s)
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} {s : Set.{u1} β} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11776 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11778 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11776 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11778) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11791 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11793 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11791 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11793)], (AntitoneOn.{u1, u2} β α _inst_3 _inst_2 f s) -> (forall (a : α), AntitoneOn.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) a (f x)) s)
Case conversion may be inaccurate. Consider using '#align antitone_on.const_mul' AntitoneOn.const_mul'ₓ'. -/
@[to_additive const_add]
theorem AntitoneOn.const_mul' [CovariantClass α α (· * ·) (· ≤ ·)] (hf : AntitoneOn f s) (a : α) :
@@ -1896,7 +1896,7 @@ theorem AntitoneOn.const_mul' [CovariantClass α α (· * ·) (· ≤ ·)] (hf :
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))], (Monotone.{u2, u1} β α _inst_3 _inst_2 f) -> (forall (a : α), Monotone.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) a))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} [_inst_4 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11875 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11877 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11875 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11877)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11890 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11892 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11890 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11892)], (Monotone.{u1, u2} β α _inst_3 _inst_2 f) -> (forall (a : α), Monotone.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) a))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} [_inst_4 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11873 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11875 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11873 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11875)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11888 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11890 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11888 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11890)], (Monotone.{u1, u2} β α _inst_3 _inst_2 f) -> (forall (a : α), Monotone.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) a))
Case conversion may be inaccurate. Consider using '#align monotone.mul_const' Monotone.mul_const'ₓ'. -/
@[to_additive add_const]
theorem Monotone.mul_const' [CovariantClass α α (swap (· * ·)) (· ≤ ·)] (hf : Monotone f) (a : α) :
@@ -1908,7 +1908,7 @@ theorem Monotone.mul_const' [CovariantClass α α (swap (· * ·)) (· ≤ ·)]
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))], (MonotoneOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (forall (a : α), MonotoneOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) a) s)
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} {s : Set.{u1} β} [_inst_4 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11964 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11966 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11964 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11966)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11979 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11981 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11979 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11981)], (MonotoneOn.{u1, u2} β α _inst_3 _inst_2 f s) -> (forall (a : α), MonotoneOn.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) a) s)
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} {s : Set.{u1} β} [_inst_4 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11962 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11964 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11962 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11964)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11977 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11979 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11977 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.11979)], (MonotoneOn.{u1, u2} β α _inst_3 _inst_2 f s) -> (forall (a : α), MonotoneOn.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) a) s)
Case conversion may be inaccurate. Consider using '#align monotone_on.mul_const' MonotoneOn.mul_const'ₓ'. -/
@[to_additive add_const]
theorem MonotoneOn.mul_const' [CovariantClass α α (swap (· * ·)) (· ≤ ·)] (hf : MonotoneOn f s)
@@ -1920,7 +1920,7 @@ theorem MonotoneOn.mul_const' [CovariantClass α α (swap (· * ·)) (· ≤ ·)
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))], (Antitone.{u2, u1} β α _inst_3 _inst_2 f) -> (forall (a : α), Antitone.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) a))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} [_inst_4 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12061 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12063 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12061 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12063)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12076 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12078 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12076 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12078)], (Antitone.{u1, u2} β α _inst_3 _inst_2 f) -> (forall (a : α), Antitone.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) a))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} [_inst_4 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12059 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12061 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12059 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12061)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12074 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12076 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12074 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12076)], (Antitone.{u1, u2} β α _inst_3 _inst_2 f) -> (forall (a : α), Antitone.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) a))
Case conversion may be inaccurate. Consider using '#align antitone.mul_const' Antitone.mul_const'ₓ'. -/
@[to_additive add_const]
theorem Antitone.mul_const' [CovariantClass α α (swap (· * ·)) (· ≤ ·)] (hf : Antitone f) (a : α) :
@@ -1932,7 +1932,7 @@ theorem Antitone.mul_const' [CovariantClass α α (swap (· * ·)) (· ≤ ·)]
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))], (AntitoneOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (forall (a : α), AntitoneOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) a) s)
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} {s : Set.{u1} β} [_inst_4 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12150 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12152 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12150 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12152)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12165 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12167 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12165 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12167)], (AntitoneOn.{u1, u2} β α _inst_3 _inst_2 f s) -> (forall (a : α), AntitoneOn.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) a) s)
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} {s : Set.{u1} β} [_inst_4 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12148 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12150 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12148 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12150)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12163 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12165 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12163 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12165)], (AntitoneOn.{u1, u2} β α _inst_3 _inst_2 f s) -> (forall (a : α), AntitoneOn.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) a) s)
Case conversion may be inaccurate. Consider using '#align antitone_on.mul_const' AntitoneOn.mul_const'ₓ'. -/
@[to_additive add_const]
theorem AntitoneOn.mul_const' [CovariantClass α α (swap (· * ·)) (· ≤ ·)] (hf : AntitoneOn f s)
@@ -1944,7 +1944,7 @@ theorem AntitoneOn.mul_const' [CovariantClass α α (swap (· * ·)) (· ≤ ·)
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {g : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))], (Monotone.{u2, u1} β α _inst_3 _inst_2 f) -> (Monotone.{u2, u1} β α _inst_3 _inst_2 g) -> (Monotone.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} {g : β -> α} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12244 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12246 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12244 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12246) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12259 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12261 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12259 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12261)] [_inst_5 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12281 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12283 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12281 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12283)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12296 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12298 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12296 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12298)], (Monotone.{u1, u2} β α _inst_3 _inst_2 f) -> (Monotone.{u1, u2} β α _inst_3 _inst_2 g) -> (Monotone.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) (g x)))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} {g : β -> α} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12242 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12244 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12242 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12244) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12257 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12259 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12257 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12259)] [_inst_5 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12279 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12281 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12279 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12281)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12294 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12296 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12294 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12296)], (Monotone.{u1, u2} β α _inst_3 _inst_2 f) -> (Monotone.{u1, u2} β α _inst_3 _inst_2 g) -> (Monotone.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) (g x)))
Case conversion may be inaccurate. Consider using '#align monotone.mul' Monotone.mul'ₓ'. -/
/-- The product of two monotone functions is monotone. -/
@[to_additive add "The sum of two monotone functions is monotone."]
@@ -1958,7 +1958,7 @@ theorem Monotone.mul' [CovariantClass α α (· * ·) (· ≤ ·)]
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {g : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))], (MonotoneOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (MonotoneOn.{u2, u1} β α _inst_3 _inst_2 g s) -> (MonotoneOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)) s)
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} {g : β -> α} {s : Set.{u1} β} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12372 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12374 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12372 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12374) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12387 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12389 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12387 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12389)] [_inst_5 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12409 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12411 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12409 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12411)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12424 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12426 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12424 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12426)], (MonotoneOn.{u1, u2} β α _inst_3 _inst_2 f s) -> (MonotoneOn.{u1, u2} β α _inst_3 _inst_2 g s) -> (MonotoneOn.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) (g x)) s)
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} {g : β -> α} {s : Set.{u1} β} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12370 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12372 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12370 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12372) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12385 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12387 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12385 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12387)] [_inst_5 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12407 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12409 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12407 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12409)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12422 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12424 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12422 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12424)], (MonotoneOn.{u1, u2} β α _inst_3 _inst_2 f s) -> (MonotoneOn.{u1, u2} β α _inst_3 _inst_2 g s) -> (MonotoneOn.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) (g x)) s)
Case conversion may be inaccurate. Consider using '#align monotone_on.mul' MonotoneOn.mul'ₓ'. -/
/-- The product of two monotone functions is monotone. -/
@[to_additive add "The sum of two monotone functions is monotone."]
@@ -1972,7 +1972,7 @@ theorem MonotoneOn.mul' [CovariantClass α α (· * ·) (· ≤ ·)]
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {g : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))], (Antitone.{u2, u1} β α _inst_3 _inst_2 f) -> (Antitone.{u2, u1} β α _inst_3 _inst_2 g) -> (Antitone.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} {g : β -> α} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12511 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12513 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12511 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12513) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12526 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12528 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12526 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12528)] [_inst_5 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12548 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12550 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12548 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12550)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12563 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12565 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12563 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12565)], (Antitone.{u1, u2} β α _inst_3 _inst_2 f) -> (Antitone.{u1, u2} β α _inst_3 _inst_2 g) -> (Antitone.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) (g x)))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} {g : β -> α} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12509 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12511 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12509 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12511) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12524 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12526 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12524 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12526)] [_inst_5 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12546 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12548 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12546 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12548)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12561 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12563 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12561 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12563)], (Antitone.{u1, u2} β α _inst_3 _inst_2 f) -> (Antitone.{u1, u2} β α _inst_3 _inst_2 g) -> (Antitone.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) (g x)))
Case conversion may be inaccurate. Consider using '#align antitone.mul' Antitone.mul'ₓ'. -/
/-- The product of two antitone functions is antitone. -/
@[to_additive add "The sum of two antitone functions is antitone."]
@@ -1986,7 +1986,7 @@ theorem Antitone.mul' [CovariantClass α α (· * ·) (· ≤ ·)]
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {g : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))], (AntitoneOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (AntitoneOn.{u2, u1} β α _inst_3 _inst_2 g s) -> (AntitoneOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)) s)
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} {g : β -> α} {s : Set.{u1} β} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12639 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12641 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12639 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12641) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12654 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12656 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12654 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12656)] [_inst_5 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12676 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12678 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12676 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12678)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12691 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12693 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12691 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12693)], (AntitoneOn.{u1, u2} β α _inst_3 _inst_2 f s) -> (AntitoneOn.{u1, u2} β α _inst_3 _inst_2 g s) -> (AntitoneOn.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) (g x)) s)
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} {g : β -> α} {s : Set.{u1} β} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12637 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12639 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12637 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12639) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12652 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12654 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12652 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12654)] [_inst_5 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12674 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12676 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12674 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12676)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12689 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12691 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12689 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.12691)], (AntitoneOn.{u1, u2} β α _inst_3 _inst_2 f s) -> (AntitoneOn.{u1, u2} β α _inst_3 _inst_2 g s) -> (AntitoneOn.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) (g x)) s)
Case conversion may be inaccurate. Consider using '#align antitone_on.mul' AntitoneOn.mul'ₓ'. -/
/-- The product of two antitone functions is antitone. -/
@[to_additive add "The sum of two antitone functions is antitone."]
@@ -2076,7 +2076,7 @@ end Right
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {g : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))], (StrictMono.{u2, u1} β α _inst_3 _inst_2 f) -> (StrictMono.{u2, u1} β α _inst_3 _inst_2 g) -> (StrictMono.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} {g : β -> α} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13627 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13629 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13627 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13629) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13642 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13644 : α) => LT.lt.{u2} α (Preorder.toLT.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13642 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13644)] [_inst_5 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13664 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13666 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13664 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13666)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13679 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13681 : α) => LT.lt.{u2} α (Preorder.toLT.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13679 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13681)], (StrictMono.{u1, u2} β α _inst_3 _inst_2 f) -> (StrictMono.{u1, u2} β α _inst_3 _inst_2 g) -> (StrictMono.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) (g x)))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} {g : β -> α} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13625 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13627 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13625 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13627) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13640 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13642 : α) => LT.lt.{u2} α (Preorder.toLT.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13640 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13642)] [_inst_5 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13662 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13664 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13662 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13664)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13677 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13679 : α) => LT.lt.{u2} α (Preorder.toLT.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13677 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13679)], (StrictMono.{u1, u2} β α _inst_3 _inst_2 f) -> (StrictMono.{u1, u2} β α _inst_3 _inst_2 g) -> (StrictMono.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) (g x)))
Case conversion may be inaccurate. Consider using '#align strict_mono.mul' StrictMono.mul'ₓ'. -/
/-- The product of two strictly monotone functions is strictly monotone. -/
@[to_additive add "The sum of two strictly monotone functions is strictly monotone."]
@@ -2090,7 +2090,7 @@ theorem StrictMono.mul' [CovariantClass α α (· * ·) (· < ·)]
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {g : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))], (StrictMonoOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (StrictMonoOn.{u2, u1} β α _inst_3 _inst_2 g s) -> (StrictMonoOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)) s)
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} {g : β -> α} {s : Set.{u1} β} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13755 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13757 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13755 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13757) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13770 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13772 : α) => LT.lt.{u2} α (Preorder.toLT.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13770 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13772)] [_inst_5 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13792 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13794 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13792 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13794)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13807 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13809 : α) => LT.lt.{u2} α (Preorder.toLT.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13807 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13809)], (StrictMonoOn.{u1, u2} β α _inst_3 _inst_2 f s) -> (StrictMonoOn.{u1, u2} β α _inst_3 _inst_2 g s) -> (StrictMonoOn.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) (g x)) s)
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} {g : β -> α} {s : Set.{u1} β} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13753 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13755 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13753 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13755) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13768 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13770 : α) => LT.lt.{u2} α (Preorder.toLT.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13768 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13770)] [_inst_5 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13790 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13792 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13790 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13792)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13805 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13807 : α) => LT.lt.{u2} α (Preorder.toLT.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13805 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13807)], (StrictMonoOn.{u1, u2} β α _inst_3 _inst_2 f s) -> (StrictMonoOn.{u1, u2} β α _inst_3 _inst_2 g s) -> (StrictMonoOn.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) (g x)) s)
Case conversion may be inaccurate. Consider using '#align strict_mono_on.mul' StrictMonoOn.mul'ₓ'. -/
/-- The product of two strictly monotone functions is strictly monotone. -/
@[to_additive add "The sum of two strictly monotone functions is strictly monotone."]
@@ -2105,7 +2105,7 @@ theorem StrictMonoOn.mul' [CovariantClass α α (· * ·) (· < ·)]
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {g : β -> α} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))], (StrictAnti.{u2, u1} β α _inst_3 _inst_2 f) -> (StrictAnti.{u2, u1} β α _inst_3 _inst_2 g) -> (StrictAnti.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} {g : β -> α} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13894 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13896 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13894 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13896) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13909 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13911 : α) => LT.lt.{u2} α (Preorder.toLT.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13909 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13911)] [_inst_5 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13931 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13933 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13931 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13933)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13946 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13948 : α) => LT.lt.{u2} α (Preorder.toLT.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13946 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13948)], (StrictAnti.{u1, u2} β α _inst_3 _inst_2 f) -> (StrictAnti.{u1, u2} β α _inst_3 _inst_2 g) -> (StrictAnti.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) (g x)))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} {g : β -> α} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13892 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13894 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13892 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13894) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13907 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13909 : α) => LT.lt.{u2} α (Preorder.toLT.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13907 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13909)] [_inst_5 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13929 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13931 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13929 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13931)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13944 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13946 : α) => LT.lt.{u2} α (Preorder.toLT.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13944 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.13946)], (StrictAnti.{u1, u2} β α _inst_3 _inst_2 f) -> (StrictAnti.{u1, u2} β α _inst_3 _inst_2 g) -> (StrictAnti.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) (g x)))
Case conversion may be inaccurate. Consider using '#align strict_anti.mul' StrictAnti.mul'ₓ'. -/
/-- The product of two strictly antitone functions is strictly antitone. -/
@[to_additive add "The sum of two strictly antitone functions is strictly antitone."]
@@ -2119,7 +2119,7 @@ theorem StrictAnti.mul' [CovariantClass α α (· * ·) (· < ·)]
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {f : β -> α} {g : β -> α} {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))], (StrictAntiOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (StrictAntiOn.{u2, u1} β α _inst_3 _inst_2 g s) -> (StrictAntiOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)) s)
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} {g : β -> α} {s : Set.{u1} β} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14022 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14024 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14022 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14024) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14037 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14039 : α) => LT.lt.{u2} α (Preorder.toLT.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14037 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14039)] [_inst_5 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14059 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14061 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14059 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14061)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14074 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14076 : α) => LT.lt.{u2} α (Preorder.toLT.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14074 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14076)], (StrictAntiOn.{u1, u2} β α _inst_3 _inst_2 f s) -> (StrictAntiOn.{u1, u2} β α _inst_3 _inst_2 g s) -> (StrictAntiOn.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) (g x)) s)
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {f : β -> α} {g : β -> α} {s : Set.{u1} β} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14020 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14022 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14020 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14022) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14035 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14037 : α) => LT.lt.{u2} α (Preorder.toLT.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14035 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14037)] [_inst_5 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14057 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14059 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14057 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14059)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14072 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14074 : α) => LT.lt.{u2} α (Preorder.toLT.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14072 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14074)], (StrictAntiOn.{u1, u2} β α _inst_3 _inst_2 f s) -> (StrictAntiOn.{u1, u2} β α _inst_3 _inst_2 g s) -> (StrictAntiOn.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) (g x)) s)
Case conversion may be inaccurate. Consider using '#align strict_anti_on.mul' StrictAntiOn.mul'ₓ'. -/
/-- The product of two strictly antitone functions is strictly antitone. -/
@[to_additive add "The sum of two strictly antitone functions is strictly antitone."]
