algebra.order.field.pi
⟷
Mathlib.Algebra.Order.Field.Pi
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) 2014 Robert Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
-import Mathbin.Algebra.Order.Field.Basic
-import Mathbin.Data.Fintype.Lattice
+import Algebra.Order.Field.Basic
+import Data.Fintype.Lattice
#align_import algebra.order.field.pi from "leanprover-community/mathlib"@"327c3c0d9232d80e250dc8f65e7835b82b266ea5"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2014 Robert Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-
-! This file was ported from Lean 3 source module algebra.order.field.pi
-! leanprover-community/mathlib commit 327c3c0d9232d80e250dc8f65e7835b82b266ea5
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Algebra.Order.Field.Basic
import Mathbin.Data.Fintype.Lattice
+#align_import algebra.order.field.pi from "leanprover-community/mathlib"@"327c3c0d9232d80e250dc8f65e7835b82b266ea5"
+
/-!
# Lemmas about (finite domain) functions into fields.
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -23,6 +23,7 @@ We split this from `algebra.order.field.basic` to avoid importing the finiteness
variable {α ι : Type _} [LinearOrderedSemifield α]
+#print Pi.exists_forall_pos_add_lt /-
theorem Pi.exists_forall_pos_add_lt [ExistsAddOfLE α] [Finite ι] {x y : ι → α}
(h : ∀ i, x i < y i) : ∃ ε, 0 < ε ∧ ∀ i, x i + ε < y i :=
by
@@ -36,4 +37,5 @@ theorem Pi.exists_forall_pos_add_lt [ExistsAddOfLE α] [Finite ι] {x y : ι →
⟨_, half_pos hε, fun i =>
add_lt_add_left ((half_lt_self hε).trans_le <| Finset.inf'_le _ <| Finset.mem_univ _) _⟩
#align pi.exists_forall_pos_add_lt Pi.exists_forall_pos_add_lt
+-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -23,12 +23,6 @@ We split this from `algebra.order.field.basic` to avoid importing the finiteness
variable {α ι : Type _} [LinearOrderedSemifield α]
-/- warning: pi.exists_forall_pos_add_lt -> Pi.exists_forall_pos_add_lt is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : LinearOrderedSemifield.{u1} α] [_inst_2 : ExistsAddOfLE.{u1} α (Distrib.toHasAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1)))))))) (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1)))))))] [_inst_3 : Finite.{succ u2} ι] {x : ι -> α} {y : ι -> α}, (forall (i : ι), LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1))))))) (x i) (y i)) -> (Exists.{succ u1} α (fun (ε : α) => And (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1))))))))))) ε) (forall (i : ι), LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1))))))))) (x i) ε) (y i))))
-but is expected to have type
- forall {α : Type.{u2}} {ι : Type.{u1}} [_inst_1 : LinearOrderedSemifield.{u2} α] [_inst_2 : ExistsAddOfLE.{u2} α (Distrib.toAdd.{u2} α (NonUnitalNonAssocSemiring.toDistrib.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α _inst_1)))))))) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (StrictOrderedSemiring.toPartialOrder.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α _inst_1))))))] [_inst_3 : Finite.{succ u1} ι] {x : ι -> α} {y : ι -> α}, (forall (i : ι), LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (StrictOrderedSemiring.toPartialOrder.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α _inst_1)))))) (x i) (y i)) -> (Exists.{succ u2} α (fun (ε : α) => And (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (StrictOrderedSemiring.toPartialOrder.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α _inst_1)))))) (OfNat.ofNat.{u2} α 0 (Zero.toOfNat0.{u2} α (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α _inst_1)))))) ε) (forall (i : ι), LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (StrictOrderedSemiring.toPartialOrder.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α _inst_1)))))) (HAdd.hAdd.{u2, u2, u2} α α α (instHAdd.{u2} α (Distrib.toAdd.{u2} α (NonUnitalNonAssocSemiring.toDistrib.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α _inst_1))))))))) (x i) ε) (y i))))
-Case conversion may be inaccurate. Consider using '#align pi.exists_forall_pos_add_lt Pi.exists_forall_pos_add_ltₓ'. -/
theorem Pi.exists_forall_pos_add_lt [ExistsAddOfLE α] [Finite ι] {x y : ι → α}
(h : ∀ i, x i < y i) : ∃ ε, 0 < ε ∧ ∀ i, x i + ε < y i :=
by
mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
@@ -25,7 +25,7 @@ variable {α ι : Type _} [LinearOrderedSemifield α]
