algebra.field.power
⟷
Mathlib.Algebra.Field.Power
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
@@ -3,9 +3,9 @@ Copyright (c) 2014 Robert Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Lewis, Leonardo de Moura, Johannes Hölzl, Mario Carneiro
-/
-import Mathbin.Algebra.Field.Defs
-import Mathbin.Algebra.GroupWithZero.Power
-import Mathbin.Algebra.Parity
+import Algebra.Field.Defs
+import Algebra.GroupWithZero.Power
+import Algebra.Parity
#align_import algebra.field.power from "leanprover-community/mathlib"@"c3291da49cfa65f0d43b094750541c0731edc932"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,16 +2,13 @@
Copyright (c) 2014 Robert Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Lewis, Leonardo de Moura, Johannes Hölzl, Mario Carneiro
-
-! This file was ported from Lean 3 source module algebra.field.power
-! 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.Algebra.Field.Defs
import Mathbin.Algebra.GroupWithZero.Power
import Mathbin.Algebra.Parity
+#align_import algebra.field.power from "leanprover-community/mathlib"@"c3291da49cfa65f0d43b094750541c0731edc932"
+
/-!
# Results about powers in fields or division rings.
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -30,17 +30,23 @@ section DivisionRing
variable [DivisionRing α] {n : ℤ}
+#print zpow_bit1_neg /-
@[simp]
theorem zpow_bit1_neg (a : α) (n : ℤ) : (-a) ^ bit1 n = -a ^ bit1 n := by
rw [zpow_bit1', zpow_bit1', neg_mul_neg, neg_mul_eq_mul_neg]
#align zpow_bit1_neg zpow_bit1_neg
+-/
+#print Odd.neg_zpow /-
theorem Odd.neg_zpow (h : Odd n) (a : α) : (-a) ^ n = -a ^ n := by obtain ⟨k, rfl⟩ := h.exists_bit1;
exact zpow_bit1_neg _ _
#align odd.neg_zpow Odd.neg_zpow
+-/
+#print Odd.neg_one_zpow /-
theorem Odd.neg_one_zpow (h : Odd n) : (-1 : α) ^ n = -1 := by rw [h.neg_zpow, one_zpow]
#align odd.neg_one_zpow Odd.neg_one_zpow
+-/
end DivisionRing
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -30,33 +30,15 @@ section DivisionRing
variable [DivisionRing α] {n : ℤ}
-/- warning: zpow_bit1_neg -> zpow_bit1_neg is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : DivisionRing.{u1} α] (a : α) (n : Int), Eq.{succ u1} α (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (DivisionRing.toDivInvMonoid.{u1} α _inst_1))) (Neg.neg.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α _inst_1)))))) a) (bit1.{0} Int Int.hasOne Int.hasAdd n)) (Neg.neg.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α _inst_1)))))) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (DivisionRing.toDivInvMonoid.{u1} α _inst_1))) a (bit1.{0} Int Int.hasOne Int.hasAdd n)))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : DivisionRing.{u1} α] (a : α) (n : Int), Eq.{succ u1} α (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (DivisionRing.toDivInvMonoid.{u1} α _inst_1))) (Neg.neg.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α _inst_1)) a) (bit1.{0} Int (Semiring.toOne.{0} Int Int.instSemiringInt) Int.instAddInt n)) (Neg.neg.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α _inst_1)) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (DivisionRing.toDivInvMonoid.{u1} α _inst_1))) a (bit1.{0} Int (Semiring.toOne.{0} Int Int.instSemiringInt) Int.instAddInt n)))
-Case conversion may be inaccurate. Consider using '#align zpow_bit1_neg zpow_bit1_negₓ'. -/
@[simp]
theorem zpow_bit1_neg (a : α) (n : ℤ) : (-a) ^ bit1 n = -a ^ bit1 n := by
rw [zpow_bit1', zpow_bit1', neg_mul_neg, neg_mul_eq_mul_neg]
#align zpow_bit1_neg zpow_bit1_neg
