number_theory.zsqrtd.to_real
⟷
Mathlib.NumberTheory.Zsqrtd.ToReal
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) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
-import Mathbin.Data.Real.Sqrt
-import Mathbin.NumberTheory.Zsqrtd.Basic
+import Data.Real.Sqrt
+import NumberTheory.Zsqrtd.Basic
#align_import number_theory.zsqrtd.to_real from "leanprover-community/mathlib"@"97eab48559068f3d6313da387714ef25768fb730"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-
-! This file was ported from Lean 3 source module number_theory.zsqrtd.to_real
-! leanprover-community/mathlib commit 97eab48559068f3d6313da387714ef25768fb730
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Data.Real.Sqrt
import Mathbin.NumberTheory.Zsqrtd.Basic
+#align_import number_theory.zsqrtd.to_real from "leanprover-community/mathlib"@"97eab48559068f3d6313da387714ef25768fb730"
+
/-!
# Image of `zsqrtd` in `ℝ`
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -34,10 +34,12 @@ noncomputable def toReal {d : ℤ} (h : 0 ≤ d) : ℤ√d →+* ℝ :=
#align zsqrtd.to_real Zsqrtd.toReal
-/
+#print Zsqrtd.toReal_injective /-
theorem toReal_injective {d : ℤ} (h0d : 0 ≤ d) (hd : ∀ n : ℤ, d ≠ n * n) :
Function.Injective (toReal h0d) :=
lift_injective _ hd
#align zsqrtd.to_real_injective Zsqrtd.toReal_injective
+-/
end Zsqrtd
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -34,12 +34,6 @@ noncomputable def toReal {d : ℤ} (h : 0 ≤ d) : ℤ√d →+* ℝ :=
#align zsqrtd.to_real Zsqrtd.toReal
-/
-/- warning: zsqrtd.to_real_injective -> Zsqrtd.toReal_injective is a dubious translation:
-lean 3 declaration is
- forall {d : Int} (h0d : LE.le.{0} Int Int.hasLe (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero))) d), (forall (n : Int), Ne.{1} Int d (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) n n)) -> (Function.Injective.{1, 1} (Zsqrtd d) Real (coeFn.{1, 1} (RingHom.{0, 0} (Zsqrtd d) Real (NonAssocRing.toNonAssocSemiring.{0} (Zsqrtd d) (Ring.toNonAssocRing.{0} (Zsqrtd d) (Zsqrtd.ring d))) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (fun (_x : RingHom.{0, 0} (Zsqrtd d) Real (NonAssocRing.toNonAssocSemiring.{0} (Zsqrtd d) (Ring.toNonAssocRing.{0} (Zsqrtd d) (Zsqrtd.ring d))) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) => (Zsqrtd d) -> Real) (RingHom.hasCoeToFun.{0, 0} (Zsqrtd d) Real (NonAssocRing.toNonAssocSemiring.{0} (Zsqrtd d) (Ring.toNonAssocRing.{0} (Zsqrtd d) (Zsqrtd.ring d))) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (Zsqrtd.toReal d h0d)))
-but is expected to have type
- forall {d : Int} (h0d : LE.le.{0} Int Int.instLEInt (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) d), (forall (n : Int), Ne.{1} Int d (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) n n)) -> (Function.Injective.{1, 1} (Zsqrtd d) Real (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} (Zsqrtd d) Real (Semiring.toNonAssocSemiring.{0} (Zsqrtd d) (Zsqrtd.instSemiringZsqrtd d)) (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (Zsqrtd d) (fun (_x : Zsqrtd d) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Zsqrtd d) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} (Zsqrtd d) Real (Semiring.toNonAssocSemiring.{0} (Zsqrtd d) (Zsqrtd.instSemiringZsqrtd d)) (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (Zsqrtd d) Real (NonUnitalNonAssocSemiring.toMul.{0} (Zsqrtd d) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} (Zsqrtd d) (Semiring.toNonAssocSemiring.{0} (Zsqrtd d) (Zsqrtd.instSemiringZsqrtd d)))) (NonUnitalNonAssocSemiring.toMul.