@@ -2134,7 +2134,7 @@ theorem StrictAntiOn.mul' [CovariantClass α α (· * ·) (· < ·)]
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {f : β -> α} {g : β -> α}, (Monotone.{u2, u1} β α _inst_3 _inst_2 f) -> (StrictMono.{u2, u1} β α _inst_3 _inst_2 g) -> (StrictMono.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14161 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14163 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14161 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14163) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14176 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14178 : α) => LT.lt.{u2} α (Preorder.toLT.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14176 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14178)] [_inst_5 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14198 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14200 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14198 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14200)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14213 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14215 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14213 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14215)] {f : β -> α} {g : β -> α}, (Monotone.{u1, u2} β α _inst_3 _inst_2 f) -> (StrictMono.{u1, u2} β α _inst_3 _inst_2 g) -> (StrictMono.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) (g x)))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14159 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14161 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14159 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14161) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14174 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14176 : α) => LT.lt.{u2} α (Preorder.toLT.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14174 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14176)] [_inst_5 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14196 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14198 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14196 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14198)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14211 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14213 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14211 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14213)] {f : β -> α} {g : β -> α}, (Monotone.{u1, u2} β α _inst_3 _inst_2 f) -> (StrictMono.{u1, u2} β α _inst_3 _inst_2 g) -> (StrictMono.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) (g x)))
Case conversion may be inaccurate. Consider using '#align monotone.mul_strict_mono' Monotone.mul_strictMono'ₓ'. -/
/-- The product of a monotone function and a strictly monotone function is strictly monotone. -/
@[to_additive add_strict_mono
@@ -2150,7 +2150,7 @@ theorem Monotone.mul_strictMono' [CovariantClass α α (· * ·) (· < ·)]
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {f : β -> α} {g : β -> α}, (MonotoneOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (StrictMonoOn.{u2, u1} β α _inst_3 _inst_2 g s) -> (StrictMonoOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)) s)
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {s : Set.{u1} β} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14295 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14297 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14295 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14297) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14310 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14312 : α) => LT.lt.{u2} α (Preorder.toLT.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14310 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14312)] [_inst_5 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14332 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14334 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14332 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14334)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14347 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14349 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14347 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14349)] {f : β -> α} {g : β -> α}, (MonotoneOn.{u1, u2} β α _inst_3 _inst_2 f s) -> (StrictMonoOn.{u1, u2} β α _inst_3 _inst_2 g s) -> (StrictMonoOn.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) (g x)) s)
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {s : Set.{u1} β} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14293 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14295 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14293 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14295) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14308 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14310 : α) => LT.lt.{u2} α (Preorder.toLT.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14308 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14310)] [_inst_5 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14330 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14332 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14330 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14332)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14345 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14347 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14345 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14347)] {f : β -> α} {g : β -> α}, (MonotoneOn.{u1, u2} β α _inst_3 _inst_2 f s) -> (StrictMonoOn.{u1, u2} β α _inst_3 _inst_2 g s) -> (StrictMonoOn.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) (g x)) s)
Case conversion may be inaccurate. Consider using '#align monotone_on.mul_strict_mono' MonotoneOn.mul_strictMono'ₓ'. -/
/-- The product of a monotone function and a strictly monotone function is strictly monotone. -/
@[to_additive add_strict_mono
@@ -2166,7 +2166,7 @@ theorem MonotoneOn.mul_strictMono' [CovariantClass α α (· * ·) (· < ·)]
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {f : β -> α} {g : β -> α}, (Antitone.{u2, u1} β α _inst_3 _inst_2 f) -> (StrictAnti.{u2, u1} β α _inst_3 _inst_2 g) -> (StrictAnti.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)))
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14440 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14442 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14440 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14442) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14455 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14457 : α) => LT.lt.{u2} α (Preorder.toLT.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14455 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14457)] [_inst_5 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14477 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14479 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14477 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14479)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14492 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14494 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14492 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14494)] {f : β -> α} {g : β -> α}, (Antitone.{u1, u2} β α _inst_3 _inst_2 f) -> (StrictAnti.{u1, u2} β α _inst_3 _inst_2 g) -> (StrictAnti.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) (g x)))
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14438 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14440 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14438 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14440) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14453 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14455 : α) => LT.lt.{u2} α (Preorder.toLT.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14453 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14455)] [_inst_5 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14475 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14477 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14475 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14477)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14490 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14492 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14490 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14492)] {f : β -> α} {g : β -> α}, (Antitone.{u1, u2} β α _inst_3 _inst_2 f) -> (StrictAnti.{u1, u2} β α _inst_3 _inst_2 g) -> (StrictAnti.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) (g x)))
Case conversion may be inaccurate. Consider using '#align antitone.mul_strict_anti' Antitone.mul_strictAnti'ₓ'. -/
/-- The product of a antitone function and a strictly antitone function is strictly antitone. -/
@[to_additive add_strict_anti
@@ -2182,7 +2182,7 @@ theorem Antitone.mul_strictAnti' [CovariantClass α α (· * ·) (· < ·)]
lean 3 declaration is
forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Mul.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : Preorder.{u2} β] {s : Set.{u2} β} [_inst_4 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1)) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2))] [_inst_5 : CovariantClass.{u1, u1} α α (Function.swap.{succ u1, succ u1, succ u1} α α (fun (ᾰ : α) (ᾰ : α) => α) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1))) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2))] {f : β -> α} {g : β -> α}, (AntitoneOn.{u2, u1} β α _inst_3 _inst_2 f s) -> (StrictAntiOn.{u2, u1} β α _inst_3 _inst_2 g s) -> (StrictAntiOn.{u2, u1} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α _inst_1) (f x) (g x)) s)
but is expected to have type
- forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {s : Set.{u1} β} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14574 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14576 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14574 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14576) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14589 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14591 : α) => LT.lt.{u2} α (Preorder.toLT.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14589 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14591)] [_inst_5 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14611 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14613 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14611 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14613)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14626 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14628 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14626 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14628)] {f : β -> α} {g : β -> α}, (AntitoneOn.{u1, u2} β α _inst_3 _inst_2 f s) -> (StrictAntiOn.{u1, u2} β α _inst_3 _inst_2 g s) -> (StrictAntiOn.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) (g x)) s)
+ forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Mul.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : Preorder.{u1} β] {s : Set.{u1} β} [_inst_4 : CovariantClass.{u2, u2} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14572 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14574 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14572 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14574) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14587 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14589 : α) => LT.lt.{u2} α (Preorder.toLT.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14587 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14589)] [_inst_5 : CovariantClass.{u2, u2} α α (Function.swap.{succ u2, succ u2, succ u2} α α (fun (ᾰ : α) (ᾰ : α) => α) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14609 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14611 : α) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14609 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14611)) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14624 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14626 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14624 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.14626)] {f : β -> α} {g : β -> α}, (AntitoneOn.{u1, u2} β α _inst_3 _inst_2 f s) -> (StrictAntiOn.{u1, u2} β α _inst_3 _inst_2 g s) -> (StrictAntiOn.{u1, u2} β α _inst_3 _inst_2 (fun (x : β) => HMul.hMul.{u2, u2, u2} α α α (instHMul.{u2} α _inst_1) (f x) (g x)) s)
Case conversion may be inaccurate. Consider using '#align antitone_on.mul_strict_anti' AntitoneOn.mul_strictAnti'ₓ'. -/
/-- The product of a antitone function and a strictly antitone function is strictly antitone. -/
@[to_additive add_strict_anti
@@ -2352,7 +2352,7 @@ protected theorem mul_le_mul_iff_left [Mul α] [CovariantClass α α (· * ·) (
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] [_inst_2 : CommSemigroup.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α (CommSemigroup.toSemigroup.{u1} α _inst_2)))) (LE.le.{u1} α _inst_1)] {a : α} {b : α} {c : α}, (MulLECancellable.{u1} α (Semigroup.toHasMul.{u1} α (CommSemigroup.toSemigroup.{u1} α _inst_2)) _inst_1 a) -> (Iff (LE.le.{u1} α _inst_1 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α (CommSemigroup.toSemigroup.{u1} α _inst_2))) b a) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toHasMul.{u1} α (CommSemigroup.toSemigroup.{u1} α _inst_2))) c a)) (LE.le.{u1} α _inst_1 b c))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] [_inst_2 : CommSemigroup.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16067 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16069 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α (CommSemigroup.toSemigroup.{u1} α _inst_2))) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16067 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16069) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16082 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16084 : α) => LE.le.{u1} α _inst_1 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16082 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16084)] {a : α} {b : α} {c : α}, (MulLECancellable.{u1} α (Semigroup.toMul.{u1} α (CommSemigroup.toSemigroup.{u1} α _inst_2)) _inst_1 a) -> (Iff (LE.le.{u1} α _inst_1 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α (CommSemigroup.toSemigroup.{u1} α _inst_2))) b a) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α (CommSemigroup.toSemigroup.{u1} α _inst_2))) c a)) (LE.le.{u1} α _inst_1 b c))
+ forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] [_inst_2 : CommSemigroup.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16065 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16067 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α (CommSemigroup.toSemigroup.{u1} α _inst_2))) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16065 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16067) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16080 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16082 : α) => LE.le.{u1} α _inst_1 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16080 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16082)] {a : α} {b : α} {c : α}, (MulLECancellable.{u1} α (Semigroup.toMul.{u1} α (CommSemigroup.toSemigroup.{u1} α _inst_2)) _inst_1 a) -> (Iff (LE.le.{u1} α _inst_1 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α (CommSemigroup.toSemigroup.{u1} α _inst_2))) b a) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Semigroup.toMul.{u1} α (CommSemigroup.toSemigroup.{u1} α _inst_2))) c a)) (LE.le.{u1} α _inst_1 b c))
Case conversion may be inaccurate. Consider using '#align mul_le_cancellable.mul_le_mul_iff_right MulLECancellable.mul_le_mul_iff_rightₓ'. -/
@[to_additive]
protected theorem mul_le_mul_iff_right [CommSemigroup α] [CovariantClass α α (· * ·) (· ≤ ·)]
@@ -2365,7 +2365,7 @@ protected theorem mul_le_mul_iff_right [CommSemigroup α] [CovariantClass α α
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] [_inst_2 : MulOneClass.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_2))) (LE.le.{u1} α _inst_1)] {a : α} {b : α}, (MulLECancellable.{u1} α (MulOneClass.toHasMul.{u1} α _inst_2) _inst_1 a) -> (Iff (LE.le.{u1} α _inst_1 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_2)) a b)) (LE.le.{u1} α _inst_1 (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_2)))) b))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] [_inst_2 : MulOneClass.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16166 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16168 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16166 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16168) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16181 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16183 : α) => LE.le.{u1} α _inst_1 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16181 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16183)] {a : α} {b : α}, (MulLECancellable.{u1} α (MulOneClass.toMul.{u1} α _inst_2) _inst_1 a) -> (Iff (LE.le.{u1} α _inst_1 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_2)) a b)) (LE.le.{u1} α _inst_1 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_2))) b))
+ forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] [_inst_2 : MulOneClass.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16164 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16166 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16164 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16166) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16179 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16181 : α) => LE.le.{u1} α _inst_1 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16179 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16181)] {a : α} {b : α}, (MulLECancellable.{u1} α (MulOneClass.toMul.{u1} α _inst_2) _inst_1 a) -> (Iff (LE.le.{u1} α _inst_1 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_2)) a b)) (LE.le.{u1} α _inst_1 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_2))) b))
Case conversion may be inaccurate. Consider using '#align mul_le_cancellable.le_mul_iff_one_le_right MulLECancellable.le_mul_iff_one_le_rightₓ'. -/
@[to_additive]
protected theorem le_mul_iff_one_le_right [MulOneClass α] [CovariantClass α α (· * ·) (· ≤ ·)]
@@ -2378,7 +2378,7 @@ protected theorem le_mul_iff_one_le_right [MulOneClass α] [CovariantClass α α
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] [_inst_2 : MulOneClass.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_2))) (LE.le.{u1} α _inst_1)] {a : α} {b : α}, (MulLECancellable.{u1} α (MulOneClass.toHasMul.{u1} α _inst_2) _inst_1 a) -> (Iff (LE.le.{u1} α _inst_1 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α _inst_2)) a b) a) (LE.le.{u1} α _inst_1 b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α _inst_2))))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] [_inst_2 : MulOneClass.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16262 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16264 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16262 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16264) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16277 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16279 : α) => LE.le.{u1} α _inst_1 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16277 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16279)] {a : α} {b : α}, (MulLECancellable.{u1} α (MulOneClass.toMul.{u1} α _inst_2) _inst_1 a) -> (Iff (LE.le.{u1} α _inst_1 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_2)) a b) a) (LE.le.{u1} α _inst_1 b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_2)))))
+ forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] [_inst_2 : MulOneClass.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16260 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16262 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_2)) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16260 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16262) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16275 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16277 : α) => LE.le.{u1} α _inst_1 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16275 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16277)] {a : α} {b : α}, (MulLECancellable.{u1} α (MulOneClass.toMul.{u1} α _inst_2) _inst_1 a) -> (Iff (LE.le.{u1} α _inst_1 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α _inst_2)) a b) a) (LE.le.{u1} α _inst_1 b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (MulOneClass.toOne.{u1} α _inst_2)))))
Case conversion may be inaccurate. Consider using '#align mul_le_cancellable.mul_le_iff_le_one_right MulLECancellable.mul_le_iff_le_one_rightₓ'. -/
@[to_additive]
protected theorem mul_le_iff_le_one_right [MulOneClass α] [CovariantClass α α (· * ·) (· ≤ ·)]
@@ -2391,7 +2391,7 @@ protected theorem mul_le_iff_le_one_right [MulOneClass α] [CovariantClass α α
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] [_inst_2 : CommMonoid.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2))))) (LE.le.{u1} α _inst_1)] {a : α} {b : α}, (MulLECancellable.{u1} α (MulOneClass.toHasMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2))) _inst_1 a) -> (Iff (LE.le.{u1} α _inst_1 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2)))) b a)) (LE.le.{u1} α _inst_1 (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2)))))) b))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] [_inst_2 : CommMonoid.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16358 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16360 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2)))) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16358 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16360) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16373 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16375 : α) => LE.le.{u1} α _inst_1 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16373 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16375)] {a : α} {b : α}, (MulLECancellable.{u1} α (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2))) _inst_1 a) -> (Iff (LE.le.{u1} α _inst_1 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2)))) b a)) (LE.le.{u1} α _inst_1 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2)))) b))
+ forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] [_inst_2 : CommMonoid.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16356 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16358 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2)))) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16356 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16358) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16371 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16373 : α) => LE.le.{u1} α _inst_1 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16371 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16373)] {a : α} {b : α}, (MulLECancellable.{u1} α (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2))) _inst_1 a) -> (Iff (LE.le.{u1} α _inst_1 a (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2)))) b a)) (LE.le.{u1} α _inst_1 (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2)))) b))
Case conversion may be inaccurate. Consider using '#align mul_le_cancellable.le_mul_iff_one_le_left MulLECancellable.le_mul_iff_one_le_leftₓ'. -/
@[to_additive]
protected theorem le_mul_iff_one_le_left [CommMonoid α] [CovariantClass α α (· * ·) (· ≤ ·)]
@@ -2404,7 +2404,7 @@ protected theorem le_mul_iff_one_le_left [CommMonoid α] [CovariantClass α α (
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] [_inst_2 : CommMonoid.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2))))) (LE.le.{u1} α _inst_1)] {a : α} {b : α}, (MulLECancellable.{u1} α (MulOneClass.toHasMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2))) _inst_1 a) -> (Iff (LE.le.{u1} α _inst_1 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2)))) b a) a) (LE.le.{u1} α _inst_1 b (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (MulOneClass.toHasOne.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2))))))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] [_inst_2 : CommMonoid.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16451 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16453 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2)))) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16451 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16453) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16466 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16468 : α) => LE.le.{u1} α _inst_1 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16466 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16468)] {a : α} {b : α}, (MulLECancellable.{u1} α (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2))) _inst_1 a) -> (Iff (LE.le.{u1} α _inst_1 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2)))) b a) a) (LE.le.{u1} α _inst_1 b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2))))))
+ forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] [_inst_2 : CommMonoid.{u1} α] [_inst_3 : CovariantClass.{u1, u1} α α (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16449 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16451 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2)))) x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16449 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16451) (fun (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16464 : α) (x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16466 : α) => LE.le.{u1} α _inst_1 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16464 x._@.Mathlib.Algebra.Order.Monoid.Lemmas._hyg.16466)] {a : α} {b : α}, (MulLECancellable.{u1} α (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2))) _inst_1 a) -> (Iff (LE.le.{u1} α _inst_1 (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2)))) b a) a) (LE.le.{u1} α _inst_1 b (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Monoid.toOne.{u1} α (CommMonoid.toMonoid.{u1} α _inst_2))))))
Case conversion may be inaccurate. Consider using '#align mul_le_cancellable.mul_le_iff_le_one_left MulLECancellable.mul_le_iff_le_one_leftₓ'. -/
@[to_additive]
protected theorem mul_le_iff_le_one_left [CommMonoid α] [CovariantClass α α (· * ·) (· ≤ ·)]
mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442
@@ -743,7 +743,7 @@ theorem mul_le_of_le_of_le_one [CovariantClass α α (· * ·) (· ≤ ·)] {a b
(ha : a ≤ 1) : b * a ≤ c :=
calc
b * a ≤ b * 1 := mul_le_mul_left' ha b
- _ = b := mul_one b
+ _ = b := (mul_one b)
_ ≤ c := hbc
#align mul_le_of_le_of_le_one mul_le_of_le_of_le_one
@@ -760,7 +760,7 @@ theorem mul_lt_of_le_of_lt_one [CovariantClass α α (· * ·) (· < ·)] {a b c
(ha : a < 1) : b * a < c :=
calc
b * a < b * 1 := mul_lt_mul_left' ha b
- _ = b := mul_one b
+ _ = b := (mul_one b)
_ ≤ c := hbc
#align mul_lt_of_le_of_lt_one mul_lt_of_le_of_lt_one
@@ -777,7 +777,7 @@ theorem mul_lt_of_lt_of_le_one [CovariantClass α α (· * ·) (· ≤ ·)] {a b
(ha : a ≤ 1) : b * a < c :=
calc
b * a ≤ b * 1 := mul_le_mul_left' ha b
- _ = b := mul_one b
+ _ = b := (mul_one b)
_ < c := hbc
#align mul_lt_of_lt_of_le_one mul_lt_of_lt_of_le_one
@@ -794,7 +794,7 @@ theorem mul_lt_of_lt_of_lt_one [CovariantClass α α (· * ·) (· < ·)] {a b c
(ha : a < 1) : b * a < c :=
calc
b * a < b * 1 := mul_lt_mul_left' ha b
- _ = b := mul_one b
+ _ = b := (mul_one b)
_ < c := hbc
#align mul_lt_of_lt_of_lt_one mul_lt_of_lt_of_lt_one
@@ -1071,7 +1071,7 @@ theorem mul_le_of_le_one_of_le [CovariantClass α α (swap (· * ·)) (· ≤ ·
(hbc : b ≤ c) : a * b ≤ c :=
calc
a * b ≤ 1 * b := mul_le_mul_right' ha b
- _ = b := one_mul b
+ _ = b := (one_mul b)
_ ≤ c := hbc
#align mul_le_of_le_one_of_le mul_le_of_le_one_of_le
@@ -1088,7 +1088,7 @@ theorem mul_lt_of_lt_one_of_le [CovariantClass α α (swap (· * ·)) (· < ·)]
(hbc : b ≤ c) : a * b < c :=
calc
a * b < 1 * b := mul_lt_mul_right' ha b
- _ = b := one_mul b
+ _ = b := (one_mul b)
_ ≤ c := hbc
#align mul_lt_of_lt_one_of_le mul_lt_of_lt_one_of_le
@@ -1105,7 +1105,7 @@ theorem mul_lt_of_le_one_of_lt [CovariantClass α α (swap (· * ·)) (· ≤ ·
(hb : b < c) : a * b < c :=
calc
a * b ≤ 1 * b := mul_le_mul_right' ha b
- _ = b := one_mul b
+ _ = b := (one_mul b)
_ < c := hb
#align mul_lt_of_le_one_of_lt mul_lt_of_le_one_of_lt
@@ -1122,7 +1122,7 @@ theorem mul_lt_of_lt_one_of_lt [CovariantClass α α (swap (· * ·)) (· < ·)]
(hb : b < c) : a * b < c :=
calc
a * b < 1 * b := mul_lt_mul_right' ha b
- _ = b := one_mul b
+ _ = b := (one_mul b)
_ < c := hb
#align mul_lt_of_lt_one_of_lt mul_lt_of_lt_one_of_lt
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
Homogenises porting notes via capitalisation and addition of whitespace.