-/- warning: odd.neg_zpow -> Odd.neg_zpow is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : DivisionRing.{u1} α] {n : Int}, (Odd.{0} Int Int.semiring n) -> (forall (a : α), Eq.{succ u1} α (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (DivisionRing.toDivInvMonoid.{u1} α _inst_1))) (Neg.neg.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α _inst_1)))))) a) n) (Neg.neg.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α _inst_1)))))) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (DivisionRing.toDivInvMonoid.{u1} α _inst_1))) a n)))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : DivisionRing.{u1} α] {n : Int}, (Odd.{0} Int Int.instSemiringInt n) -> (forall (a : α), Eq.{succ u1} α (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (DivisionRing.toDivInvMonoid.{u1} α _inst_1))) (Neg.neg.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α _inst_1)) a) n) (Neg.neg.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α _inst_1)) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (DivisionRing.toDivInvMonoid.{u1} α _inst_1))) a n)))
-Case conversion may be inaccurate. Consider using '#align odd.neg_zpow Odd.neg_zpowₓ'. -/
theorem Odd.neg_zpow (h : Odd n) (a : α) : (-a) ^ n = -a ^ n := by obtain ⟨k, rfl⟩ := h.exists_bit1;
exact zpow_bit1_neg _ _
#align odd.neg_zpow Odd.neg_zpow
-/- warning: odd.neg_one_zpow -> Odd.neg_one_zpow is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : DivisionRing.{u1} α] {n : Int}, (Odd.{0} Int Int.semiring n) -> (Eq.{succ u1} α (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (DivisionRing.toDivInvMonoid.{u1} α _inst_1))) (Neg.neg.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α _inst_1)))))) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α _inst_1))))))))) n) (Neg.neg.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α _inst_1)))))) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α _inst_1))))))))))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : DivisionRing.{u1} α] {n : Int}, (Odd.{0} Int Int.instSemiringInt n) -> (Eq.{succ u1} α (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (DivisionRing.toDivInvMonoid.{u1} α _inst_1))) (Neg.neg.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α _inst_1)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Semiring.toOne.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α _inst_1)))))) n) (Neg.neg.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α _inst_1)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Semiring.toOne.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α _inst_1)))))))
-Case conversion may be inaccurate. Consider using '#align odd.neg_one_zpow Odd.neg_one_zpowₓ'. -/
theorem Odd.neg_one_zpow (h : Odd n) : (-1 : α) ^ n = -1 := by rw [h.neg_zpow, one_zpow]
#align odd.neg_one_zpow Odd.neg_one_zpow
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -47,9 +47,7 @@ lean 3 declaration is
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : DivisionRing.{u1} α] {n : Int}, (Odd.{0} Int Int.instSemiringInt n) -> (forall (a : α), Eq.{succ u1} α (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (DivisionRing.toDivInvMonoid.{u1} α _inst_1))) (Neg.neg.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α _inst_1)) a) n) (Neg.neg.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α _inst_1)) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (DivisionRing.toDivInvMonoid.{u1} α _inst_1))) a n)))
Case conversion may be inaccurate. Consider using '#align odd.neg_zpow Odd.neg_zpowₓ'. -/
-theorem Odd.neg_zpow (h : Odd n) (a : α) : (-a) ^ n = -a ^ n :=
- by
- obtain ⟨k, rfl⟩ := h.exists_bit1
+theorem Odd.neg_zpow (h : Odd n) (a : α) : (-a) ^ n = -a ^ n := by obtain ⟨k, rfl⟩ := h.exists_bit1;
exact zpow_bit1_neg _ _
#align odd.neg_zpow Odd.neg_zpow
mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1
@@ -34,7 +34,7 @@ variable [DivisionRing α] {n : ℤ}