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} (Zsqrtd d) Real (Semiring.toNonAssocSemiring.{0} (Zsqrtd d) (Zsqrtd.instSemiringZsqrtd d)) (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (Zsqrtd d) Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} (Zsqrtd d) (Semiring.toNonAssocSemiring.{0} (Zsqrtd d) (Zsqrtd.instSemiringZsqrtd d))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} (Zsqrtd d) Real (Semiring.toNonAssocSemiring.{0} (Zsqrtd d) (Zsqrtd.instSemiringZsqrtd d)) (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (Zsqrtd d) Real (Semiring.toNonAssocSemiring.{0} (Zsqrtd d) (Zsqrtd.instSemiringZsqrtd d)) (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (RingHom.instRingHomClassRingHom.{0, 0} (Zsqrtd d) Real (Semiring.toNonAssocSemiring.{0} (Zsqrtd d) (Zsqrtd.instSemiringZsqrtd d)) (Semiring.toNonAssocSemiring.{0} Real Real.semiring))))) (Zsqrtd.toReal d h0d)))
-Case conversion may be inaccurate. Consider using '#align zsqrtd.to_real_injective Zsqrtd.toReal_injectiveₓ'. -/
theorem toReal_injective {d : ℤ} (h0d : 0 ≤ d) (hd : ∀ n : ℤ, d ≠ n * n) :
Function.Injective (toReal h0d) :=
lift_injective _ hd
mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4
@@ -38,7 +38,7 @@ noncomputable def toReal {d : ℤ} (h : 0 ≤ d) : ℤ√d →+* ℝ :=
lean 3 declaration is
forall {d : Int} (h0d : LE.le.{0} Int Int.hasLe (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero))) d), (forall (n : Int), Ne.{1} Int d (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) n n)) -> (Function.Injective.{1, 1} (Zsqrtd d) Real (coeFn.{1, 1} (RingHom.{0, 0} (Zsqrtd d) Real (NonAssocRing.toNonAssocSemiring.{0} (Zsqrtd d) (Ring.toNonAssocRing.{0} (Zsqrtd d) (Zsqrtd.ring d))) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (fun (_x : RingHom.{0, 0} (Zsqrtd d) Real (NonAssocRing.toNonAssocSemiring.{0} (Zsqrtd d) (Ring.toNonAssocRing.{0} (Zsqrtd d) (Zsqrtd.ring d))) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) => (Zsqrtd d) -> Real) (RingHom.hasCoeToFun.{0, 0} (Zsqrtd d) Real (NonAssocRing.toNonAssocSemiring.{0} (Zsqrtd d) (Ring.toNonAssocRing.{0} (Zsqrtd d) (Zsqrtd.ring d))) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (Zsqrtd.toReal d h0d)))
but is expected to have type
- forall {d : Int} (h0d : LE.le.{0} Int Int.instLEInt (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) d), (forall (n : Int), Ne.{1} Int d (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) n n)) -> (Function.Injective.{1, 1} (Zsqrtd d) Real (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} (Zsqrtd d) Real (Semiring.toNonAssocSemiring.{0} (Zsqrtd d) (Zsqrtd.instSemiringZsqrtd d)) (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (Zsqrtd d) (fun (_x : Zsqrtd d) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Zsqrtd d) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} (Zsqrtd d) Real (Semiring.toNonAssocSemiring.{0} (Zsqrtd d) (Zsqrtd.instSemiringZsqrtd d)) (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (Zsqrtd d) Real (NonUnitalNonAssocSemiring.toMul.{0} (Zsqrtd d) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} (Zsqrtd d) (Semiring.toNonAssocSemiring.{0} (Zsqrtd d) (Zsqrtd.instSemiringZsqrtd d)))) (NonUnitalNonAssocSemiring.toMul.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} (Zsqrtd d) Real (Semiring.toNonAssocSemiring.{0} (Zsqrtd d) (Zsqrtd.instSemiringZsqrtd d)) (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (Zsqrtd d) Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} (Zsqrtd d) (Semiring.toNonAssocSemiring.