It makes the following changes:
@@ -1188,7 +1188,7 @@ theorem mul_eq_one_iff' [CovariantClass α α (· * ·) (· ≤ ·)]
have : b = 1 := le_antisymm this hb
And.intro ‹a = 1› ‹b = 1›)
(by rintro ⟨rfl, rfl⟩; rw [mul_one])
- -- porting note: original proof of the second implication,
+ -- Porting note: original proof of the second implication,
-- `fun ⟨ha', hb'⟩ => by rw [ha', hb', mul_one]`,
-- had its `to_additive`-ization fail due to some bug
#align mul_eq_one_iff' mul_eq_one_iff'
@[gcongr]
tags around (#9393)
import Mathlib.Tactic.GCongr.Core
to Algebra/Order/Ring/Lemmas
.@[gcongr]
tags next to the lemmas.See Zulip thread
Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>
@@ -46,7 +46,7 @@ variable [LE α]
/- The prime on this lemma is present only on the multiplicative version. The unprimed version
is taken by the analogous lemma for semiring, with an extra non-negativity assumption. -/
-@[to_additive add_le_add_left]
+@[to_additive (attr := gcongr) add_le_add_left]
theorem mul_le_mul_left' [CovariantClass α α (· * ·) (· ≤ ·)] {b c : α} (bc : b ≤ c) (a : α) :
a * b ≤ a * c :=
CovariantClass.elim _ bc
@@ -63,7 +63,7 @@ theorem le_of_mul_le_mul_left' [ContravariantClass α α (· * ·) (· ≤ ·)]
/- The prime on this lemma is present only on the multiplicative version. The unprimed version
is taken by the analogous lemma for semiring, with an extra non-negativity assumption. -/
-@[to_additive add_le_add_right]
+@[to_additive (attr := gcongr) add_le_add_right]
theorem mul_le_mul_right' [i : CovariantClass α α (swap (· * ·)) (· ≤ ·)] {b c : α} (bc : b ≤ c)
(a : α) :
b * a ≤ c * a :=
@@ -117,7 +117,7 @@ theorem mul_lt_mul_iff_right [CovariantClass α α (swap (· * ·)) (· < ·)]
#align mul_lt_mul_iff_right mul_lt_mul_iff_right
#align add_lt_add_iff_right add_lt_add_iff_right
-@[to_additive add_lt_add_left]
+@[to_additive (attr := gcongr) add_lt_add_left]
theorem mul_lt_mul_left' [CovariantClass α α (· * ·) (· < ·)] {b c : α} (bc : b < c) (a : α) :
a * b < a * c :=
CovariantClass.elim _ bc
@@ -132,7 +132,7 @@ theorem lt_of_mul_lt_mul_left' [ContravariantClass α α (· * ·) (· < ·)] {a
#align lt_of_mul_lt_mul_left' lt_of_mul_lt_mul_left'
#align lt_of_add_lt_add_left lt_of_add_lt_add_left
-@[to_additive add_lt_add_right]
+@[to_additive (attr := gcongr) add_lt_add_right]
theorem mul_lt_mul_right' [i : CovariantClass α α (swap (· * ·)) (· < ·)] {b c : α} (bc : b < c)
(a : α) :
b * a < c * a :=
@@ -154,7 +154,7 @@ section Preorder
variable [Preorder α]
-@[to_additive]
+@[to_additive (attr := gcongr)]
theorem mul_lt_mul_of_lt_of_lt [CovariantClass α α (· * ·) (· < ·)]
[CovariantClass α α (swap (· * ·)) (· < ·)]
{a b c d : α} (h₁ : a < b) (h₂ : c < d) : a * c < b * d :=
@@ -202,7 +202,7 @@ theorem Right.mul_lt_mul [CovariantClass α α (· * ·) (· ≤ ·)]
#align right.mul_lt_mul Right.mul_lt_mul
#align right.add_lt_add Right.add_lt_add
-@[to_additive add_le_add]
+@[to_additive (attr := gcongr) add_le_add]
theorem mul_le_mul' [CovariantClass α α (· * ·) (· ≤ ·)] [CovariantClass α α (swap (· * ·)) (· ≤ ·)]
{a b c d : α} (h₁ : a ≤ b) (h₂ : c ≤ d) :
a * c ≤ b * d :=
(· op ·) a
by (a op ·)
(#8843)
I used the regex \(\(· (.) ·\) (.)\)
, replacing with ($2 $1 ·)
.
@@ -1616,7 +1616,7 @@ namespace MulLECancellable
@[to_additive]
protected theorem Injective [Mul α] [PartialOrder α] {a : α} (ha : MulLECancellable a) :
- Injective ((· * ·) a) :=
+ Injective (a * ·) :=
fun _ _ h => le_antisymm (ha h.le) (ha h.ge)
#align mul_le_cancellable.injective MulLECancellable.Injective
#align add_le_cancellable.injective AddLECancellable.Injective
Forward-ports https://github.com/leanprover-community/mathlib/pull/18797
The changes to Mathlib.Data.Set.Intervals.Basic
were independently added to mathlib4 in Mathlib.Data.Set.Intervals.Image
, so the #align
s have been added there instead of the original file.
Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
@@ -9,7 +9,7 @@ import Mathlib.Init.Data.Ordering.Basic
import Mathlib.Order.MinMax
import Mathlib.Tactic.Contrapose
-#align_import algebra.order.monoid.lemmas from "leanprover-community/mathlib"@"2ed7e4aec72395b6a7c3ac4ac7873a7a43ead17c"
+#align_import algebra.order.monoid.lemmas from "leanprover-community/mathlib"@"3ba15165bd6927679be7c22d6091a87337e3cd0c"
/-!
# Ordered monoids
@@ -355,6 +355,27 @@ variable [LinearOrder α] {a b c d : α}
#align min_le_max_of_add_le_add min_le_max_of_add_le_add
#align min_le_max_of_mul_le_mul min_le_max_of_mul_le_mul
+end LinearOrder
+
+section LinearOrder
+variable [LinearOrder α] [CovariantClass α α (· * ·) (· ≤ ·)]
+ [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c d : α}
+
+@[to_additive max_add_add_le_max_add_max]
+theorem max_mul_mul_le_max_mul_max' : max (a * b) (c * d) ≤ max a c * max b d :=
+ max_le (mul_le_mul' (le_max_left _ _) <| le_max_left _ _) <|
+ mul_le_mul' (le_max_right _ _) <| le_max_right _ _
+#align max_mul_mul_le_max_mul_max' max_mul_mul_le_max_mul_max'
+#align max_add_add_le_max_add_max max_add_add_le_max_add_max
+
+--TODO: Also missing `min_mul_min_le_min_mul_mul`
+@[to_additive min_add_min_le_min_add_add]
+theorem min_mul_min_le_min_mul_mul' : min a c * min b d ≤ min (a * b) (c * d) :=
+ le_min (mul_le_mul' (min_le_left _ _) <| min_le_left _ _) <|
+ mul_le_mul' (min_le_right _ _) <| min_le_right _ _
+#align min_mul_min_le_min_mul_mul' min_mul_min_le_min_mul_mul'
+#align min_add_min_le_min_add_add min_add_min_le_min_add_add
+
end LinearOrder
end Mul
4 files have major changes:
Algebra/CovariantAndContravariant.lean
contravariant_le_iff_contravariant_lt_and_eq
.covariantClass_le_of_lt
generalizing and replacing Mul.to_covariantClass_left/right
in Algebra/Order/Monoid/Defs.leanCommSemigroup
by IsSymmOp N N mu
and replace CancelSemigroup
by IsMulCancel
, removing superfluous associativity assumption.covariant_lt_of_covariant_le_of_contravariant_eq
and contravariant_le_of_contravariant_eq_and_lt
that could replace eight instances when appropriate refactoring is in place.Algebra/Order/Monoid/Lemmas.lean
mul_eq_mul_iff_eq_and_eq
and remove the less general Left/Right.mul_eq_mul_iff_eq_and_eq
.mul_le_mul_iff_of_ge
.min_le_max_of_mul_le_mul
.min_lt_max_of_mul_lt_mul
here from Algebra/GroupPower/Order.lean.CommSemigroup
by IsSymmOp
.Algebra/Order/Monoid/Basic.lean
eq_and_eq_of_le_of_le_of_mul_le
as it's just one direction of mul_le_mul_iff_of_ge
but with more assumptions.Algebra/Order/Ring/Lemmas.lean
mul_eq_mul_iff_eq_and_eq_of_pos
Changes to Algebra/Group/UniqueProds.lean and Algebra/MonoidAlgebra/NoZeroDivisors.lean are in declarations that will be removed by #6723.
Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>
@@ -300,18 +300,58 @@ theorem mul_left_cancel'' [ContravariantClass α α (· * ·) (· ≤ ·)] {a b
theorem mul_right_cancel'' [ContravariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α}
(h : a * b = c * b) :
a = c :=
- le_antisymm (le_of_mul_le_mul_right' h.le) (le_of_mul_le_mul_right' h.ge)
+ (le_of_mul_le_mul_right' h.le).antisymm (le_of_mul_le_mul_right' h.ge)
#align mul_right_cancel'' mul_right_cancel''
#align add_right_cancel'' add_right_cancel''
+@[to_additive] lemma mul_le_mul_iff_of_ge [CovariantClass α α (· * ·) (· < ·)]
+ [CovariantClass α α (swap (· * ·)) (· < ·)] {a₁ a₂ b₁ b₂ : α} (ha : a₁ ≤ a₂) (hb : b₁ ≤ b₂) :
+ a₂ * b₂ ≤ a₁ * b₁ ↔ a₁ = a₂ ∧ b₁ = b₂ := by
+ haveI := covariantClass_le_of_lt α α (· * ·)
+ haveI := covariantClass_le_of_lt α α (swap (· * ·))
+ refine' ⟨fun h ↦ _, by rintro ⟨rfl, rfl⟩; rfl⟩
+ simp only [eq_iff_le_not_lt, ha, hb, true_and]
+ refine' ⟨fun ha ↦ h.not_lt _, fun hb ↦ h.not_lt _⟩
+ exacts [mul_lt_mul_of_lt_of_le ha hb, mul_lt_mul_of_le_of_lt ha hb]
+#align add_le_add_iff_of_ge add_le_add_iff_of_geₓ
+#align mul_le_mul_iff_of_ge mul_le_mul_iff_of_geₓ
+
+@[to_additive] theorem mul_eq_mul_iff_eq_and_eq [CovariantClass α α (· * ·) (· < ·)]
+ [CovariantClass α α (swap (· * ·)) (· < ·)] {a b c d : α} (hac : a ≤ c) (hbd : b ≤ d) :
+ a * b = c * d ↔ a = c ∧ b = d := by
+ haveI := covariantClass_le_of_lt α α (· * ·)
+ haveI := covariantClass_le_of_lt α α (swap (· * ·))
+ rw [le_antisymm_iff, eq_true (mul_le_mul' hac hbd), true_and, mul_le_mul_iff_of_ge hac hbd]
+#align mul_eq_mul_iff_eq_and_eq mul_eq_mul_iff_eq_and_eqₓ
+#align add_eq_add_iff_eq_and_eq add_eq_add_iff_eq_and_eqₓ
+
end PartialOrder
section LinearOrder
-variable [LinearOrder α] {a b c d : α} [CovariantClass α α (· * ·) (· < ·)]
- [CovariantClass α α (swap (· * ·)) (· < ·)]
-
-@[to_additive] lemma min_le_max_of_mul_le_mul (h : a * b ≤ c * d) : min a b ≤ max c d :=
-by simp_rw [min_le_iff, le_max_iff]; contrapose! h; exact mul_lt_mul_of_lt_of_lt h.1.1 h.2.2
+variable [LinearOrder α] {a b c d : α}
+
+@[to_additive] lemma min_lt_max_of_mul_lt_mul
+ [CovariantClass α α (· * ·) (· ≤ ·)] [CovariantClass α α (swap (· * ·)) (· ≤ ·)]
+ (h : a * b < c * d) : min a b < max c d := by
+ simp_rw [min_lt_iff, lt_max_iff]; contrapose! h; exact mul_le_mul' h.1.1 h.2.2
+#align min_lt_max_of_mul_lt_mul min_lt_max_of_mul_lt_mulₓ
+#align min_lt_max_of_add_lt_add min_lt_max_of_add_lt_addₓ
+
+@[to_additive] lemma Left.min_le_max_of_mul_le_mul
+ [CovariantClass α α (· * ·) (· < ·)] [CovariantClass α α (swap (· * ·)) (· ≤ ·)]
+ (h : a * b ≤ c * d) : min a b ≤ max c d := by
+ simp_rw [min_le_iff, le_max_iff]; contrapose! h; exact mul_lt_mul_of_le_of_lt h.1.1.le h.2.2
+
+@[to_additive] lemma Right.min_le_max_of_mul_le_mul
+ [CovariantClass α α (· * ·) (· ≤ ·)] [CovariantClass α α (swap (· * ·)) (· < ·)]
+ (h : a * b ≤ c * d) : min a b ≤ max c d := by
+ simp_rw [min_le_iff, le_max_iff]; contrapose! h; exact mul_lt_mul_of_lt_of_le h.1.1 h.2.2.le
+
+@[to_additive] lemma min_le_max_of_mul_le_mul
+ [CovariantClass α α (· * ·) (· < ·)] [CovariantClass α α (swap (· * ·)) (· < ·)]
+ (h : a * b ≤ c * d) : min a b ≤ max c d :=
+ let _ := covariantClass_le_of_lt α α (swap (· * ·))
+ Left.min_le_max_of_mul_le_mul h
#align min_le_max_of_add_le_add min_le_max_of_add_le_add
#align min_le_max_of_mul_le_mul min_le_max_of_mul_le_mul
@@ -1133,18 +1173,6 @@ theorem mul_eq_one_iff' [CovariantClass α α (· * ·) (· ≤ ·)]
#align mul_eq_one_iff' mul_eq_one_iff'
#align add_eq_zero_iff' add_eq_zero_iff'
-@[to_additive] lemma mul_le_mul_iff_of_ge [CovariantClass α α (· * ·) (· ≤ ·)]
- [CovariantClass α α (swap (· * ·)) (· ≤ ·)] [CovariantClass α α (· * ·) (· < ·)]
- [CovariantClass α α (swap (· * ·)) (· < ·)] {a₁ a₂ b₁ b₂ : α} (ha : a₁ ≤ a₂) (hb : b₁ ≤ b₂) :
- a₂ * b₂ ≤ a₁ * b₁ ↔ a₁ = a₂ ∧ b₁ = b₂ := by
- refine' ⟨fun h ↦ _, by rintro ⟨rfl, rfl⟩; rfl⟩
- simp only [eq_iff_le_not_lt, ha, hb, true_and]
- refine' ⟨fun ha ↦ h.not_lt _, fun hb ↦ h.not_lt _⟩
- { exact mul_lt_mul_of_lt_of_le ha hb }
- { exact mul_lt_mul_of_le_of_lt ha hb }
-#align add_le_add_iff_of_ge add_le_add_iff_of_ge
-#align mul_le_mul_iff_of_ge mul_le_mul_iff_of_ge
-
section Left
variable [CovariantClass α α (· * ·) (· ≤ ·)] {a b : α}
@@ -1188,7 +1216,7 @@ section LinearOrder
variable [LinearOrder α]
theorem exists_square_le [CovariantClass α α (· * ·) (· < ·)] (a : α) : ∃ b : α, b * b ≤ a := by
- by_cases h:a < 1
+ by_cases h : a < 1
· use a
have : a * a < a * 1 := mul_lt_mul_left' h a
rw [mul_one] at this
@@ -1236,43 +1264,12 @@ def Contravariant.toRightCancelSemigroup [ContravariantClass α α (swap (· *
#align contravariant.to_right_cancel_semigroup Contravariant.toRightCancelSemigroup
#align contravariant.to_right_cancel_add_semigroup Contravariant.toAddRightCancelSemigroup
-@[to_additive]
-theorem Left.mul_eq_mul_iff_eq_and_eq [CovariantClass α α (· * ·) (· < ·)]
- [CovariantClass α α (swap (· * ·)) (· ≤ ·)] [ContravariantClass α α (· * ·) (· ≤ ·)]
- [ContravariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c d : α} (hac : a ≤ c) (hbd : b ≤ d) :
- a * b = c * d ↔ a = c ∧ b = d := by
- refine' ⟨fun h => _, fun h => congr_arg₂ (· * ·) h.1 h.2⟩
- rcases hac.eq_or_lt with (rfl | hac)
- · exact ⟨rfl, mul_left_cancel'' h⟩
-
- rcases eq_or_lt_of_le hbd with (rfl | hbd)
- · exact ⟨mul_right_cancel'' h, rfl⟩
-
- exact ((Left.mul_lt_mul hac hbd).ne h).elim
-#align left.mul_eq_mul_iff_eq_and_eq Left.mul_eq_mul_iff_eq_and_eq
-#align left.add_eq_add_iff_eq_and_eq Left.add_eq_add_iff_eq_and_eq
-
-@[to_additive]
-theorem Right.mul_eq_mul_iff_eq_and_eq [CovariantClass α α (· * ·) (· ≤ ·)]
- [ContravariantClass α α (· * ·) (· ≤ ·)] [CovariantClass α α (swap (· * ·)) (· < ·)]
- [ContravariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c d : α} (hac : a ≤ c) (hbd : b ≤ d) :
- a * b = c * d ↔ a = c ∧ b = d := by
- refine' ⟨fun h => _, fun h => congr_arg₂ (· * ·) h.1 h.2⟩
- rcases hac.eq_or_lt with (rfl | hac)
- · exact ⟨rfl, mul_left_cancel'' h⟩
-
- rcases eq_or_lt_of_le hbd with (rfl | hbd)
- · exact ⟨mul_right_cancel'' h, rfl⟩
-
- exact ((Right.mul_lt_mul hac hbd).ne h).elim
-#align right.mul_eq_mul_iff_eq_and_eq Right.mul_eq_mul_iff_eq_and_eq
-#align right.add_eq_add_iff_eq_and_eq Right.add_eq_add_iff_eq_and_eq
-
-alias mul_eq_mul_iff_eq_and_eq := Left.mul_eq_mul_iff_eq_and_eq
-#align mul_eq_mul_iff_eq_and_eq mul_eq_mul_iff_eq_and_eq
-
-attribute [to_additive] mul_eq_mul_iff_eq_and_eq
-#align add_eq_add_iff_eq_and_eq add_eq_add_iff_eq_and_eq
+#noalign eq_and_eq_of_le_of_le_of_mul_le
+#noalign eq_and_eq_of_le_of_le_of_add_le
+#noalign left.mul_eq_mul_iff_eq_and_eq
+#noalign left.add_eq_add_iff_eq_and_eq
+#noalign right.mul_eq_mul_iff_eq_and_eq
+#noalign right.add_eq_add_iff_eq_and_eq
end PartialOrder
@@ -1611,19 +1608,19 @@ protected theorem inj [Mul α] [PartialOrder α] {a b c : α} (ha : MulLECancell
#align add_le_cancellable.inj AddLECancellable.inj
@[to_additive]
-protected theorem injective_left [CommSemigroup α] [PartialOrder α] {a : α}
+protected theorem injective_left [Mul α] [i : IsSymmOp α α (· * ·)] [PartialOrder α] {a : α}
(ha : MulLECancellable a) :
- Injective (· * a) := fun b c h => ha.Injective <| by dsimp; rwa [mul_comm a, mul_comm a]
-#align mul_le_cancellable.injective_left MulLECancellable.injective_left
-#align add_le_cancellable.injective_left AddLECancellable.injective_left
+ Injective (· * a) := fun b c h => ha.Injective <| by dsimp; rwa [i.symm_op a, i.symm_op a]
+#align mul_le_cancellable.injective_left MulLECancellable.injective_leftₓ
+#align add_le_cancellable.injective_left AddLECancellable.injective_leftₓ
@[to_additive]
-protected theorem inj_left [CommSemigroup α] [PartialOrder α] {a b c : α}
+protected theorem inj_left [Mul α] [IsSymmOp α α (· * ·)] [PartialOrder α] {a b c : α}
(hc : MulLECancellable c) :
a * c = b * c ↔ a = b :=
hc.injective_left.eq_iff
-#align mul_le_cancellable.inj_left MulLECancellable.inj_left
-#align add_le_cancellable.inj_left AddLECancellable.inj_left
+#align mul_le_cancellable.inj_left MulLECancellable.inj_leftₓ
+#align add_le_cancellable.inj_left AddLECancellable.inj_leftₓ
variable [LE α]
@@ -1635,11 +1632,11 @@ protected theorem mul_le_mul_iff_left [Mul α] [CovariantClass α α (· * ·) (
#align add_le_cancellable.add_le_add_iff_left AddLECancellable.add_le_add_iff_left
@[to_additive]
-protected theorem mul_le_mul_iff_right [CommSemigroup α] [CovariantClass α α (· * ·) (· ≤ ·)]
- {a b c : α} (ha : MulLECancellable a) :
- b * a ≤ c * a ↔ b ≤ c := by rw [mul_comm b, mul_comm c, ha.mul_le_mul_iff_left]
-#align mul_le_cancellable.mul_le_mul_iff_right MulLECancellable.mul_le_mul_iff_right
-#align add_le_cancellable.add_le_add_iff_right AddLECancellable.add_le_add_iff_right
+protected theorem mul_le_mul_iff_right [Mul α] [i : IsSymmOp α α (· * ·)]
+ [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (ha : MulLECancellable a) :
+ b * a ≤ c * a ↔ b ≤ c := by rw [i.symm_op b, i.symm_op c, ha.mul_le_mul_iff_left]
+#align mul_le_cancellable.mul_le_mul_iff_right MulLECancellable.mul_le_mul_iff_rightₓ
+#align add_le_cancellable.add_le_add_iff_right AddLECancellable.add_le_add_iff_rightₓ
@[to_additive]
protected theorem le_mul_iff_one_le_right [MulOneClass α] [CovariantClass α α (· * ·) (· ≤ ·)]
@@ -1658,18 +1655,18 @@ protected theorem mul_le_iff_le_one_right [MulOneClass α] [CovariantClass α α
#align add_le_cancellable.add_le_iff_nonpos_right AddLECancellable.add_le_iff_nonpos_right
@[to_additive]
-protected theorem le_mul_iff_one_le_left [CommMonoid α] [CovariantClass α α (· * ·) (· ≤ ·)]
- {a b : α} (ha : MulLECancellable a) :
- a ≤ b * a ↔ 1 ≤ b := by rw [mul_comm, ha.le_mul_iff_one_le_right]
-#align mul_le_cancellable.le_mul_iff_one_le_left MulLECancellable.le_mul_iff_one_le_left
-#align add_le_cancellable.le_add_iff_nonneg_left AddLECancellable.le_add_iff_nonneg_left
+protected theorem le_mul_iff_one_le_left [MulOneClass α] [i : IsSymmOp α α (· * ·)]
+ [CovariantClass α α (· * ·) (· ≤ ·)] {a b : α} (ha : MulLECancellable a) :
+ a ≤ b * a ↔ 1 ≤ b := by rw [i.symm_op, ha.le_mul_iff_one_le_right]
+#align mul_le_cancellable.le_mul_iff_one_le_left MulLECancellable.le_mul_iff_one_le_leftₓ
+#align add_le_cancellable.le_add_iff_nonneg_left AddLECancellable.le_add_iff_nonneg_leftₓ
@[to_additive]
-protected theorem mul_le_iff_le_one_left [CommMonoid α] [CovariantClass α α (· * ·) (· ≤ ·)]
- {a b : α} (ha : MulLECancellable a) :
- b * a ≤ a ↔ b ≤ 1 := by rw [mul_comm, ha.mul_le_iff_le_one_right]
-#align mul_le_cancellable.mul_le_iff_le_one_left MulLECancellable.mul_le_iff_le_one_left
-#align add_le_cancellable.add_le_iff_nonpos_left AddLECancellable.add_le_iff_nonpos_left
+protected theorem mul_le_iff_le_one_left [MulOneClass α] [i : IsSymmOp α α (· * ·)]
+ [CovariantClass α α (· * ·) (· ≤ ·)] {a b : α} (ha : MulLECancellable a) :
+ b * a ≤ a ↔ b ≤ 1 := by rw [i.symm_op, ha.mul_le_iff_le_one_right]
+#align mul_le_cancellable.mul_le_iff_le_one_left MulLECancellable.mul_le_iff_le_one_leftₓ
+#align add_le_cancellable.add_le_iff_nonpos_left AddLECancellable.add_le_iff_nonpos_leftₓ
end MulLECancellable
I know that this is contrary to what we've done previously, but:
norm_num
/ ring
/ linarith
)(Oh
Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
@@ -7,6 +7,7 @@ Yuyang Zhao
import Mathlib.Algebra.CovariantAndContravariant
import Mathlib.Init.Data.Ordering.Basic
import Mathlib.Order.MinMax
+import Mathlib.Tactic.Contrapose
#align_import algebra.order.monoid.lemmas from "leanprover-community/mathlib"@"2ed7e4aec72395b6a7c3ac4ac7873a7a43ead17c"
Move 3 line breaks, so that they no longer separate inputs to Co*variantClass
es.
@@ -1677,8 +1677,7 @@ set_option linter.deprecated false
variable [Add α] [Preorder α]
@[deprecated]
-theorem bit0_mono [CovariantClass α α (· + ·) (· ≤ ·)] [CovariantClass α α (swap (· + ·))
-(· ≤ ·)] :
+theorem bit0_mono [CovariantClass α α (· + ·) (· ≤ ·)] [CovariantClass α α (swap (· + ·)) (· ≤ ·)] :
Monotone (bit0 : α → α) := fun _ _ h => add_le_add h h
#align bit0_mono bit0_mono
@@ -163,7 +163,7 @@ theorem mul_lt_mul_of_lt_of_lt [CovariantClass α α (· * ·) (· < ·)]
#align mul_lt_mul_of_lt_of_lt mul_lt_mul_of_lt_of_lt
#align add_lt_add_of_lt_of_lt add_lt_add_of_lt_of_lt
-alias add_lt_add_of_lt_of_lt ← add_lt_add
+alias add_lt_add := add_lt_add_of_lt_of_lt
#align add_lt_add add_lt_add
@[to_additive]
@@ -980,19 +980,19 @@ theorem Right.one_lt_mul' [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a
#align right.one_lt_mul' Right.one_lt_mul'
#align right.add_pos' Right.add_pos'
-alias Left.mul_le_one ← mul_le_one'
+alias mul_le_one' := Left.mul_le_one
#align mul_le_one' mul_le_one'
-alias Left.mul_lt_one_of_le_of_lt ← mul_lt_one_of_le_of_lt
+alias mul_lt_one_of_le_of_lt := Left.mul_lt_one_of_le_of_lt
#align mul_lt_one_of_le_of_lt mul_lt_one_of_le_of_lt
-alias Left.mul_lt_one_of_lt_of_le ← mul_lt_one_of_lt_of_le
+alias mul_lt_one_of_lt_of_le := Left.mul_lt_one_of_lt_of_le
#align mul_lt_one_of_lt_of_le mul_lt_one_of_lt_of_le
-alias Left.mul_lt_one ← mul_lt_one
+alias mul_lt_one := Left.mul_lt_one
#align mul_lt_one mul_lt_one
-alias Left.mul_lt_one' ← mul_lt_one'
+alias mul_lt_one' := Left.mul_lt_one'
#align mul_lt_one' mul_lt_one'
attribute [to_additive add_nonpos "**Alias** of `Left.add_nonpos`."] mul_le_one'
@@ -1012,19 +1012,19 @@ attribute [to_additive "**Alias** of `Left.add_neg`."] mul_lt_one
attribute [to_additive "**Alias** of `Left.add_neg'`."] mul_lt_one'
#align add_neg' add_neg'
-alias Left.one_le_mul ← one_le_mul
+alias one_le_mul := Left.one_le_mul
#align one_le_mul one_le_mul
-alias Left.one_lt_mul_of_le_of_lt ← one_lt_mul_of_le_of_lt'
+alias one_lt_mul_of_le_of_lt' := Left.one_lt_mul_of_le_of_lt
#align one_lt_mul_of_le_of_lt' one_lt_mul_of_le_of_lt'
-alias Left.one_lt_mul_of_lt_of_le ← one_lt_mul_of_lt_of_le'
+alias one_lt_mul_of_lt_of_le' := Left.one_lt_mul_of_lt_of_le
#align one_lt_mul_of_lt_of_le' one_lt_mul_of_lt_of_le'
-alias Left.one_lt_mul ← one_lt_mul'
+alias one_lt_mul' := Left.one_lt_mul
#align one_lt_mul' one_lt_mul'
-alias Left.one_lt_mul' ← one_lt_mul''
+alias one_lt_mul'' := Left.one_lt_mul'
#align one_lt_mul'' one_lt_mul''
attribute [to_additive add_nonneg "**Alias** of `Left.add_nonneg`."] one_le_mul
@@ -1267,7 +1267,7 @@ theorem Right.mul_eq_mul_iff_eq_and_eq [CovariantClass α α (· * ·) (· ≤
#align right.mul_eq_mul_iff_eq_and_eq Right.mul_eq_mul_iff_eq_and_eq
#align right.add_eq_add_iff_eq_and_eq Right.add_eq_add_iff_eq_and_eq
-alias Left.mul_eq_mul_iff_eq_and_eq ← mul_eq_mul_iff_eq_and_eq
+alias mul_eq_mul_iff_eq_and_eq := Left.mul_eq_mul_iff_eq_and_eq
#align mul_eq_mul_iff_eq_and_eq mul_eq_mul_iff_eq_and_eq
attribute [to_additive] mul_eq_mul_iff_eq_and_eq
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -33,7 +33,7 @@ Almost no monoid is actually present in this file: most assumptions have been ge
-- after the `ordered`-refactor is done.
open Function
-variable {α β : Type _}
+variable {α β : Type*}
section Mul
@@ -1547,7 +1547,7 @@ theorem StrictAntiOn.mul_antitone' (hf : StrictAntiOn f s) (hg : AntitoneOn g s)
#align strict_anti_on.add_antitone StrictAntiOn.add_antitone
@[to_additive (attr := simp) cmp_add_left]
-theorem cmp_mul_left' {α : Type _} [Mul α] [LinearOrder α] [CovariantClass α α (· * ·) (· < ·)]
+theorem cmp_mul_left' {α : Type*} [Mul α] [LinearOrder α] [CovariantClass α α (· * ·) (· < ·)]
(a b c : α) :
cmp (a * b) (a * c) = cmp b c :=
(strictMono_id.const_mul' a).cmp_map_eq b c
@@ -1555,7 +1555,7 @@ theorem cmp_mul_left' {α : Type _} [Mul α] [LinearOrder α] [CovariantClass α
#align cmp_add_left cmp_add_left
@[to_additive (attr := simp) cmp_add_right]
-theorem cmp_mul_right' {α : Type _} [Mul α] [LinearOrder α]
+theorem cmp_mul_right' {α : Type*} [Mul α] [LinearOrder α]
[CovariantClass α α (swap (· * ·)) (· < ·)] (a b c : α) :
cmp (a * c) (b * c) = cmp a b :=
(strictMono_id.mul_const' c).cmp_map_eq a b
@@ -3,16 +3,13 @@ Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro, Johannes Hölzl, Damiano Testa,
Yuyang Zhao
-
-! This file was ported from Lean 3 source module algebra.order.monoid.lemmas
-! leanprover-community/mathlib commit 2ed7e4aec72395b6a7c3ac4ac7873a7a43ead17c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Algebra.CovariantAndContravariant
import Mathlib.Init.Data.Ordering.Basic
import Mathlib.Order.MinMax
+#align_import algebra.order.monoid.lemmas from "leanprover-community/mathlib"@"2ed7e4aec72395b6a7c3ac4ac7873a7a43ead17c"
+
/-!