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : DivisionRing.{u1} α] (a : α) (n : Int), Eq.{succ u1} α (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (DivisionRing.toDivInvMonoid.{u1} α _inst_1))) (Neg.neg.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α _inst_1)))))) a) (bit1.{0} Int Int.hasOne Int.hasAdd n)) (Neg.neg.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α _inst_1)))))) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (DivisionRing.toDivInvMonoid.{u1} α _inst_1))) a (bit1.{0} Int Int.hasOne Int.hasAdd n)))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : DivisionRing.{u1} α] (a : α) (n : Int), Eq.{succ u1} α (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (DivisionRing.toDivInvMonoid.{u1} α _inst_1))) (Neg.neg.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α _inst_1)) a) (bit1.{0} Int (NonAssocRing.toOne.{0} Int (Ring.toNonAssocRing.{0} Int Int.instRingInt)) Int.instAddInt n)) (Neg.neg.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α _inst_1)) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (DivisionRing.toDivInvMonoid.{u1} α _inst_1))) a (bit1.{0} Int (NonAssocRing.toOne.{0} Int (Ring.toNonAssocRing.{0} Int Int.instRingInt)) Int.instAddInt n)))
+ forall {α : Type.{u1}} [_inst_1 : DivisionRing.{u1} α] (a : α) (n : Int), Eq.{succ u1} α (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (DivisionRing.toDivInvMonoid.{u1} α _inst_1))) (Neg.neg.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α _inst_1)) a) (bit1.{0} Int (Semiring.toOne.{0} Int Int.instSemiringInt) Int.instAddInt n)) (Neg.neg.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α _inst_1)) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (DivisionRing.toDivInvMonoid.{u1} α _inst_1))) a (bit1.{0} Int (Semiring.toOne.{0} Int Int.instSemiringInt) Int.instAddInt n)))
Case conversion may be inaccurate. Consider using '#align zpow_bit1_neg zpow_bit1_negₓ'. -/
@[simp]
theorem zpow_bit1_neg (a : α) (n : ℤ) : (-a) ^ bit1 n = -a ^ bit1 n := by
@@ -57,7 +57,7 @@ theorem Odd.neg_zpow (h : Odd n) (a : α) : (-a) ^ n = -a ^ n :=
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : DivisionRing.{u1} α] {n : Int}, (Odd.{0} Int Int.semiring n) -> (Eq.{succ u1} α (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (DivisionRing.toDivInvMonoid.{u1} α _inst_1))) (Neg.neg.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α _inst_1)))))) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α _inst_1))))))))) n) (Neg.neg.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α _inst_1)))))) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α _inst_1))))))))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : DivisionRing.{u1} α] {n : Int}, (Odd.{0} Int Int.instSemiringInt n) -> (Eq.{succ u1} α (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (DivisionRing.toDivInvMonoid.{u1} α _inst_1))) (Neg.neg.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α _inst_1)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (NonAssocRing.toOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α _inst_1)))))) n) (Neg.neg.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α _inst_1)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (NonAssocRing.toOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α _inst_1)))))))
+ forall {α : Type.{u1}} [_inst_1 : DivisionRing.{u1} α] {n : Int}, (Odd.{0} Int Int.instSemiringInt n) -> (Eq.{succ u1} α (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (DivisionRing.toDivInvMonoid.{u1} α _inst_1))) (Neg.neg.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α _inst_1)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Semiring.toOne.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α _inst_1)))))) n) (Neg.neg.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α _inst_1)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Semiring.toOne.{u1} α (DivisionSemiring.toSemiring.{u1} α (DivisionRing.toDivisionSemiring.{u1} α _inst_1)))))))
Case conversion may be inaccurate. Consider using '#align odd.neg_one_zpow Odd.neg_one_zpowₓ'. -/
theorem Odd.neg_one_zpow (h : Odd n) : (-1 : α) ^ n = -1 := by rw [h.neg_zpow, one_zpow]
#align odd.neg_one_zpow Odd.neg_one_zpow
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce86f4e05e9a9b8da5e316b22c76ce76440c56a1
@@ -32,7 +32,7 @@ variable [DivisionRing α] {n : ℤ}