{0} (Zsqrtd d) (Zsqrtd.instSemiringZsqrtd d))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} (Zsqrtd d) Real (Semiring.toNonAssocSemiring.{0} (Zsqrtd d) (Zsqrtd.instSemiringZsqrtd d)) (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (Zsqrtd d) Real (Semiring.toNonAssocSemiring.{0} (Zsqrtd d) (Zsqrtd.instSemiringZsqrtd d)) (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (RingHom.instRingHomClassRingHom.{0, 0} (Zsqrtd d) Real (Semiring.toNonAssocSemiring.{0} (Zsqrtd d) (Zsqrtd.instSemiringZsqrtd d)) (Semiring.toNonAssocSemiring.{0} Real Real.semiring))))) (Zsqrtd.toReal d h0d)))
+ forall {d : Int} (h0d : LE.le.{0} Int Int.instLEInt (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) d), (forall (n : Int), Ne.{1} Int d (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) n n)) -> (Function.Injective.{1, 1} (Zsqrtd d) Real (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} (Zsqrtd d) Real (Semiring.toNonAssocSemiring.{0} (Zsqrtd d) (Zsqrtd.instSemiringZsqrtd d)) (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (Zsqrtd d) (fun (_x : Zsqrtd d) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Zsqrtd d) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} (Zsqrtd d) Real (Semiring.toNonAssocSemiring.{0} (Zsqrtd d) (Zsqrtd.instSemiringZsqrtd d)) (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (Zsqrtd d) Real (NonUnitalNonAssocSemiring.toMul.{0} (Zsqrtd d) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} (Zsqrtd d) (Semiring.toNonAssocSemiring.{0} (Zsqrtd d) (Zsqrtd.instSemiringZsqrtd d)))) (NonUnitalNonAssocSemiring.toMul.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} (Zsqrtd d) Real (Semiring.toNonAssocSemiring.{0} (Zsqrtd d) (Zsqrtd.instSemiringZsqrtd d)) (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (Zsqrtd d) Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} (Zsqrtd d) (Semiring.toNonAssocSemiring.{0} (Zsqrtd d) (Zsqrtd.instSemiringZsqrtd d))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} (Zsqrtd d) Real (Semiring.toNonAssocSemiring.{0} (Zsqrtd d) (Zsqrtd.instSemiringZsqrtd d)) (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (Zsqrtd d) Real (Semiring.toNonAssocSemiring.{0} (Zsqrtd d) (Zsqrtd.instSemiringZsqrtd d)) (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (RingHom.instRingHomClassRingHom.{0, 0} (Zsqrtd d) Real (Semiring.toNonAssocSemiring.{0} (Zsqrtd d) (Zsqrtd.instSemiringZsqrtd d)) (Semiring.toNonAssocSemiring.{0} Real Real.semiring))))) (Zsqrtd.toReal d h0d)))
Case conversion may be inaccurate. Consider using '#align zsqrtd.to_real_injective Zsqrtd.toReal_injectiveₓ'. -/
theorem toReal_injective {d : ℤ} (h0d : 0 ≤ d) (hd : ∀ n : ℤ, d ≠ n * n) :
Function.Injective (toReal h0d) :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1
@@ -38,7 +38,7 @@ noncomputable def toReal {d : ℤ} (h : 0 ≤ d) : ℤ√d →+* ℝ :=
lean 3 declaration is
forall {d : Int} (h0d : LE.le.{0} Int Int.hasLe (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero))) d), (forall (n : Int), Ne.{1} Int d (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) n n)) -> (Function.Injective.{1, 1} (Zsqrtd d) Real (coeFn.{1, 1} (RingHom.{0, 0} (Zsqrtd d) Real (NonAssocRing.toNonAssocSemiring.{0} (Zsqrtd d) (Ring.toNonAssocRing.{0} (Zsqrtd d) (Zsqrtd.ring d))) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (fun (_x : RingHom.{0, 0} (Zsqrtd d) Real (NonAssocRing.toNonAssocSemiring.{0} (Zsqrtd d) (Ring.toNonAssocRing.{0} (Zsqrtd d) (Zsqrtd.ring d))) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) => (Zsqrtd d) -> Real) (RingHom.hasCoeToFun.{0, 0} (Zsqrtd d) Real (NonAssocRing.toNonAssocSemiring.{0} (Zsqrtd d) (Ring.toNonAssocRing.{0} (Zsqrtd d) (Zsqrtd.ring d))) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (Zsqrtd.toReal d h0d)))