# Ordered monoids
at
and goals (#5387)
Changes are of the form
some_tactic at h⊢
-> some_tactic at h ⊢
some_tactic at h
-> some_tactic at h
@@ -1196,7 +1196,7 @@ theorem exists_square_le [CovariantClass α α (· * ·) (· < ·)] (a : α) :
rw [mul_one] at this
exact le_of_lt this
· use 1
- push_neg at h
+ push_neg at h
rwa [mul_one]
#align exists_square_le exists_square_le
@@ -1489,8 +1489,8 @@ theorem MonotoneOn.mul_strictMono' [CovariantClass α α (· * ·) (· < ·)]
#align monotone_on.mul_strict_mono' MonotoneOn.mul_strictMono'
#align monotone_on.add_strict_mono MonotoneOn.add_strictMono
-/-- The product of a antitone function and a strictly antitone function is strictly antitone. -/
-@[to_additive add_strictAnti "The sum of a antitone function and a strictly antitone function is
+/-- The product of an antitone function and a strictly antitone function is strictly antitone. -/
+@[to_additive add_strictAnti "The sum of an antitone function and a strictly antitone function is
strictly antitone."]
theorem Antitone.mul_strictAnti' [CovariantClass α α (· * ·) (· < ·)]
[CovariantClass α α (swap (· * ·)) (· ≤ ·)] {f g : β → α} (hf : Antitone f)
@@ -1500,8 +1500,8 @@ theorem Antitone.mul_strictAnti' [CovariantClass α α (· * ·) (· < ·)]
#align antitone.mul_strict_anti' Antitone.mul_strictAnti'
#align antitone.add_strict_anti Antitone.add_strictAnti
-/-- The product of a antitone function and a strictly antitone function is strictly antitone. -/
-@[to_additive add_strictAnti "The sum of a antitone function and a strictly antitone function is
+/-- The product of an antitone function and a strictly antitone function is strictly antitone. -/
+@[to_additive add_strictAnti "The sum of an antitone function and a strictly antitone function is
strictly antitone."]
theorem AntitoneOn.mul_strictAnti' [CovariantClass α α (· * ·) (· < ·)]
[CovariantClass α α (swap (· * ·)) (· ≤ ·)] {f g : β → α} (hf : AntitoneOn f s)
@@ -1531,8 +1531,8 @@ theorem StrictMonoOn.mul_monotone' (hf : StrictMonoOn f s) (hg : MonotoneOn g s)
#align strict_mono_on.mul_monotone' StrictMonoOn.mul_monotone'
#align strict_mono_on.add_monotone StrictMonoOn.add_monotone
-/-- The product of a strictly antitone function and a antitone function is strictly antitone. -/
-@[to_additive add_antitone "The sum of a strictly antitone function and a antitone function is
+/-- The product of a strictly antitone function and an antitone function is strictly antitone. -/
+@[to_additive add_antitone "The sum of a strictly antitone function and an antitone function is
strictly antitone."]
theorem StrictAnti.mul_antitone' (hf : StrictAnti f) (hg : Antitone g) :
StrictAnti fun x => f x * g x :=
@@ -1540,8 +1540,8 @@ theorem StrictAnti.mul_antitone' (hf : StrictAnti f) (hg : Antitone g) :
#align strict_anti.mul_antitone' StrictAnti.mul_antitone'
#align strict_anti.add_antitone StrictAnti.add_antitone
-/-- The product of a strictly antitone function and a antitone function is strictly antitone. -/
-@[to_additive add_antitone "The sum of a strictly antitone function and a antitone function is
+/-- The product of a strictly antitone function and an antitone function is strictly antitone. -/
+@[to_additive add_antitone "The sum of a strictly antitone function and an antitone function is
strictly antitone."]
theorem StrictAntiOn.mul_antitone' (hf : StrictAntiOn f s) (hg : AntitoneOn g s) :
StrictAntiOn (fun x => f x * g x) s :=
This makes a mathlib4 version of mathlib3's tactic.basic
, now called Mathlib.Tactic.Common
, which imports all tactics which do not have significant theory requirements, and then is imported all across the base of the hierarchy.
This ensures that all common tactics are available nearly everywhere in the library, rather than having to be imported one-by-one as you need them.
Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
@@ -12,9 +12,6 @@ Yuyang Zhao
import Mathlib.Algebra.CovariantAndContravariant
import Mathlib.Init.Data.Ordering.Basic
import Mathlib.Order.MinMax
-import Mathlib.Tactic.Contrapose
-import Mathlib.Tactic.PushNeg
-import Mathlib.Tactic.Use
/-!
# Ordered monoids
This PR is the result of a slight variant on the following "algorithm"
_
and make all uppercase letters into lowercase_
and make all uppercase letters into lowercase(original_lean3_name, OriginalLean4Name)
#align
statement just before the next empty line#align
statement to have been inserted too early)@@ -55,12 +55,16 @@ is taken by the analogous lemma for semiring, with an extra non-negativity assum
theorem mul_le_mul_left' [CovariantClass α α (· * ·) (· ≤ ·)] {b c : α} (bc : b ≤ c) (a : α) :
a * b ≤ a * c :=
CovariantClass.elim _ bc
+#align mul_le_mul_left' mul_le_mul_left'
+#align add_le_add_left add_le_add_left
@[to_additive le_of_add_le_add_left]
theorem le_of_mul_le_mul_left' [ContravariantClass α α (· * ·) (· ≤ ·)] {a b c : α}
(bc : a * b ≤ a * c) :
b ≤ c :=
ContravariantClass.elim _ bc
+#align le_of_mul_le_mul_left' le_of_mul_le_mul_left'
+#align le_of_add_le_add_left le_of_add_le_add_left
/- The prime on this lemma is present only on the multiplicative version. The unprimed version
is taken by the analogous lemma for semiring, with an extra non-negativity assumption. -/
@@ -69,24 +73,32 @@ theorem mul_le_mul_right' [i : CovariantClass α α (swap (· * ·)) (· ≤ ·)
(a : α) :
b * a ≤ c * a :=
i.elim a bc
+#align mul_le_mul_right' mul_le_mul_right'
+#align add_le_add_right add_le_add_right
@[to_additive le_of_add_le_add_right]
theorem le_of_mul_le_mul_right' [i : ContravariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α}
(bc : b * a ≤ c * a) :
b ≤ c :=
i.elim a bc
+#align le_of_mul_le_mul_right' le_of_mul_le_mul_right'
+#align le_of_add_le_add_right le_of_add_le_add_right
@[to_additive (attr := simp)]
theorem mul_le_mul_iff_left [CovariantClass α α (· * ·) (· ≤ ·)]
[ContravariantClass α α (· * ·) (· ≤ ·)] (a : α) {b c : α} :
a * b ≤ a * c ↔ b ≤ c :=
rel_iff_cov α α (· * ·) (· ≤ ·) a
+#align mul_le_mul_iff_left mul_le_mul_iff_left
+#align add_le_add_iff_left add_le_add_iff_left
@[to_additive (attr := simp)]
theorem mul_le_mul_iff_right [CovariantClass α α (swap (· * ·)) (· ≤ ·)]
[ContravariantClass α α (swap (· * ·)) (· ≤ ·)] (a : α) {b c : α} :
b * a ≤ c * a ↔ b ≤ c :=
rel_iff_cov α α (swap (· * ·)) (· ≤ ·) a
+#align mul_le_mul_iff_right mul_le_mul_iff_right
+#align add_le_add_iff_right add_le_add_iff_right
end LE
@@ -99,35 +111,47 @@ theorem mul_lt_mul_iff_left [CovariantClass α α (· * ·) (· < ·)]
[ContravariantClass α α (· * ·) (· < ·)] (a : α) {b c : α} :
a * b < a * c ↔ b < c :=
rel_iff_cov α α (· * ·) (· < ·) a
+#align mul_lt_mul_iff_left mul_lt_mul_iff_left
+#align add_lt_add_iff_left add_lt_add_iff_left
@[to_additive (attr := simp)]
theorem mul_lt_mul_iff_right [CovariantClass α α (swap (· * ·)) (· < ·)]
[ContravariantClass α α (swap (· * ·)) (· < ·)] (a : α) {b c : α} :
b * a < c * a ↔ b < c :=
rel_iff_cov α α (swap (· * ·)) (· < ·) a
+#align mul_lt_mul_iff_right mul_lt_mul_iff_right
+#align add_lt_add_iff_right add_lt_add_iff_right
@[to_additive add_lt_add_left]
theorem mul_lt_mul_left' [CovariantClass α α (· * ·) (· < ·)] {b c : α} (bc : b < c) (a : α) :
a * b < a * c :=
CovariantClass.elim _ bc
+#align mul_lt_mul_left' mul_lt_mul_left'
+#align add_lt_add_left add_lt_add_left
@[to_additive lt_of_add_lt_add_left]
theorem lt_of_mul_lt_mul_left' [ContravariantClass α α (· * ·) (· < ·)] {a b c : α}
(bc : a * b < a * c) :
b < c :=
ContravariantClass.elim _ bc
+#align lt_of_mul_lt_mul_left' lt_of_mul_lt_mul_left'
+#align lt_of_add_lt_add_left lt_of_add_lt_add_left
@[to_additive add_lt_add_right]
theorem mul_lt_mul_right' [i : CovariantClass α α (swap (· * ·)) (· < ·)] {b c : α} (bc : b < c)
(a : α) :
b * a < c * a :=
i.elim a bc
+#align mul_lt_mul_right' mul_lt_mul_right'
+#align add_lt_add_right add_lt_add_right
@[to_additive lt_of_add_lt_add_right]
theorem lt_of_mul_lt_mul_right' [i : ContravariantClass α α (swap (· * ·)) (· < ·)] {a b c : α}
(bc : b * a < c * a) :
b < c :=
i.elim a bc
+#align lt_of_mul_lt_mul_right' lt_of_mul_lt_mul_right'
+#align lt_of_add_lt_add_right lt_of_add_lt_add_right
end LT
@@ -142,20 +166,27 @@ theorem mul_lt_mul_of_lt_of_lt [CovariantClass α α (· * ·) (· < ·)]
calc
a * c < a * d := mul_lt_mul_left' h₂ a
_ < b * d := mul_lt_mul_right' h₁ d
+#align mul_lt_mul_of_lt_of_lt mul_lt_mul_of_lt_of_lt
+#align add_lt_add_of_lt_of_lt add_lt_add_of_lt_of_lt
alias add_lt_add_of_lt_of_lt ← add_lt_add
+#align add_lt_add add_lt_add
@[to_additive]
theorem mul_lt_mul_of_le_of_lt [CovariantClass α α (· * ·) (· < ·)]
[CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c d : α} (h₁ : a ≤ b) (h₂ : c < d) :
a * c < b * d :=
(mul_le_mul_right' h₁ _).trans_lt (mul_lt_mul_left' h₂ b)
+#align mul_lt_mul_of_le_of_lt mul_lt_mul_of_le_of_lt
+#align add_lt_add_of_le_of_lt add_lt_add_of_le_of_lt
@[to_additive]
theorem mul_lt_mul_of_lt_of_le [CovariantClass α α (· * ·) (· ≤ ·)]
[CovariantClass α α (swap (· * ·)) (· < ·)] {a b c d : α} (h₁ : a < b) (h₂ : c ≤ d) :
a * c < b * d :=
(mul_le_mul_left' h₂ _).trans_lt (mul_lt_mul_right' h₁ d)
+#align mul_lt_mul_of_lt_of_le mul_lt_mul_of_lt_of_le
+#align add_lt_add_of_lt_of_le add_lt_add_of_lt_of_le
/-- Only assumes left strict covariance. -/
@[to_additive "Only assumes left strict covariance"]
@@ -181,6 +212,8 @@ theorem mul_le_mul' [CovariantClass α α (· * ·) (· ≤ ·)] [CovariantClass
{a b c d : α} (h₁ : a ≤ b) (h₂ : c ≤ d) :
a * c ≤ b * d :=
(mul_le_mul_left' h₂ _).trans (mul_le_mul_right' h₁ d)
+#align mul_le_mul' mul_le_mul'
+#align add_le_add add_le_add
@[to_additive]
theorem mul_le_mul_three [CovariantClass α α (· * ·) (· ≤ ·)]
@@ -188,54 +221,72 @@ theorem mul_le_mul_three [CovariantClass α α (· * ·) (· ≤ ·)]
(h₃ : c ≤ f) :
a * b * c ≤ d * e * f :=
mul_le_mul' (mul_le_mul' h₁ h₂) h₃
+#align mul_le_mul_three mul_le_mul_three
+#align add_le_add_three add_le_add_three
@[to_additive]
theorem mul_lt_of_mul_lt_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b c d : α} (h : a * b < c)
(hle : d ≤ b) :
a * d < c :=
(mul_le_mul_left' hle a).trans_lt h
+#align mul_lt_of_mul_lt_left mul_lt_of_mul_lt_left
+#align add_lt_of_add_lt_left add_lt_of_add_lt_left
@[to_additive]
theorem mul_le_of_mul_le_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b c d : α} (h : a * b ≤ c)
(hle : d ≤ b) :
a * d ≤ c :=
@act_rel_of_rel_of_act_rel _ _ _ (· ≤ ·) _ _ a _ _ _ hle h
+#align mul_le_of_mul_le_left mul_le_of_mul_le_left
+#align add_le_of_add_le_left add_le_of_add_le_left
@[to_additive]
theorem mul_lt_of_mul_lt_right [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c d : α}
(h : a * b < c) (hle : d ≤ a) :
d * b < c :=
(mul_le_mul_right' hle b).trans_lt h
+#align mul_lt_of_mul_lt_right mul_lt_of_mul_lt_right
+#align add_lt_of_add_lt_right add_lt_of_add_lt_right
@[to_additive]
theorem mul_le_of_mul_le_right [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c d : α}
(h : a * b ≤ c) (hle : d ≤ a) :
d * b ≤ c :=
(mul_le_mul_right' hle b).trans h
+#align mul_le_of_mul_le_right mul_le_of_mul_le_right
+#align add_le_of_add_le_right add_le_of_add_le_right
@[to_additive]
theorem lt_mul_of_lt_mul_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b c d : α} (h : a < b * c)
(hle : c ≤ d) :
a < b * d :=
h.trans_le (mul_le_mul_left' hle b)
+#align lt_mul_of_lt_mul_left lt_mul_of_lt_mul_left
+#align lt_add_of_lt_add_left lt_add_of_lt_add_left
@[to_additive]
theorem le_mul_of_le_mul_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b c d : α} (h : a ≤ b * c)
(hle : c ≤ d) :
a ≤ b * d :=
@rel_act_of_rel_of_rel_act _ _ _ (· ≤ ·) _ _ b _ _ _ hle h
+#align le_mul_of_le_mul_left le_mul_of_le_mul_left