/- warning: zpow_bit1_neg -> zpow_bit1_neg is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : DivisionRing.{u1} α] (a : α) (n : Int), Eq.{succ u1} α (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (DivisionRing.toDivInvMonoid.{u1} α _inst_1))) (Neg.neg.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α _inst_1)))))) a) (bit1.{0} Int Int.hasOne Int.hasAdd n)) (Neg.neg.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α _inst_1)))))) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (DivisionRing.toDivInvMonoid.{u1} α _inst_1))) a (bit1.{0} Int Int.hasOne Int.hasAdd n)))
+ forall {α : Type.{u1}} [_inst_1 : DivisionRing.{u1} α] (a : α) (n : Int), Eq.{succ u1} α (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (DivisionRing.toDivInvMonoid.{u1} α _inst_1))) (Neg.neg.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α _inst_1)))))) a) (bit1.{0} Int Int.hasOne Int.hasAdd n)) (Neg.neg.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α _inst_1)))))) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (DivisionRing.toDivInvMonoid.{u1} α _inst_1))) a (bit1.{0} Int Int.hasOne Int.hasAdd n)))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : DivisionRing.{u1} α] (a : α) (n : Int), Eq.{succ u1} α (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (DivisionRing.toDivInvMonoid.{u1} α _inst_1))) (Neg.neg.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α _inst_1)) a) (bit1.{0} Int (NonAssocRing.toOne.{0} Int (Ring.toNonAssocRing.{0} Int Int.instRingInt)) Int.instAddInt n)) (Neg.neg.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α _inst_1)) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (DivisionRing.toDivInvMonoid.{u1} α _inst_1))) a (bit1.{0} Int (NonAssocRing.toOne.{0} Int (Ring.toNonAssocRing.{0} Int Int.instRingInt)) Int.instAddInt n)))
Case conversion may be inaccurate. Consider using '#align zpow_bit1_neg zpow_bit1_negₓ'. -/
@@ -43,7 +43,7 @@ theorem zpow_bit1_neg (a : α) (n : ℤ) : (-a) ^ bit1 n = -a ^ bit1 n := by
/- warning: odd.neg_zpow -> Odd.neg_zpow is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : DivisionRing.{u1} α] {n : Int}, (Odd.{0} Int Int.semiring n) -> (forall (a : α), Eq.{succ u1} α (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (DivisionRing.toDivInvMonoid.{u1} α _inst_1))) (Neg.neg.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α _inst_1)))))) a) n) (Neg.neg.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α _inst_1)))))) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (DivisionRing.toDivInvMonoid.{u1} α _inst_1))) a n)))
+ forall {α : Type.{u1}} [_inst_1 : DivisionRing.{u1} α] {n : Int}, (Odd.{0} Int Int.semiring n) -> (forall (a : α), Eq.{succ u1} α (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (DivisionRing.toDivInvMonoid.{u1} α _inst_1))) (Neg.neg.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α _inst_1)))))) a) n) (Neg.neg.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α _inst_1)))))) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (DivisionRing.toDivInvMonoid.{u1} α _inst_1))) a n)))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : DivisionRing.{u1} α] {n : Int}, (Odd.{0} Int Int.instSemiringInt n) -> (forall (a : α), Eq.{succ u1} α (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (DivisionRing.toDivInvMonoid.{u1} α _inst_1))) (Neg.neg.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α _inst_1)) a) n) (Neg.neg.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α _inst_1)) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (DivisionRing.toDivInvMonoid.{u1} α _inst_1))) a n)))
Case conversion may be inaccurate. Consider using '#align odd.neg_zpow Odd.neg_zpowₓ'. -/
@@ -55,7 +55,7 @@ theorem Odd.neg_zpow (h : Odd n) (a : α) : (-a) ^ n = -a ^ n :=
/- warning: odd.neg_one_zpow -> Odd.neg_one_zpow is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : DivisionRing.{u1} α] {n : Int}, (Odd.{0} Int Int.semiring n) -> (Eq.{succ u1} α (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (DivisionRing.toDivInvMonoid.{u1} α _inst_1))) (Neg.neg.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α _inst_1)))))) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α _inst_1))))))))) n) (Neg.neg.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α _inst_1)))))) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α _inst_1))))))))))