but is expected to have type
- forall {d : Int} (h0d : LE.le.{0} Int Int.instLEInt (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) d), (forall (n : Int), Ne.{1} Int d (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) n n)) -> (Function.Injective.{1, 1} (Zsqrtd d) Real (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} (Zsqrtd d) Real (NonAssocRing.toNonAssocSemiring.{0} (Zsqrtd d) (Ring.toNonAssocRing.{0} (Zsqrtd d) (Zsqrtd.instRingZsqrtd d))) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (Zsqrtd d) (fun (_x : Zsqrtd d) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Zsqrtd d) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} (Zsqrtd d) Real (NonAssocRing.toNonAssocSemiring.{0} (Zsqrtd d) (Ring.toNonAssocRing.{0} (Zsqrtd d) (Zsqrtd.instRingZsqrtd d))) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (Zsqrtd d) Real (NonUnitalNonAssocSemiring.toMul.{0} (Zsqrtd d) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} (Zsqrtd d) (NonAssocRing.toNonAssocSemiring.{0} (Zsqrtd d) (Ring.toNonAssocRing.{0} (Zsqrtd d) (Zsqrtd.instRingZsqrtd d))))) (NonUnitalNonAssocSemiring.toMul.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} (Zsqrtd d) Real (NonAssocRing.toNonAssocSemiring.{0} (Zsqrtd d) (Ring.toNonAssocRing.{0} (Zsqrtd d) (Zsqrtd.instRingZsqrtd d))) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (Zsqrtd d) Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} (Zsqrtd d) (NonAssocRing.toNonAssocSemiring.{0} (Zsqrtd d) (Ring.toNonAssocRing.{0} (Zsqrtd d) (Zsqrtd.instRingZsqrtd d)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} (Zsqrtd d) Real (NonAssocRing.toNonAssocSemiring.{0} (Zsqrtd d) (Ring.toNonAssocRing.{0} (Zsqrtd d) (Zsqrtd.instRingZsqrtd d))) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (Zsqrtd d) Real (NonAssocRing.toNonAssocSemiring.{0} (Zsqrtd d) (Ring.toNonAssocRing.{0} (Zsqrtd d) (Zsqrtd.instRingZsqrtd d))) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) (RingHom.instRingHomClassRingHom.{0, 0} (Zsqrtd d) Real (NonAssocRing.toNonAssocSemiring.{0} (Zsqrtd d) (Ring.toNonAssocRing.{0} (Zsqrtd d) (Zsqrtd.instRingZsqrtd d))) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))))) (Zsqrtd.toReal d h0d)))
+ forall {d : Int} (h0d : LE.le.{0} Int Int.instLEInt (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) d), (forall (n : Int), Ne.{1} Int d (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) n n)) -> (Function.Injective.{1, 1} (Zsqrtd d) Real (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} (Zsqrtd d) Real (Semiring.toNonAssocSemiring.{0} (Zsqrtd d) (Zsqrtd.instSemiringZsqrtd d)) (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (Zsqrtd d) (fun (_x : Zsqrtd d) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Zsqrtd d) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} (Zsqrtd d) Real (Semiring.toNonAssocSemiring.{0} (Zsqrtd d) (Zsqrtd.instSemiringZsqrtd d)) (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (Zsqrtd d) Real (NonUnitalNonAssocSemiring.toMul.{0} (Zsqrtd d) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} (Zsqrtd d) (Semiring.toNonAssocSemiring.{0} (Zsqrtd d) (Zsqrtd.instSemiringZsqrtd d)))) (NonUnitalNonAssocSemiring.toMul.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} (Zsqrtd d) Real (Semiring.toNonAssocSemiring.