+#align le_add_of_le_add_left le_add_of_le_add_left
@[to_additive]
theorem lt_mul_of_lt_mul_right [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c d : α}
(h : a < b * c) (hle : b ≤ d) :
a < d * c :=
h.trans_le (mul_le_mul_right' hle c)
+#align lt_mul_of_lt_mul_right lt_mul_of_lt_mul_right
+#align lt_add_of_lt_add_right lt_add_of_lt_add_right
@[to_additive]
theorem le_mul_of_le_mul_right [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c d : α}
(h : a ≤ b * c) (hle : b ≤ d) :
a ≤ d * c :=
h.trans (mul_le_mul_right' hle c)
+#align le_mul_of_le_mul_right le_mul_of_le_mul_right
+#align le_add_of_le_add_right le_add_of_le_add_right
end Preorder
@@ -247,12 +298,16 @@ variable [PartialOrder α]
theorem mul_left_cancel'' [ContravariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (h : a * b = a * c) :
b = c :=
(le_of_mul_le_mul_left' h.le).antisymm (le_of_mul_le_mul_left' h.ge)
+#align mul_left_cancel'' mul_left_cancel''
+#align add_left_cancel'' add_left_cancel''
@[to_additive]
theorem mul_right_cancel'' [ContravariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α}
(h : a * b = c * b) :
a = c :=
le_antisymm (le_of_mul_le_mul_right' h.le) (le_of_mul_le_mul_right' h.ge)
+#align mul_right_cancel'' mul_right_cancel''
+#align add_right_cancel'' add_right_cancel''
end PartialOrder
@@ -262,6 +317,8 @@ variable [LinearOrder α] {a b c d : α} [CovariantClass α α (· * ·) (· <
@[to_additive] lemma min_le_max_of_mul_le_mul (h : a * b ≤ c * d) : min a b ≤ max c d :=
by simp_rw [min_le_iff, le_max_iff]; contrapose! h; exact mul_lt_mul_of_lt_of_lt h.1.1 h.2.2
+#align min_le_max_of_add_le_add min_le_max_of_add_le_add
+#align min_le_max_of_mul_le_mul min_le_max_of_mul_le_mul
end LinearOrder
end Mul
@@ -281,6 +338,8 @@ theorem le_mul_of_one_le_right' [CovariantClass α α (· * ·) (· ≤ ·)] {a
calc
a = a * 1 := (mul_one a).symm
_ ≤ a * b := mul_le_mul_left' h a
+#align le_mul_of_one_le_right' le_mul_of_one_le_right'
+#align le_add_of_nonneg_right le_add_of_nonneg_right
@[to_additive add_le_of_nonpos_right]
theorem mul_le_of_le_one_right' [CovariantClass α α (· * ·) (· ≤ ·)] {a b : α} (h : b ≤ 1) :
@@ -288,6 +347,8 @@ theorem mul_le_of_le_one_right' [CovariantClass α α (· * ·) (· ≤ ·)] {a
calc
a * b ≤ a * 1 := mul_le_mul_left' h a
_ = a := mul_one a
+#align mul_le_of_le_one_right' mul_le_of_le_one_right'
+#align add_le_of_nonpos_right add_le_of_nonpos_right
@[to_additive le_add_of_nonneg_left]
theorem le_mul_of_one_le_left' [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b : α} (h : 1 ≤ b) :
@@ -295,6 +356,8 @@ theorem le_mul_of_one_le_left' [CovariantClass α α (swap (· * ·)) (· ≤ ·
calc
a = 1 * a := (one_mul a).symm
_ ≤ b * a := mul_le_mul_right' h a
+#align le_mul_of_one_le_left' le_mul_of_one_le_left'
+#align le_add_of_nonneg_left le_add_of_nonneg_left
@[to_additive add_le_of_nonpos_left]
theorem mul_le_of_le_one_left' [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b : α} (h : b ≤ 1) :
@@ -302,52 +365,70 @@ theorem mul_le_of_le_one_left' [CovariantClass α α (swap (· * ·)) (· ≤ ·
calc
b * a ≤ 1 * a := mul_le_mul_right' h a
_ = a := one_mul a
+#align mul_le_of_le_one_left' mul_le_of_le_one_left'
+#align add_le_of_nonpos_left add_le_of_nonpos_left
@[to_additive]
theorem one_le_of_le_mul_right [ContravariantClass α α (· * ·) (· ≤ ·)] {a b : α} (h : a ≤ a * b) :
1 ≤ b :=
le_of_mul_le_mul_left' <| by simpa only [mul_one]
+#align one_le_of_le_mul_right one_le_of_le_mul_right
+#align nonneg_of_le_add_right nonneg_of_le_add_right
@[to_additive]
theorem le_one_of_mul_le_right [ContravariantClass α α (· * ·) (· ≤ ·)] {a b : α} (h : a * b ≤ a) :
b ≤ 1 :=
le_of_mul_le_mul_left' <| by simpa only [mul_one]
+#align le_one_of_mul_le_right le_one_of_mul_le_right
+#align nonpos_of_add_le_right nonpos_of_add_le_right
@[to_additive]
theorem one_le_of_le_mul_left [ContravariantClass α α (swap (· * ·)) (· ≤ ·)] {a b : α}
(h : b ≤ a * b) :
1 ≤ a :=
le_of_mul_le_mul_right' <| by simpa only [one_mul]
+#align one_le_of_le_mul_left one_le_of_le_mul_left
+#align nonneg_of_le_add_left nonneg_of_le_add_left
@[to_additive]
theorem le_one_of_mul_le_left [ContravariantClass α α (swap (· * ·)) (· ≤ ·)] {a b : α}
(h : a * b ≤ b) :
a ≤ 1 :=
le_of_mul_le_mul_right' <| by simpa only [one_mul]
+#align le_one_of_mul_le_left le_one_of_mul_le_left
+#align nonpos_of_add_le_left nonpos_of_add_le_left
@[to_additive (attr := simp) le_add_iff_nonneg_right]
theorem le_mul_iff_one_le_right' [CovariantClass α α (· * ·) (· ≤ ·)]
[ContravariantClass α α (· * ·) (· ≤ ·)] (a : α) {b : α} :
a ≤ a * b ↔ 1 ≤ b :=
Iff.trans (by rw [mul_one]) (mul_le_mul_iff_left a)
+#align le_mul_iff_one_le_right' le_mul_iff_one_le_right'
+#align le_add_iff_nonneg_right le_add_iff_nonneg_right
@[to_additive (attr := simp) le_add_iff_nonneg_left]
theorem le_mul_iff_one_le_left' [CovariantClass α α (swap (· * ·)) (· ≤ ·)]
[ContravariantClass α α (swap (· * ·)) (· ≤ ·)] (a : α) {b : α} :
a ≤ b * a ↔ 1 ≤ b :=
Iff.trans (by rw [one_mul]) (mul_le_mul_iff_right a)
+#align le_mul_iff_one_le_left' le_mul_iff_one_le_left'
+#align le_add_iff_nonneg_left le_add_iff_nonneg_left
@[to_additive (attr := simp) add_le_iff_nonpos_right]
theorem mul_le_iff_le_one_right' [CovariantClass α α (· * ·) (· ≤ ·)]
[ContravariantClass α α (· * ·) (· ≤ ·)] (a : α) {b : α} :
a * b ≤ a ↔ b ≤ 1 :=
Iff.trans (by rw [mul_one]) (mul_le_mul_iff_left a)
+#align mul_le_iff_le_one_right' mul_le_iff_le_one_right'
+#align add_le_iff_nonpos_right add_le_iff_nonpos_right
@[to_additive (attr := simp) add_le_iff_nonpos_left]
theorem mul_le_iff_le_one_left' [CovariantClass α α (swap (· * ·)) (· ≤ ·)]
[ContravariantClass α α (swap (· * ·)) (· ≤ ·)] {a b : α} :
a * b ≤ b ↔ a ≤ 1 :=
Iff.trans (by rw [one_mul]) (mul_le_mul_iff_right b)
+#align mul_le_iff_le_one_left' mul_le_iff_le_one_left'
+#align add_le_iff_nonpos_left add_le_iff_nonpos_left
end LE
@@ -361,6 +442,8 @@ theorem lt_mul_of_one_lt_right' [CovariantClass α α (· * ·) (· < ·)] (a :
calc
a = a * 1 := (mul_one a).symm
_ < a * b := mul_lt_mul_left' h a
+#align lt_mul_of_one_lt_right' lt_mul_of_one_lt_right'
+#align lt_add_of_pos_right lt_add_of_pos_right
@[to_additive add_lt_of_neg_right]
theorem mul_lt_of_lt_one_right' [CovariantClass α α (· * ·) (· < ·)] (a : α) {b : α} (h : b < 1) :
@@ -368,6 +451,8 @@ theorem mul_lt_of_lt_one_right' [CovariantClass α α (· * ·) (· < ·)] (a :
calc
a * b < a * 1 := mul_lt_mul_left' h a
_ = a := mul_one a
+#align mul_lt_of_lt_one_right' mul_lt_of_lt_one_right'
+#align add_lt_of_neg_right add_lt_of_neg_right
@[to_additive lt_add_of_pos_left]
theorem lt_mul_of_one_lt_left' [CovariantClass α α (swap (· * ·)) (· < ·)] (a : α) {b : α}
@@ -376,6 +461,8 @@ theorem lt_mul_of_one_lt_left' [CovariantClass α α (swap (· * ·)) (· < ·)]
calc
a = 1 * a := (one_mul a).symm
_ < b * a := mul_lt_mul_right' h a
+#align lt_mul_of_one_lt_left' lt_mul_of_one_lt_left'
+#align lt_add_of_pos_left lt_add_of_pos_left
@[to_additive add_lt_of_neg_left]
theorem mul_lt_of_lt_one_left' [CovariantClass α α (swap (· * ·)) (· < ·)] (a : α) {b : α}
@@ -384,50 +471,68 @@ theorem mul_lt_of_lt_one_left' [CovariantClass α α (swap (· * ·)) (· < ·)]
calc
b * a < 1 * a := mul_lt_mul_right' h a
_ = a := one_mul a
+#align mul_lt_of_lt_one_left' mul_lt_of_lt_one_left'
+#align add_lt_of_neg_left add_lt_of_neg_left
@[to_additive]
theorem one_lt_of_lt_mul_right [ContravariantClass α α (· * ·) (· < ·)] {a b : α} (h : a < a * b) :
1 < b :=
lt_of_mul_lt_mul_left' <| by simpa only [mul_one]
+#align one_lt_of_lt_mul_right one_lt_of_lt_mul_right
+#align pos_of_lt_add_right pos_of_lt_add_right
@[to_additive]
theorem lt_one_of_mul_lt_right [ContravariantClass α α (· * ·) (· < ·)] {a b : α} (h : a * b < a) :
b < 1 :=
lt_of_mul_lt_mul_left' <| by simpa only [mul_one]
+#align lt_one_of_mul_lt_right lt_one_of_mul_lt_right
+#align neg_of_add_lt_right neg_of_add_lt_right
@[to_additive]
theorem one_lt_of_lt_mul_left [ContravariantClass α α (swap (· * ·)) (· < ·)] {a b : α}
(h : b < a * b) :
1 < a :=
lt_of_mul_lt_mul_right' <| by simpa only [one_mul]
+#align one_lt_of_lt_mul_left one_lt_of_lt_mul_left
+#align pos_of_lt_add_left pos_of_lt_add_left
@[to_additive]
theorem lt_one_of_mul_lt_left [ContravariantClass α α (swap (· * ·)) (· < ·)] {a b : α}
(h : a * b < b) :
a < 1 :=
lt_of_mul_lt_mul_right' <| by simpa only [one_mul]
+#align lt_one_of_mul_lt_left lt_one_of_mul_lt_left
+#align neg_of_add_lt_left neg_of_add_lt_left
@[to_additive (attr := simp) lt_add_iff_pos_right]
theorem lt_mul_iff_one_lt_right' [CovariantClass α α (· * ·) (· < ·)]
[ContravariantClass α α (· * ·) (· < ·)] (a : α) {b : α} :
a < a * b ↔ 1 < b :=
Iff.trans (by rw [mul_one]) (mul_lt_mul_iff_left a)
+#align lt_mul_iff_one_lt_right' lt_mul_iff_one_lt_right'
+#align lt_add_iff_pos_right lt_add_iff_pos_right
@[to_additive (attr := simp) lt_add_iff_pos_left]
theorem lt_mul_iff_one_lt_left' [CovariantClass α α (swap (· * ·)) (· < ·)]
[ContravariantClass α α (swap (· * ·)) (· < ·)] (a : α) {b : α} : a < b * a ↔ 1 < b :=
Iff.trans (by rw [one_mul]) (mul_lt_mul_iff_right a)
+#align lt_mul_iff_one_lt_left' lt_mul_iff_one_lt_left'
+#align lt_add_iff_pos_left lt_add_iff_pos_left
@[to_additive (attr := simp) add_lt_iff_neg_left]
theorem mul_lt_iff_lt_one_left' [CovariantClass α α (· * ·) (· < ·)]
[ContravariantClass α α (· * ·) (· < ·)] {a b : α} :
a * b < a ↔ b < 1 :=
Iff.trans (by rw [mul_one]) (mul_lt_mul_iff_left a)
+#align mul_lt_iff_lt_one_left' mul_lt_iff_lt_one_left'
+#align add_lt_iff_neg_left add_lt_iff_neg_left
@[to_additive (attr := simp) add_lt_iff_neg_right]
theorem mul_lt_iff_lt_one_right' [CovariantClass α α (swap (· * ·)) (· < ·)]
[ContravariantClass α α (swap (· * ·)) (· < ·)] {a : α} (b : α) : a * b < b ↔ a < 1 :=
Iff.trans (by rw [one_mul]) (mul_lt_mul_iff_right b)
+#align mul_lt_iff_lt_one_right' mul_lt_iff_lt_one_right'
+#align add_lt_iff_neg_right add_lt_iff_neg_right
end LT
@@ -447,6 +552,8 @@ theorem mul_le_of_le_of_le_one [CovariantClass α α (· * ·) (· ≤ ·)] {a b
b * a ≤ b * 1 := mul_le_mul_left' ha b
_ = b := mul_one b
_ ≤ c := hbc
+#align mul_le_of_le_of_le_one mul_le_of_le_of_le_one
+#align add_le_of_le_of_nonpos add_le_of_le_of_nonpos
@[to_additive]
theorem mul_lt_of_le_of_lt_one [CovariantClass α α (· * ·) (· < ·)] {a b c : α} (hbc : b ≤ c)
@@ -456,6 +563,8 @@ theorem mul_lt_of_le_of_lt_one [CovariantClass α α (· * ·) (· < ·)] {a b c
b * a < b * 1 := mul_lt_mul_left' ha b
_ = b := mul_one b
_ ≤ c := hbc
+#align mul_lt_of_le_of_lt_one mul_lt_of_le_of_lt_one
+#align add_lt_of_le_of_neg add_lt_of_le_of_neg
@[to_additive]
theorem mul_lt_of_lt_of_le_one [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (hbc : b < c)
@@ -465,6 +574,8 @@ theorem mul_lt_of_lt_of_le_one [CovariantClass α α (· * ·) (· ≤ ·)] {a b
b * a ≤ b * 1 := mul_le_mul_left' ha b
_ = b := mul_one b
_ < c := hbc
+#align mul_lt_of_lt_of_le_one mul_lt_of_lt_of_le_one
+#align add_lt_of_lt_of_nonpos add_lt_of_lt_of_nonpos
@[to_additive]
theorem mul_lt_of_lt_of_lt_one [CovariantClass α α (· * ·) (· < ·)] {a b c : α} (hbc : b < c)
@@ -474,12 +585,16 @@ theorem mul_lt_of_lt_of_lt_one [CovariantClass α α (· * ·) (· < ·)] {a b c
b * a < b * 1 := mul_lt_mul_left' ha b
_ = b := mul_one b
_ < c := hbc
+#align mul_lt_of_lt_of_lt_one mul_lt_of_lt_of_lt_one
+#align add_lt_of_lt_of_neg add_lt_of_lt_of_neg
@[to_additive]
theorem mul_lt_of_lt_of_lt_one' [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (hbc : b < c)
(ha : a < 1) :
b * a < c :=
mul_lt_of_lt_of_le_one hbc ha.le
+#align mul_lt_of_lt_of_lt_one' mul_lt_of_lt_of_lt_one'
+#align add_lt_of_lt_of_neg' add_lt_of_lt_of_neg'
/-- Assumes left covariance.