/- warning: pi.exists_forall_pos_add_lt -> Pi.exists_forall_pos_add_lt is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : LinearOrderedSemifield.{u1} α] [_inst_2 : ExistsAddOfLE.{u1} α (Distrib.toHasAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1)))))))) (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1)))))))] [_inst_3 : Finite.{succ u2} ι] {x : ι -> α} {y : ι -> α}, (forall (i : ι), LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1))))))) (x i) (y i)) -> (Exists.{succ u1} α (fun (ε : α) => And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1))))))))))) ε) (forall (i : ι), LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1))))))))) (x i) ε) (y i))))
+ forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : LinearOrderedSemifield.{u1} α] [_inst_2 : ExistsAddOfLE.{u1} α (Distrib.toHasAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1)))))))) (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1)))))))] [_inst_3 : Finite.{succ u2} ι] {x : ι -> α} {y : ι -> α}, (forall (i : ι), LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1))))))) (x i) (y i)) -> (Exists.{succ u1} α (fun (ε : α) => And (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1))))))))))) ε) (forall (i : ι), LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCancelAddCommMonoid.toPartialOrder.{u1} α (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} α (Semiring.toNonAssocSemiring.{u1} α (StrictOrderedSemiring.toSemiring.{u1} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α _inst_1))))))))) (x i) ε) (y i))))
but is expected to have type
forall {α : Type.{u2}} {ι : Type.{u1}} [_inst_1 : LinearOrderedSemifield.{u2} α] [_inst_2 : ExistsAddOfLE.{u2} α (Distrib.toAdd.{u2} α (NonUnitalNonAssocSemiring.toDistrib.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α _inst_1)))))))) (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (StrictOrderedSemiring.toPartialOrder.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α _inst_1))))))] [_inst_3 : Finite.{succ u1} ι] {x : ι -> α} {y : ι -> α}, (forall (i : ι), LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (StrictOrderedSemiring.toPartialOrder.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α _inst_1)))))) (x i) (y i)) -> (Exists.{succ u2} α (fun (ε : α) => And (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (StrictOrderedSemiring.toPartialOrder.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α _inst_1)))))) (OfNat.ofNat.{u2} α 0 (Zero.toOfNat0.{u2} α (CommMonoidWithZero.toZero.{u2} α (CommGroupWithZero.toCommMonoidWithZero.{u2} α (Semifield.toCommGroupWithZero.{u2} α (LinearOrderedSemifield.toSemifield.{u2} α _inst_1)))))) ε) (forall (i : ι), LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (StrictOrderedSemiring.toPartialOrder.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α _inst_1)))))) (HAdd.hAdd.{u2, u2, u2} α α α (instHAdd.{u2} α (Distrib.toAdd.{u2} α (NonUnitalNonAssocSemiring.toDistrib.{u2} α (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} α (Semiring.toNonAssocSemiring.{u2} α (StrictOrderedSemiring.toSemiring.{u2} α (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} α (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α _inst_1))))))))) (x i) ε) (y i))))
Case conversion may be inaccurate. Consider using '#align pi.exists_forall_pos_add_lt Pi.exists_forall_pos_add_ltₓ'. -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
@@ -4,7 +4,8 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Algebra.Order.Field.Basic
-import Mathlib.Data.Fintype.Lattice
+import Mathlib.Data.Finset.Lattice
+import Mathlib.Data.Fintype.Card
#align_import algebra.order.field.pi from "leanprover-community/mathlib"@"509de852e1de55e1efa8eacfa11df0823f26f226"
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -15,7 +15,7 @@ We split this from `Algebra.Order.Field.Basic` to avoid importing the finiteness
-/
-variable {α ι : Type _} [LinearOrderedSemifield α]
+variable {α ι : Type*} [LinearOrderedSemifield α]
theorem Pi.exists_forall_pos_add_lt [ExistsAddOfLE α] [Finite ι] {x y : ι → α}
(h : ∀ i, x i < y i) : ∃ ε, 0 < ε ∧ ∀ i, x i + ε < y i := by
@@ -2,15 +2,12 @@
Copyright (c) 2014 Robert Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-
-! This file was ported from Lean 3 source module algebra.order.field.pi
-! leanprover-community/mathlib commit 509de852e1de55e1efa8eacfa11df0823f26f226
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Algebra.Order.Field.Basic
import Mathlib.Data.Fintype.Lattice
+#align_import algebra.order.field.pi from "leanprover-community/mathlib"@"509de852e1de55e1efa8eacfa11df0823f26f226"
+
/-!
# Lemmas about (finite domain) functions into fields.
The unported dependencies are