algebra.order.group.bounds
⟷
Mathlib.Algebra.Order.Group.Bounds
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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mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yury Kudryashov
-/
-import Mathbin.Order.Bounds.Basic
-import Mathbin.Algebra.Order.Group.Defs
+import Order.Bounds.Basic
+import Algebra.Order.Group.Defs
#align_import algebra.order.group.bounds from "leanprover-community/mathlib"@"c3291da49cfa65f0d43b094750541c0731edc932"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yury Kudryashov
-
-! This file was ported from Lean 3 source module algebra.order.group.bounds
-! leanprover-community/mathlib commit c3291da49cfa65f0d43b094750541c0731edc932
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Order.Bounds.Basic
import Mathbin.Algebra.Order.Group.Defs
+#align_import algebra.order.group.bounds from "leanprover-community/mathlib"@"c3291da49cfa65f0d43b094750541c0731edc932"
+
/-!
# Least upper bound and the greatest lower bound in linear ordered additive commutative groups
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -25,23 +25,31 @@ section LinearOrderedAddCommGroup
variable [LinearOrderedAddCommGroup α] {s : Set α} {a ε : α}
+#print IsGLB.exists_between_self_add /-
theorem IsGLB.exists_between_self_add (h : IsGLB s a) (hε : 0 < ε) : ∃ b ∈ s, a ≤ b ∧ b < a + ε :=
h.exists_between <| lt_add_of_pos_right _ hε
#align is_glb.exists_between_self_add IsGLB.exists_between_self_add
+-/
+#print IsGLB.exists_between_self_add' /-
theorem IsGLB.exists_between_self_add' (h : IsGLB s a) (h₂ : a ∉ s) (hε : 0 < ε) :
∃ b ∈ s, a < b ∧ b < a + ε :=
h.exists_between' h₂ <| lt_add_of_pos_right _ hε
#align is_glb.exists_between_self_add' IsGLB.exists_between_self_add'
+-/
+#print IsLUB.exists_between_sub_self /-
theorem IsLUB.exists_between_sub_self (h : IsLUB s a) (hε : 0 < ε) : ∃ b ∈ s, a - ε < b ∧ b ≤ a :=
h.exists_between <| sub_lt_self _ hε
#align is_lub.exists_between_sub_self IsLUB.exists_between_sub_self
+-/
+#print IsLUB.exists_between_sub_self' /-
theorem IsLUB.exists_between_sub_self' (h : IsLUB s a) (h₂ : a ∉ s) (hε : 0 < ε) :
∃ b ∈ s, a - ε < b ∧ b < a :=
h.exists_between' h₂ <| sub_lt_self _ hε
#align is_lub.exists_between_sub_self' IsLUB.exists_between_sub_self'
+-/
end LinearOrderedAddCommGroup
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -25,43 +25,19 @@ section LinearOrderedAddCommGroup
variable [LinearOrderedAddCommGroup α] {s : Set α} {a ε : α}
-/- warning: is_glb.exists_between_self_add -> IsGLB.exists_between_self_add is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {s : Set.{u1} α} {a : α} {ε : α}, (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))) s a) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))))))) ε) -> (Exists.{succ u1} α (fun (b : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => And (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) a b) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) b (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))))) a ε)))))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {s : Set.{u1} α} {a : α} {ε : α}, (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))) s a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))))))) ε) -> (Exists.{succ u1} α (fun (b : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) (And (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) a b) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) b (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))))) a ε)))))
-Case conversion may be inaccurate. Consider using '#align is_glb.exists_between_self_add IsGLB.exists_between_self_addₓ'. -/
theorem IsGLB.exists_between_self_add (h : IsGLB s a) (hε : 0 < ε) : ∃ b ∈ s, a ≤ b ∧ b < a + ε :=
h.exists_between <| lt_add_of_pos_right _ hε
#align is_glb.exists_between_self_add IsGLB.exists_between_self_add
-/- warning: is_glb.exists_between_self_add' -> IsGLB.exists_between_self_add' is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {s : Set.{u1} α} {a : α} {ε : α}, (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))) s a) -> (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s)) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))))))) ε) -> (Exists.{succ u1} α (fun (b : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => And (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) a b) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) b (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))))) a ε)))))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {s : Set.{u1} α} {a : α} {ε : α}, (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))) s a) -> (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s)) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))))))) ε) -> (Exists.{succ u1} α (fun (b : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) (And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) a b) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) b (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))))) a ε)))))
-Case conversion may be inaccurate. Consider using '#align is_glb.exists_between_self_add' IsGLB.exists_between_self_add'ₓ'. -/
theorem IsGLB.exists_between_self_add' (h : IsGLB s a) (h₂ : a ∉ s) (hε : 0 < ε) :
∃ b ∈ s, a < b ∧ b < a + ε :=
h.exists_between' h₂ <| lt_add_of_pos_right _ hε
#align is_glb.exists_between_self_add' IsGLB.exists_between_self_add'
-/- warning: is_lub.exists_between_sub_self -> IsLUB.exists_between_sub_self is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {s : Set.{u1} α} {a : α} {ε : α}, (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))) s a) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))))))) ε) -> (Exists.{succ u1} α (fun (b : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => And (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) a ε) b) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) b a))))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {s : Set.{u1} α} {a : α} {ε : α}, (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))) s a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))))))) ε) -> (Exists.{succ u1} α (fun (b : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) (And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) a ε) b) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) b a))))