The lemma assuming right covariance is `Right.mul_le_one`. -/
@@ -547,6 +662,8 @@ theorem le_mul_of_le_of_one_le [CovariantClass α α (· * ·) (· ≤ ·)] {a b
b ≤ c := hbc
_ = c * 1 := (mul_one c).symm
_ ≤ c * a := mul_le_mul_left' ha c
+#align le_mul_of_le_of_one_le le_mul_of_le_of_one_le
+#align le_add_of_le_of_nonneg le_add_of_le_of_nonneg
@[to_additive]
theorem lt_mul_of_le_of_one_lt [CovariantClass α α (· * ·) (· < ·)] {a b c : α} (hbc : b ≤ c)
@@ -556,6 +673,8 @@ theorem lt_mul_of_le_of_one_lt [CovariantClass α α (· * ·) (· < ·)] {a b c
b ≤ c := hbc
_ = c * 1 := (mul_one c).symm
_ < c * a := mul_lt_mul_left' ha c
+#align lt_mul_of_le_of_one_lt lt_mul_of_le_of_one_lt
+#align lt_add_of_le_of_pos lt_add_of_le_of_pos
@[to_additive]
theorem lt_mul_of_lt_of_one_le [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (hbc : b < c)
@@ -565,6 +684,8 @@ theorem lt_mul_of_lt_of_one_le [CovariantClass α α (· * ·) (· ≤ ·)] {a b
b < c := hbc
_ = c * 1 := (mul_one c).symm
_ ≤ c * a := mul_le_mul_left' ha c
+#align lt_mul_of_lt_of_one_le lt_mul_of_lt_of_one_le
+#align lt_add_of_lt_of_nonneg lt_add_of_lt_of_nonneg
@[to_additive]
theorem lt_mul_of_lt_of_one_lt [CovariantClass α α (· * ·) (· < ·)] {a b c : α} (hbc : b < c)
@@ -574,12 +695,16 @@ theorem lt_mul_of_lt_of_one_lt [CovariantClass α α (· * ·) (· < ·)] {a b c
b < c := hbc
_ = c * 1 := (mul_one c).symm
_ < c * a := mul_lt_mul_left' ha c
+#align lt_mul_of_lt_of_one_lt lt_mul_of_lt_of_one_lt
+#align lt_add_of_lt_of_pos lt_add_of_lt_of_pos
@[to_additive]
theorem lt_mul_of_lt_of_one_lt' [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (hbc : b < c)
(ha : 1 < a) :
b < c * a :=
lt_mul_of_lt_of_one_le hbc ha.le
+#align lt_mul_of_lt_of_one_lt' lt_mul_of_lt_of_one_lt'
+#align lt_add_of_lt_of_pos' lt_add_of_lt_of_pos'
/-- Assumes left covariance.
The lemma assuming right covariance is `Right.one_le_mul`. -/
@@ -647,6 +772,8 @@ theorem mul_le_of_le_one_of_le [CovariantClass α α (swap (· * ·)) (· ≤ ·
a * b ≤ 1 * b := mul_le_mul_right' ha b
_ = b := one_mul b
_ ≤ c := hbc
+#align mul_le_of_le_one_of_le mul_le_of_le_one_of_le
+#align add_le_of_nonpos_of_le add_le_of_nonpos_of_le
@[to_additive]
theorem mul_lt_of_lt_one_of_le [CovariantClass α α (swap (· * ·)) (· < ·)] {a b c : α} (ha : a < 1)
@@ -656,6 +783,8 @@ theorem mul_lt_of_lt_one_of_le [CovariantClass α α (swap (· * ·)) (· < ·)]
a * b < 1 * b := mul_lt_mul_right' ha b
_ = b := one_mul b
_ ≤ c := hbc
+#align mul_lt_of_lt_one_of_le mul_lt_of_lt_one_of_le
+#align add_lt_of_neg_of_le add_lt_of_neg_of_le
@[to_additive]
theorem mul_lt_of_le_one_of_lt [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α} (ha : a ≤ 1)
@@ -665,6 +794,8 @@ theorem mul_lt_of_le_one_of_lt [CovariantClass α α (swap (· * ·)) (· ≤ ·
a * b ≤ 1 * b := mul_le_mul_right' ha b
_ = b := one_mul b
_ < c := hb
+#align mul_lt_of_le_one_of_lt mul_lt_of_le_one_of_lt
+#align add_lt_of_nonpos_of_lt add_lt_of_nonpos_of_lt
@[to_additive]
theorem mul_lt_of_lt_one_of_lt [CovariantClass α α (swap (· * ·)) (· < ·)] {a b c : α} (ha : a < 1)
@@ -674,12 +805,16 @@ theorem mul_lt_of_lt_one_of_lt [CovariantClass α α (swap (· * ·)) (· < ·)]
a * b < 1 * b := mul_lt_mul_right' ha b
_ = b := one_mul b
_ < c := hb
+#align mul_lt_of_lt_one_of_lt mul_lt_of_lt_one_of_lt
+#align add_lt_of_neg_of_lt add_lt_of_neg_of_lt
@[to_additive]
theorem mul_lt_of_lt_one_of_lt' [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α} (ha : a < 1)
(hbc : b < c) :
a * b < c :=
mul_lt_of_le_one_of_lt ha.le hbc
+#align mul_lt_of_lt_one_of_lt' mul_lt_of_lt_one_of_lt'
+#align add_lt_of_neg_of_lt' add_lt_of_neg_of_lt'
/-- Assumes right covariance.
The lemma assuming left covariance is `Left.mul_le_one`. -/
@@ -750,6 +885,8 @@ theorem le_mul_of_one_le_of_le [CovariantClass α α (swap (· * ·)) (· ≤ ·
b ≤ c := hbc
_ = 1 * c := (one_mul c).symm
_ ≤ a * c := mul_le_mul_right' ha c
+#align le_mul_of_one_le_of_le le_mul_of_one_le_of_le
+#align le_add_of_nonneg_of_le le_add_of_nonneg_of_le
@[to_additive]
theorem lt_mul_of_one_lt_of_le [CovariantClass α α (swap (· * ·)) (· < ·)] {a b c : α} (ha : 1 < a)
@@ -759,6 +896,8 @@ theorem lt_mul_of_one_lt_of_le [CovariantClass α α (swap (· * ·)) (· < ·)]
b ≤ c := hbc
_ = 1 * c := (one_mul c).symm
_ < a * c := mul_lt_mul_right' ha c
+#align lt_mul_of_one_lt_of_le lt_mul_of_one_lt_of_le
+#align lt_add_of_pos_of_le lt_add_of_pos_of_le
@[to_additive]
theorem lt_mul_of_one_le_of_lt [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α} (ha : 1 ≤ a)
@@ -768,6 +907,8 @@ theorem lt_mul_of_one_le_of_lt [CovariantClass α α (swap (· * ·)) (· ≤ ·
b < c := hbc
_ = 1 * c := (one_mul c).symm
_ ≤ a * c := mul_le_mul_right' ha c
+#align lt_mul_of_one_le_of_lt lt_mul_of_one_le_of_lt
+#align lt_add_of_nonneg_of_lt lt_add_of_nonneg_of_lt
@[to_additive]
theorem lt_mul_of_one_lt_of_lt [CovariantClass α α (swap (· * ·)) (· < ·)] {a b c : α} (ha : 1 < a)
@@ -777,12 +918,16 @@ theorem lt_mul_of_one_lt_of_lt [CovariantClass α α (swap (· * ·)) (· < ·)]
b < c := hbc
_ = 1 * c := (one_mul c).symm
_ < a * c := mul_lt_mul_right' ha c
+#align lt_mul_of_one_lt_of_lt lt_mul_of_one_lt_of_lt
+#align lt_add_of_pos_of_lt lt_add_of_pos_of_lt
@[to_additive]
theorem lt_mul_of_one_lt_of_lt' [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α} (ha : 1 < a)
(hbc : b < c) :
b < a * c :=
lt_mul_of_one_le_of_lt ha.le hbc
+#align lt_mul_of_one_lt_of_lt' lt_mul_of_one_lt_of_lt'
+#align lt_add_of_pos_of_lt' lt_add_of_pos_of_lt'
/-- Assumes right covariance.
The lemma assuming left covariance is `Left.one_le_mul`. -/
@@ -842,96 +987,132 @@ theorem Right.one_lt_mul' [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a
#align right.add_pos' Right.add_pos'
alias Left.mul_le_one ← mul_le_one'
+#align mul_le_one' mul_le_one'
alias Left.mul_lt_one_of_le_of_lt ← mul_lt_one_of_le_of_lt
+#align mul_lt_one_of_le_of_lt mul_lt_one_of_le_of_lt
alias Left.mul_lt_one_of_lt_of_le ← mul_lt_one_of_lt_of_le
+#align mul_lt_one_of_lt_of_le mul_lt_one_of_lt_of_le
alias Left.mul_lt_one ← mul_lt_one
+#align mul_lt_one mul_lt_one
alias Left.mul_lt_one' ← mul_lt_one'
+#align mul_lt_one' mul_lt_one'
attribute [to_additive add_nonpos "**Alias** of `Left.add_nonpos`."] mul_le_one'
+#align add_nonpos add_nonpos
attribute [to_additive add_neg_of_nonpos_of_neg "**Alias** of `Left.add_neg_of_nonpos_of_neg`."]
mul_lt_one_of_le_of_lt
+#align add_neg_of_nonpos_of_neg add_neg_of_nonpos_of_neg
attribute [to_additive add_neg_of_neg_of_nonpos "**Alias** of `Left.add_neg_of_neg_of_nonpos`."]
mul_lt_one_of_lt_of_le
+#align add_neg_of_neg_of_nonpos add_neg_of_neg_of_nonpos
attribute [to_additive "**Alias** of `Left.add_neg`."] mul_lt_one
+#align add_neg add_neg
attribute [to_additive "**Alias** of `Left.add_neg'`."] mul_lt_one'
+#align add_neg' add_neg'
alias Left.one_le_mul ← one_le_mul
+#align one_le_mul one_le_mul
alias Left.one_lt_mul_of_le_of_lt ← one_lt_mul_of_le_of_lt'
+#align one_lt_mul_of_le_of_lt' one_lt_mul_of_le_of_lt'
alias Left.one_lt_mul_of_lt_of_le ← one_lt_mul_of_lt_of_le'
+#align one_lt_mul_of_lt_of_le' one_lt_mul_of_lt_of_le'
alias Left.one_lt_mul ← one_lt_mul'
+#align one_lt_mul' one_lt_mul'
alias Left.one_lt_mul' ← one_lt_mul''
+#align one_lt_mul'' one_lt_mul''
attribute [to_additive add_nonneg "**Alias** of `Left.add_nonneg`."] one_le_mul
+#align add_nonneg add_nonneg
attribute [to_additive add_pos_of_nonneg_of_pos "**Alias** of `Left.add_pos_of_nonneg_of_pos`."]
one_lt_mul_of_le_of_lt'
+#align add_pos_of_nonneg_of_pos add_pos_of_nonneg_of_pos
attribute [to_additive add_pos_of_pos_of_nonneg "**Alias** of `Left.add_pos_of_pos_of_nonneg`."]
one_lt_mul_of_lt_of_le'
+#align add_pos_of_pos_of_nonneg add_pos_of_pos_of_nonneg
attribute [to_additive add_pos "**Alias** of `Left.add_pos`."] one_lt_mul'
+#align add_pos add_pos
attribute [to_additive add_pos' "**Alias** of `Left.add_pos'`."] one_lt_mul''
+#align add_pos' add_pos'
@[to_additive]
theorem lt_of_mul_lt_of_one_le_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (h : a * b < c)
(hle : 1 ≤ b) :
a < c :=
(le_mul_of_one_le_right' hle).trans_lt h
+#align lt_of_mul_lt_of_one_le_left lt_of_mul_lt_of_one_le_left
+#align lt_of_add_lt_of_nonneg_left lt_of_add_lt_of_nonneg_left
@[to_additive]
theorem le_of_mul_le_of_one_le_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (h : a * b ≤ c)
(hle : 1 ≤ b) :
a ≤ c :=
(le_mul_of_one_le_right' hle).trans h
+#align le_of_mul_le_of_one_le_left le_of_mul_le_of_one_le_left
+#align le_of_add_le_of_nonneg_left le_of_add_le_of_nonneg_left
@[to_additive]
theorem lt_of_lt_mul_of_le_one_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (h : a < b * c)
(hle : c ≤ 1) :
a < b :=
h.trans_le (mul_le_of_le_one_right' hle)
+#align lt_of_lt_mul_of_le_one_left lt_of_lt_mul_of_le_one_left
+#align lt_of_lt_add_of_nonpos_left lt_of_lt_add_of_nonpos_left
@[to_additive]
theorem le_of_le_mul_of_le_one_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b c : α} (h : a ≤ b * c)
(hle : c ≤ 1) :
a ≤ b :=
h.trans (mul_le_of_le_one_right' hle)
+#align le_of_le_mul_of_le_one_left le_of_le_mul_of_le_one_left
+#align le_of_le_add_of_nonpos_left le_of_le_add_of_nonpos_left
@[to_additive]
theorem lt_of_mul_lt_of_one_le_right [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α}
(h : a * b < c) (hle : 1 ≤ a) :
b < c :=
(le_mul_of_one_le_left' hle).trans_lt h
+#align lt_of_mul_lt_of_one_le_right lt_of_mul_lt_of_one_le_right
+#align lt_of_add_lt_of_nonneg_right lt_of_add_lt_of_nonneg_right
@[to_additive]
theorem le_of_mul_le_of_one_le_right [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α}
(h : a * b ≤ c) (hle : 1 ≤ a) :
b ≤ c :=
(le_mul_of_one_le_left' hle).trans h
+#align le_of_mul_le_of_one_le_right le_of_mul_le_of_one_le_right
+#align le_of_add_le_of_nonneg_right le_of_add_le_of_nonneg_right
@[to_additive]
theorem lt_of_lt_mul_of_le_one_right [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α}
(h : a < b * c) (hle : b ≤ 1) :
a < c :=
h.trans_le (mul_le_of_le_one_left' hle)
+#align lt_of_lt_mul_of_le_one_right lt_of_lt_mul_of_le_one_right
+#align lt_of_lt_add_of_nonpos_right lt_of_lt_add_of_nonpos_right
@[to_additive]
theorem le_of_le_mul_of_le_one_right [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c : α}
(h : a ≤ b * c) (hle : b ≤ 1) :
a ≤ c :=
h.trans (mul_le_of_le_one_left' hle)
+#align le_of_le_mul_of_le_one_right le_of_le_mul_of_le_one_right
+#align le_of_le_add_of_nonpos_right le_of_le_add_of_nonpos_right
end Preorder
@@ -954,6 +1135,8 @@ theorem mul_eq_one_iff' [CovariantClass α α (· * ·) (· ≤ ·)]
-- porting note: original proof of the second implication,
-- `fun ⟨ha', hb'⟩ => by rw [ha', hb', mul_one]`,
-- had its `to_additive`-ization fail due to some bug
+#align mul_eq_one_iff' mul_eq_one_iff'
+#align add_eq_zero_iff' add_eq_zero_iff'
@[to_additive] lemma mul_le_mul_iff_of_ge [CovariantClass α α (· * ·) (· ≤ ·)]
[CovariantClass α α (swap (· * ·)) (· ≤ ·)] [CovariantClass α α (· * ·) (· < ·)]
@@ -964,6 +1147,8 @@ theorem mul_eq_one_iff' [CovariantClass α α (· * ·) (· ≤ ·)]
refine' ⟨fun ha ↦ h.not_lt _, fun hb ↦ h.not_lt _⟩
{ exact mul_lt_mul_of_lt_of_le ha hb }
{ exact mul_lt_mul_of_le_of_lt ha hb }
+#align add_le_add_iff_of_ge add_le_add_iff_of_ge
+#align mul_le_mul_iff_of_ge mul_le_mul_iff_of_ge
section Left
@@ -972,10 +1157,14 @@ variable [CovariantClass α α (· * ·) (· ≤ ·)] {a b : α}
@[to_additive eq_zero_of_add_nonneg_left]
theorem eq_one_of_one_le_mul_left (ha : a ≤ 1) (hb : b ≤ 1) (hab : 1 ≤ a * b) : a = 1 :=
ha.eq_of_not_lt fun h => hab.not_lt <| mul_lt_one_of_lt_of_le h hb
+#align eq_one_of_one_le_mul_left eq_one_of_one_le_mul_left
+#align eq_zero_of_add_nonneg_left eq_zero_of_add_nonneg_left
@[to_additive]
theorem eq_one_of_mul_le_one_left (ha : 1 ≤ a) (hb : 1 ≤ b) (hab : a * b ≤ 1) : a = 1 :=
ha.eq_of_not_gt fun h => hab.not_lt <| one_lt_mul_of_lt_of_le' h hb
+#align eq_one_of_mul_le_one_left eq_one_of_mul_le_one_left
+#align eq_zero_of_add_nonpos_left eq_zero_of_add_nonpos_left
end Left
@@ -986,10 +1175,14 @@ variable [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b : α}
@[to_additive eq_zero_of_add_nonneg_right]
theorem eq_one_of_one_le_mul_right (ha : a ≤ 1) (hb : b ≤ 1) (hab : 1 ≤ a * b) : b = 1 :=
hb.eq_of_not_lt fun h => hab.not_lt <| Right.mul_lt_one_of_le_of_lt ha h
+#align eq_one_of_one_le_mul_right eq_one_of_one_le_mul_right
+#align eq_zero_of_add_nonneg_right eq_zero_of_add_nonneg_right
@[to_additive]
theorem eq_one_of_mul_le_one_right (ha : 1 ≤ a) (hb : 1 ≤ b) (hab : a * b ≤ 1) : b = 1 :=
hb.eq_of_not_gt fun h => hab.not_lt <| Right.one_lt_mul_of_le_of_lt ha h
+#align eq_one_of_mul_le_one_right eq_one_of_mul_le_one_right
+#align eq_zero_of_add_nonpos_right eq_zero_of_add_nonpos_right
end Right
@@ -1005,10 +1198,10 @@ theorem exists_square_le [CovariantClass α α (· * ·) (· < ·)] (a : α) :
have : a * a < a * 1 := mul_lt_mul_left' h a
rw [mul_one] at this
exact le_of_lt this
-
· use 1
push_neg at h
rwa [mul_one]
+#align exists_square_le exists_square_le
end LinearOrder
@@ -1081,8 +1274,10 @@ theorem Right.mul_eq_mul_iff_eq_and_eq [CovariantClass α α (· * ·) (· ≤
#align right.add_eq_add_iff_eq_and_eq Right.add_eq_add_iff_eq_and_eq
alias Left.mul_eq_mul_iff_eq_and_eq ← mul_eq_mul_iff_eq_and_eq
+#align mul_eq_mul_iff_eq_and_eq mul_eq_mul_iff_eq_and_eq
attribute [to_additive] mul_eq_mul_iff_eq_and_eq
+#align add_eq_add_iff_eq_and_eq add_eq_add_iff_eq_and_eq
end PartialOrder
@@ -1362,12 +1557,16 @@ theorem cmp_mul_left' {α : Type _} [Mul α] [LinearOrder α] [CovariantClass α
(a b c : α) :
cmp (a * b) (a * c) = cmp b c :=
(strictMono_id.const_mul' a).cmp_map_eq b c
+#align cmp_mul_left' cmp_mul_left'
+#align cmp_add_left cmp_add_left
@[to_additive (attr := simp) cmp_add_right]
theorem cmp_mul_right' {α : Type _} [Mul α] [LinearOrder α]
[CovariantClass α α (swap (· * ·)) (· < ·)] (a b c : α) :
cmp (a * c) (b * c) = cmp a b :=
(strictMono_id.mul_const' c).cmp_map_eq a b
+#align cmp_mul_right' cmp_mul_right'
+#align cmp_add_right cmp_add_right
end Mono
IsTrans α r → Trans r r r
and Trans r r r → IsTrans α r
(#1522)
Now Trans.trans
conflicts with _root_.trans
.