+ forall {α : Type.{u1}} [_inst_1 : DivisionRing.{u1} α] {n : Int}, (Odd.{0} Int Int.semiring n) -> (Eq.{succ u1} α (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (DivisionRing.toDivInvMonoid.{u1} α _inst_1))) (Neg.neg.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α _inst_1)))))) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α _inst_1))))))))) n) (Neg.neg.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α _inst_1)))))) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α _inst_1))))))))))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : DivisionRing.{u1} α] {n : Int}, (Odd.{0} Int Int.instSemiringInt n) -> (Eq.{succ u1} α (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (DivisionRing.toDivInvMonoid.{u1} α _inst_1))) (Neg.neg.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α _inst_1)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (NonAssocRing.toOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α _inst_1)))))) n) (Neg.neg.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α _inst_1)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (NonAssocRing.toOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α _inst_1)))))))
Case conversion may be inaccurate. Consider using '#align odd.neg_one_zpow Odd.neg_one_zpowₓ'. -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
@@ -5,6 +5,7 @@ Authors: Robert Lewis, Leonardo de Moura, Johannes Hölzl, Mario Carneiro
-/
import Mathlib.Algebra.Field.Defs
import Mathlib.Algebra.GroupWithZero.Power
+import Mathlib.Algebra.GroupWithZero.Bitwise
import Mathlib.Algebra.Parity
#align_import algebra.field.power from "leanprover-community/mathlib"@"1e05171a5e8cf18d98d9cf7b207540acb044acae"
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -18,7 +18,7 @@ beyond those needed for the basic definition.
-/
-variable {α : Type _}
+variable {α : Type*}
section DivisionRing
@@ -2,16 +2,13 @@
Copyright (c) 2014 Robert Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Lewis, Leonardo de Moura, Johannes Hölzl, Mario Carneiro
-
-! This file was ported from Lean 3 source module algebra.field.power
-! leanprover-community/mathlib commit 1e05171a5e8cf18d98d9cf7b207540acb044acae
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Algebra.Field.Defs
import Mathlib.Algebra.GroupWithZero.Power
import Mathlib.Algebra.Parity
+#align_import algebra.field.power from "leanprover-community/mathlib"@"1e05171a5e8cf18d98d9cf7b207540acb044acae"
+
/-!
# Results about powers in fields or division rings.
by
line breaks (#1523)
During porting, I usually fix the desired format we seem to want for the line breaks around by
with
awk '{do {{if (match($0, "^ by$") && length(p) < 98) {p=p " by";} else {if (NR!=1) {print p}; p=$0}}} while (getline == 1) if (getline==0) print p}' Mathlib/File/Im/Working/On.lean
I noticed there are some more files that slipped through.
This pull request is the result of running this command:
grep -lr "^ by\$" Mathlib | xargs -n 1 awk -i inplace '{do {{if (match($0, "^ by$") && length(p) < 98 && not (match(p, "^[ \t]*--"))) {p=p " by";} else {if (NR!=1) {print p}; p=$0}}} while (getline == 1) if (getline==0) print p}'
Co-authored-by: Moritz Firsching <firsching@google.com>
@@ -33,8 +33,7 @@ theorem zpow_bit1_neg (a : α) (n : ℤ) : (-a) ^ bit1 n = -a ^ bit1 n := by
rw [zpow_bit1', zpow_bit1', neg_mul_neg, neg_mul_eq_mul_neg]
#align zpow_bit1_neg zpow_bit1_neg
-theorem Odd.neg_zpow (h : Odd n) (a : α) : (-a) ^ n = -a ^ n :=
- by
+theorem Odd.neg_zpow (h : Odd n) (a : α) : (-a) ^ n = -a ^ n := by
obtain ⟨k, rfl⟩ := h.exists_bit1
exact zpow_bit1_neg _ _
#align odd.neg_zpow Odd.neg_zpow
The unported dependencies are