-Case conversion may be inaccurate. Consider using '#align is_lub.exists_between_sub_self IsLUB.exists_between_sub_selfₓ'. -/
theorem IsLUB.exists_between_sub_self (h : IsLUB s a) (hε : 0 < ε) : ∃ b ∈ s, a - ε < b ∧ b ≤ a :=
h.exists_between <| sub_lt_self _ hε
#align is_lub.exists_between_sub_self IsLUB.exists_between_sub_self
-/- warning: is_lub.exists_between_sub_self' -> IsLUB.exists_between_sub_self' is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {s : Set.{u1} α} {a : α} {ε : α}, (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))) s a) -> (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s)) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))))))) ε) -> (Exists.{succ u1} α (fun (b : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => And (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) a ε) b) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) b a))))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {s : Set.{u1} α} {a : α} {ε : α}, (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))) s a) -> (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s)) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))))))) ε) -> (Exists.{succ u1} α (fun (b : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) (And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) a ε) b) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) b a))))
-Case conversion may be inaccurate. Consider using '#align is_lub.exists_between_sub_self' IsLUB.exists_between_sub_self'ₓ'. -/
theorem IsLUB.exists_between_sub_self' (h : IsLUB s a) (h₂ : a ∉ s) (hε : 0 < ε) :
∃ b ∈ s, a - ε < b ∧ b < a :=
h.exists_between' h₂ <| sub_lt_self _ hε
mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
@@ -27,7 +27,7 @@ variable [LinearOrderedAddCommGroup α] {s : Set α} {a ε : α}
/- warning: is_glb.exists_between_self_add -> IsGLB.exists_between_self_add is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {s : Set.{u1} α} {a : α} {ε : α}, (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))) s a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))))))) ε) -> (Exists.{succ u1} α (fun (b : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => And (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) a b) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) b (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))))) a ε)))))
+ forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {s : Set.{u1} α} {a : α} {ε : α}, (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))) s a) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))))))) ε) -> (Exists.{succ u1} α (fun (b : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => And (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) a b) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) b (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))))) a ε)))))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {s : Set.{u1} α} {a : α} {ε : α}, (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))) s a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))))))) ε) -> (Exists.{succ u1} α (fun (b : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) (And (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) a b) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) b (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))))) a ε)))))
Case conversion may be inaccurate. Consider using '#align is_glb.exists_between_self_add IsGLB.exists_between_self_addₓ'. -/
@@ -37,7 +37,7 @@ theorem IsGLB.exists_between_self_add (h : IsGLB s a) (hε : 0 < ε) : ∃ b ∈
/- warning: is_glb.exists_between_self_add' -> IsGLB.exists_between_self_add' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {s : Set.{u1} α} {a : α} {ε : α}, (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))) s a) -> (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s)) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))))))) ε) -> (Exists.{succ u1} α (fun (b : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) a b) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) b (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))))) a ε)))))
+ forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {s : Set.{u1} α} {a : α} {ε : α}, (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))) s a) -> (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s)) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))))))) ε) -> (Exists.{succ u1} α (fun (b : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => And (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) a b) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) b (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))))) a ε)))))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {s : Set.{u1} α} {a : α} {ε : α}, (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))) s a) -> (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s)) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))))))) ε) -> (Exists.{succ u1} α (fun (b : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) (And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) a b) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) b (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))))) a ε)))))
Case conversion may be inaccurate. Consider using '#align is_glb.exists_between_self_add' IsGLB.exists_between_self_add'ₓ'. -/
@@ -48,7 +48,7 @@ theorem IsGLB.exists_between_self_add' (h : IsGLB s a) (h₂ : a ∉ s) (hε : 0