@@ -199,7 +199,7 @@ theorem mul_lt_of_mul_lt_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b
theorem mul_le_of_mul_le_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b c d : α} (h : a * b ≤ c)
(hle : d ≤ b) :
a * d ≤ c :=
- @act_rel_of_rel_of_act_rel _ _ _ (· ≤ ·) _ ⟨le_trans⟩ a _ _ _ hle h
+ @act_rel_of_rel_of_act_rel _ _ _ (· ≤ ·) _ _ a _ _ _ hle h
@[to_additive]
theorem mul_lt_of_mul_lt_right [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c d : α}
@@ -223,7 +223,7 @@ theorem lt_mul_of_lt_mul_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b
theorem le_mul_of_le_mul_left [CovariantClass α α (· * ·) (· ≤ ·)] {a b c d : α} (h : a ≤ b * c)
(hle : c ≤ d) :
a ≤ b * d :=
- @rel_act_of_rel_of_rel_act _ _ _ (· ≤ ·) _ ⟨le_trans⟩ b _ _ _ hle h
+ @rel_act_of_rel_of_rel_act _ _ _ (· ≤ ·) _ _ b _ _ _ hle h
@[to_additive]
theorem lt_mul_of_lt_mul_right [CovariantClass α α (swap (· * ·)) (· ≤ ·)] {a b c d : α}
@@ -1277,47 +1277,47 @@ theorem StrictAntiOn.mul' [CovariantClass α α (· * ·) (· < ·)]
#align strict_anti_on.add StrictAntiOn.add
/-- The product of a monotone function and a strictly monotone function is strictly monotone. -/
-@[to_additive add_strict_mono "The sum of a monotone function and a strictly monotone function is
+@[to_additive add_strictMono "The sum of a monotone function and a strictly monotone function is
strictly monotone."]
-theorem Monotone.mul_strict_mono' [CovariantClass α α (· * ·) (· < ·)]
+theorem Monotone.mul_strictMono' [CovariantClass α α (· * ·) (· < ·)]
[CovariantClass α α (swap (· * ·)) (· ≤ ·)] {f g : β → α} (hf : Monotone f)
(hg : StrictMono g) :
StrictMono fun x => f x * g x :=
fun _ _ h => mul_lt_mul_of_le_of_lt (hf h.le) (hg h)
-#align monotone.mul_strict_mono' Monotone.mul_strict_mono'
-#align monotone.add_strict_mono Monotone.add_strict_mono
+#align monotone.mul_strict_mono' Monotone.mul_strictMono'
+#align monotone.add_strict_mono Monotone.add_strictMono
/-- The product of a monotone function and a strictly monotone function is strictly monotone. -/
-@[to_additive add_strict_mono "The sum of a monotone function and a strictly monotone function is
+@[to_additive add_strictMono "The sum of a monotone function and a strictly monotone function is
strictly monotone."]
-theorem MonotoneOn.mul_strict_mono' [CovariantClass α α (· * ·) (· < ·)]
+theorem MonotoneOn.mul_strictMono' [CovariantClass α α (· * ·) (· < ·)]
[CovariantClass α α (swap (· * ·)) (· ≤ ·)] {f g : β → α} (hf : MonotoneOn f s)
(hg : StrictMonoOn g s) : StrictMonoOn (fun x => f x * g x) s :=
fun _ hx _ hy h => mul_lt_mul_of_le_of_lt (hf hx hy h.le) (hg hx hy h)
-#align monotone_on.mul_strict_mono' MonotoneOn.mul_strict_mono'
-#align monotone_on.add_strict_mono MonotoneOn.add_strict_mono
+#align monotone_on.mul_strict_mono' MonotoneOn.mul_strictMono'
+#align monotone_on.add_strict_mono MonotoneOn.add_strictMono
/-- The product of a antitone function and a strictly antitone function is strictly antitone. -/
-@[to_additive add_strict_anti "The sum of a antitone function and a strictly antitone function is
+@[to_additive add_strictAnti "The sum of a antitone function and a strictly antitone function is
strictly antitone."]
-theorem Antitone.mul_strict_anti' [CovariantClass α α (· * ·) (· < ·)]
+theorem Antitone.mul_strictAnti' [CovariantClass α α (· * ·) (· < ·)]
[CovariantClass α α (swap (· * ·)) (· ≤ ·)] {f g : β → α} (hf : Antitone f)
(hg : StrictAnti g) :
StrictAnti fun x => f x * g x :=
fun _ _ h => mul_lt_mul_of_le_of_lt (hf h.le) (hg h)
-#align antitone.mul_strict_anti' Antitone.mul_strict_anti'
-#align antitone.add_strict_anti Antitone.add_strict_anti
+#align antitone.mul_strict_anti' Antitone.mul_strictAnti'
+#align antitone.add_strict_anti Antitone.add_strictAnti
/-- The product of a antitone function and a strictly antitone function is strictly antitone. -/
-@[to_additive add_strict_anti "The sum of a antitone function and a strictly antitone function is
+@[to_additive add_strictAnti "The sum of a antitone function and a strictly antitone function is
strictly antitone."]
-theorem AntitoneOn.mul_strict_anti' [CovariantClass α α (· * ·) (· < ·)]
+theorem AntitoneOn.mul_strictAnti' [CovariantClass α α (· * ·) (· < ·)]
[CovariantClass α α (swap (· * ·)) (· ≤ ·)] {f g : β → α} (hf : AntitoneOn f s)
(hg : StrictAntiOn g s) :
StrictAntiOn (fun x => f x * g x) s :=
fun _ hx _ hy h => mul_lt_mul_of_le_of_lt (hf hx hy h.le) (hg hx hy h)
-#align antitone_on.mul_strict_anti' AntitoneOn.mul_strict_anti'
-#align antitone_on.add_strict_anti AntitoneOn.add_strict_anti
+#align antitone_on.mul_strict_anti' AntitoneOn.mul_strictAnti'
+#align antitone_on.add_strict_anti AntitoneOn.add_strictAnti
variable [CovariantClass α α (· * ·) (· ≤ ·)] [CovariantClass α α (swap (· * ·)) (· < ·)]
@@ -1490,9 +1490,9 @@ theorem bit0_mono [CovariantClass α α (· + ·) (· ≤ ·)] [CovariantClass
#align bit0_mono bit0_mono
@[deprecated]
-theorem bit0_strict_mono [CovariantClass α α (· + ·) (· < ·)]
+theorem bit0_strictMono [CovariantClass α α (· + ·) (· < ·)]
[CovariantClass α α (swap (· + ·)) (· < ·)] :
StrictMono (bit0 : α → α) := fun _ _ h => add_lt_add h h
-#align bit0_strict_mono bit0_strict_mono
+#align bit0_strict_mono bit0_strictMono
end Bit
to_additive
is @[to_additive (attrs := simp, ext, simps)]
simp
and simps
attributes to the to_additive
-dictionary.simp
-attributes). In particular it's possible that norm_cast
might generate some auxiliary declarations.to_additive
and simps
from the Simps
file to the toAdditive
file for uniformity.@[reassoc]
Co-authored-by: Johan Commelin <johan@commelin.net> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
@@ -76,13 +76,13 @@ theorem le_of_mul_le_mul_right' [i : ContravariantClass α α (swap (· * ·)) (
b ≤ c :=
i.elim a bc
-@[simp, to_additive]
+@[to_additive (attr := simp)]
theorem mul_le_mul_iff_left [CovariantClass α α (· * ·) (· ≤ ·)]
[ContravariantClass α α (· * ·) (· ≤ ·)] (a : α) {b c : α} :
a * b ≤ a * c ↔ b ≤ c :=
rel_iff_cov α α (· * ·) (· ≤ ·) a
-@[simp, to_additive]
+@[to_additive (attr := simp)]
theorem mul_le_mul_iff_right [CovariantClass α α (swap (· * ·)) (· ≤ ·)]
[ContravariantClass α α (swap (· * ·)) (· ≤ ·)] (a : α) {b c : α} :
b * a ≤ c * a ↔ b ≤ c :=
@@ -94,13 +94,13 @@ section LT
variable [LT α]
-@[simp, to_additive]
+@[to_additive (attr := simp)]
theorem mul_lt_mul_iff_left [CovariantClass α α (· * ·) (· < ·)]
[ContravariantClass α α (· * ·) (· < ·)] (a : α) {b c : α} :
a * b < a * c ↔ b < c :=
rel_iff_cov α α (· * ·) (· < ·) a
-@[simp, to_additive]
+@[to_additive (attr := simp)]
theorem mul_lt_mul_iff_right [CovariantClass α α (swap (· * ·)) (· < ·)]
[ContravariantClass α α (swap (· * ·)) (· < ·)] (a : α) {b c : α} :
b * a < c * a ↔ b < c :=
@@ -325,25 +325,25 @@ theorem le_one_of_mul_le_left [ContravariantClass α α (swap (· * ·)) (· ≤
a ≤ 1 :=
le_of_mul_le_mul_right' <| by simpa only [one_mul]
-@[simp, to_additive le_add_iff_nonneg_right]
+@[to_additive (attr := simp) le_add_iff_nonneg_right]
theorem le_mul_iff_one_le_right' [CovariantClass α α (· * ·) (· ≤ ·)]
[ContravariantClass α α (· * ·) (· ≤ ·)] (a : α) {b : α} :
a ≤ a * b ↔ 1 ≤ b :=
Iff.trans (by rw [mul_one]) (mul_le_mul_iff_left a)
-@[simp, to_additive le_add_iff_nonneg_left]
+@[to_additive (attr := simp) le_add_iff_nonneg_left]
theorem le_mul_iff_one_le_left' [CovariantClass α α (swap (· * ·)) (· ≤ ·)]
[ContravariantClass α α (swap (· * ·)) (· ≤ ·)] (a : α) {b : α} :
a ≤ b * a ↔ 1 ≤ b :=
Iff.trans (by rw [one_mul]) (mul_le_mul_iff_right a)
-@[simp, to_additive add_le_iff_nonpos_right]
+@[to_additive (attr := simp) add_le_iff_nonpos_right]
theorem mul_le_iff_le_one_right' [CovariantClass α α (· * ·) (· ≤ ·)]
[ContravariantClass α α (· * ·) (· ≤ ·)] (a : α) {b : α} :
a * b ≤ a ↔ b ≤ 1 :=
Iff.trans (by rw [mul_one]) (mul_le_mul_iff_left a)
-@[simp, to_additive add_le_iff_nonpos_left]
+@[to_additive (attr := simp) add_le_iff_nonpos_left]
theorem mul_le_iff_le_one_left' [CovariantClass α α (swap (· * ·)) (· ≤ ·)]
[ContravariantClass α α (swap (· * ·)) (· ≤ ·)] {a b : α} :
a * b ≤ b ↔ a ≤ 1 :=
@@ -407,24 +407,24 @@ theorem lt_one_of_mul_lt_left [ContravariantClass α α (swap (· * ·)) (· <
a < 1 :=
lt_of_mul_lt_mul_right' <| by simpa only [one_mul]
-@[simp, to_additive lt_add_iff_pos_right]
+@[to_additive (attr := simp) lt_add_iff_pos_right]
theorem lt_mul_iff_one_lt_right' [CovariantClass α α (· * ·) (· < ·)]
[ContravariantClass α α (· * ·) (· < ·)] (a : α) {b : α} :
a < a * b ↔ 1 < b :=
Iff.trans (by rw [mul_one]) (mul_lt_mul_iff_left a)
-@[simp, to_additive lt_add_iff_pos_left]
+@[to_additive (attr := simp) lt_add_iff_pos_left]
theorem lt_mul_iff_one_lt_left' [CovariantClass α α (swap (· * ·)) (· < ·)]
[ContravariantClass α α (swap (· * ·)) (· < ·)] (a : α) {b : α} : a < b * a ↔ 1 < b :=
Iff.trans (by rw [one_mul]) (mul_lt_mul_iff_right a)
-@[simp, to_additive add_lt_iff_neg_left]
+@[to_additive (attr := simp) add_lt_iff_neg_left]
theorem mul_lt_iff_lt_one_left' [CovariantClass α α (· * ·) (· < ·)]
[ContravariantClass α α (· * ·) (· < ·)] {a b : α} :
a * b < a ↔ b < 1 :=
Iff.trans (by rw [mul_one]) (mul_lt_mul_iff_left a)
-@[simp, to_additive add_lt_iff_neg_right]
+@[to_additive (attr := simp) add_lt_iff_neg_right]
theorem mul_lt_iff_lt_one_right' [CovariantClass α α (swap (· * ·)) (· < ·)]
[ContravariantClass α α (swap (· * ·)) (· < ·)] {a : α} (b : α) : a * b < b ↔ a < 1 :=
Iff.trans (by rw [one_mul]) (mul_lt_mul_iff_right b)
@@ -1357,13 +1357,13 @@ theorem StrictAntiOn.mul_antitone' (hf : StrictAntiOn f s) (hg : AntitoneOn g s)
#align strict_anti_on.mul_antitone' StrictAntiOn.mul_antitone'
#align strict_anti_on.add_antitone StrictAntiOn.add_antitone
-@[simp, to_additive cmp_add_left]
+@[to_additive (attr := simp) cmp_add_left]
theorem cmp_mul_left' {α : Type _} [Mul α] [LinearOrder α] [CovariantClass α α (· * ·) (· < ·)]
(a b c : α) :
cmp (a * b) (a * c) = cmp b c :=
(strictMono_id.const_mul' a).cmp_map_eq b c
-@[simp, to_additive cmp_add_right]
+@[to_additive (attr := simp) cmp_add_right]
theorem cmp_mul_right' {α : Type _} [Mul α] [LinearOrder α]
[CovariantClass α α (swap (· * ·)) (· < ·)] (a b c : α) :
cmp (a * c) (b * c) = cmp a b :=
Update SHAs after
@@ -5,7 +5,7 @@ Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro, Johannes Hölzl, Dami
Yuyang Zhao
! This file was ported from Lean 3 source module algebra.order.monoid.lemmas
-! leanprover-community/mathlib commit 99e8971dc62f1f7ecf693d75e75fbbabd55849de
+! leanprover-community/mathlib commit 2ed7e4aec72395b6a7c3ac4ac7873a7a43ead17c
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -1024,7 +1024,7 @@ variable [PartialOrder α]
/- This is not instance, since we want to have an instance from `LeftCancelSemigroup`s
to the appropriate `CovariantClass`. -/
-/-- A semigroup with a partial order and satisfying `left_cancel_semigroup`
+/-- A semigroup with a partial order and satisfying `LeftCancelSemigroup`
(i.e. `a * c < b * c → a < b`) is a `left_cancel Semigroup`. -/
@[to_additive
"An additive semigroup with a partial order and satisfying `AddLeftCancelSemigroup`
The script used to do this is included. The yaml file was obtained from https://raw.githubusercontent.com/wiki/leanprover-community/mathlib/mathlib4-port-status.md
@@ -3,6 +3,11 @@ Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro, Johannes Hölzl, Damiano Testa,
Yuyang Zhao
+
+! This file was ported from Lean 3 source module algebra.order.monoid.lemmas
+! leanprover-community/mathlib commit 99e8971dc62f1f7ecf693d75e75fbbabd55849de
+! Please do not edit these lines, except to modify the commit id
+! if you have ported upstream changes.
-/
import Mathlib.Algebra.CovariantAndContravariant
import Mathlib.Init.Data.Ordering.Basic
All dependencies are ported!