/- warning: is_lub.exists_between_sub_self -> IsLUB.exists_between_sub_self is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {s : Set.{u1} α} {a : α} {ε : α}, (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))) s a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))))))) ε) -> (Exists.{succ u1} α (fun (b : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) a ε) b) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) b a))))
+ forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {s : Set.{u1} α} {a : α} {ε : α}, (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))) s a) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))))))) ε) -> (Exists.{succ u1} α (fun (b : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => And (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) a ε) b) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) b a))))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {s : Set.{u1} α} {a : α} {ε : α}, (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))) s a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))))))) ε) -> (Exists.{succ u1} α (fun (b : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) (And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) a ε) b) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) b a))))
Case conversion may be inaccurate. Consider using '#align is_lub.exists_between_sub_self IsLUB.exists_between_sub_selfₓ'. -/
@@ -58,7 +58,7 @@ theorem IsLUB.exists_between_sub_self (h : IsLUB s a) (hε : 0 < ε) : ∃ b ∈
/- warning: is_lub.exists_between_sub_self' -> IsLUB.exists_between_sub_self' is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {s : Set.{u1} α} {a : α} {ε : α}, (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))) s a) -> (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s)) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))))))) ε) -> (Exists.{succ u1} α (fun (b : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) a ε) b) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) b a))))
+ forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {s : Set.{u1} α} {a : α} {ε : α}, (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))) s a) -> (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s)) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))))))) ε) -> (Exists.{succ u1} α (fun (b : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => And (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) a ε) b) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) b a))))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {s : Set.{u1} α} {a : α} {ε : α}, (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))) s a) -> (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s)) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))))))) ε) -> (Exists.{succ u1} α (fun (b : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) (And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) a ε) b) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) b a))))
Case conversion may be inaccurate. Consider using '#align is_lub.exists_between_sub_self' IsLUB.exists_between_sub_self'ₓ'. -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
... or reduce its scope (the full removal is not as obvious).
@@ -12,11 +12,9 @@ import Mathlib.Algebra.Order.Group.Defs
# Least upper bound and the greatest lower bound in linear ordered additive commutative groups
-/
-set_option autoImplicit true
-
section LinearOrderedAddCommGroup
-variable [LinearOrderedAddCommGroup α] {s : Set α} {a ε : α}
+variable {α : Type*} [LinearOrderedAddCommGroup α] {s : Set α} {a ε : α}
theorem IsGLB.exists_between_self_add (h : IsGLB s a) (hε : 0 < ε) : ∃ b ∈ s, a ≤ b ∧ b < a + ε :=
h.exists_between <| lt_add_of_pos_right _ hε
Autoimplicits are highly controversial and also defeat the performance-improving work in #6474.
The intent of this PR is to make autoImplicit
opt-in on a per-file basis, by disabling it in the lakefile and enabling it again with set_option autoImplicit true
in the few files that rely on it.
That also keeps this PR small, as opposed to attempting to "fix" files to not need it any more.
I claim that many of the uses of autoImplicit
in these files are accidental; situations such as:
variables
are in scope, but pasting the lemma in the wrong sectionHaving set_option autoImplicit false
as the default prevents these types of mistake being made in the 90% of files where autoImplicit
s are not used at all, and causes them to be caught by CI during review.
I think there were various points during the port where we encouraged porters to delete the universes u v
lines; I think having autoparams for universe variables only would cover a lot of the cases we actually use them, while avoiding any real shortcomings.
A Zulip poll (after combining overlapping votes accordingly) was in favor of this change with 5:5:18
as the no:dontcare:yes
vote ratio.
While this PR was being reviewed, a handful of files gained some more likely-accidental autoImplicits. In these places, set_option autoImplicit true
has been placed locally within a section, rather than at the top of the file.
@@ -12,6 +12,8 @@ import Mathlib.Algebra.Order.Group.Defs
# Least upper bound and the greatest lower bound in linear ordered additive commutative groups
-/
+set_option autoImplicit true
+
section LinearOrderedAddCommGroup
variable [LinearOrderedAddCommGroup α] {s : Set α} {a ε : α}
@@ -2,14 +2,12 @@
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yury Kudryashov
-! This file was ported from Lean 3 source module algebra.order.group.bounds
-! leanprover-community/mathlib commit d012cd09a9b256d870751284dd6a29882b0be105
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Order.Bounds.Basic
import Mathlib.Algebra.Order.Group.Defs
+#align_import algebra.order.group.bounds from "leanprover-community/mathlib"@"d012cd09a9b256d870751284dd6a29882b0be105"
+
/-!
# Least upper bound and the greatest lower bound in linear ordered additive commutative groups
-/