{0} (Zsqrtd d) (Zsqrtd.instSemiringZsqrtd d)) (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (Zsqrtd d) Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} (Zsqrtd d) (Semiring.toNonAssocSemiring.{0} (Zsqrtd d) (Zsqrtd.instSemiringZsqrtd d))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} (Zsqrtd d) Real (Semiring.toNonAssocSemiring.{0} (Zsqrtd d) (Zsqrtd.instSemiringZsqrtd d)) (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (Zsqrtd d) Real (Semiring.toNonAssocSemiring.{0} (Zsqrtd d) (Zsqrtd.instSemiringZsqrtd d)) (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (RingHom.instRingHomClassRingHom.{0, 0} (Zsqrtd d) Real (Semiring.toNonAssocSemiring.{0} (Zsqrtd d) (Zsqrtd.instSemiringZsqrtd d)) (Semiring.toNonAssocSemiring.{0} Real Real.semiring))))) (Zsqrtd.toReal d h0d)))
Case conversion may be inaccurate. Consider using '#align zsqrtd.to_real_injective Zsqrtd.toReal_injectiveₓ'. -/
theorem toReal_injective {d : ℤ} (h0d : 0 ≤ d) (hd : ∀ n : ℤ, d ≠ n * n) :
Function.Injective (toReal h0d) :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/d11893b411025250c8e61ff2f12ccbd7ee35ab15
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
! This file was ported from Lean 3 source module number_theory.zsqrtd.to_real
-! leanprover-community/mathlib commit e59154361202a34b26176e0de9267ef8e2dcd446
+! leanprover-community/mathlib commit 97eab48559068f3d6313da387714ef25768fb730
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -14,6 +14,9 @@ import Mathbin.NumberTheory.Zsqrtd.Basic
/-!
# Image of `zsqrtd` in `ℝ`
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
This file defines `zsqrtd.to_real` and related lemmas.
It is in a separate file to avoid pulling in all of `data.real` into `data.zsqrtd`.
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/57e09a1296bfb4330ddf6624f1028ba186117d82
@@ -21,6 +21,7 @@ It is in a separate file to avoid pulling in all of `data.real` into `data.zsqrt
namespace Zsqrtd
+#print Zsqrtd.toReal /-
/-- The image of `zsqrtd` in `ℝ`, using `real.sqrt` which takes the positive root of `d`.
If the negative root is desired, use `to_real h a.conj`. -/
@@ -28,7 +29,14 @@ If the negative root is desired, use `to_real h a.conj`. -/
noncomputable def toReal {d : ℤ} (h : 0 ≤ d) : ℤ√d →+* ℝ :=
lift ⟨Real.sqrt d, Real.mul_self_sqrt (Int.cast_nonneg.mpr h)⟩
#align zsqrtd.to_real Zsqrtd.toReal
+-/
+/- warning: zsqrtd.to_real_injective -> Zsqrtd.toReal_injective is a dubious translation:
+lean 3 declaration is
+ forall {d : Int} (h0d : LE.le.{0} Int Int.hasLe (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero))) d), (forall (n : Int), Ne.{1} Int d (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) n n)) -> (Function.Injective.{1, 1} (Zsqrtd d) Real (coeFn.{1, 1} (RingHom.{0, 0} (Zsqrtd d) Real (NonAssocRing.toNonAssocSemiring.{0} (Zsqrtd d) (Ring.toNonAssocRing.{0} (Zsqrtd d) (Zsqrtd.ring d))) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (fun (_x : RingHom.{0, 0} (Zsqrtd d) Real (NonAssocRing.toNonAssocSemiring.{0} (Zsqrtd d) (Ring.toNonAssocRing.{0} (Zsqrtd d) (Zsqrtd.ring d))) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) => (Zsqrtd d) -> Real) (RingHom.hasCoeToFun.{0, 0} (Zsqrtd d) Real (NonAssocRing.toNonAssocSemiring.{0} (Zsqrtd d) (Ring.toNonAssocRing.{0} (Zsqrtd d) (Zsqrtd.ring d))) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring))) (Zsqrtd.toReal d h0d)))
+but is expected to have type
+ forall {d : Int} (h0d : LE.le.{0} Int Int.instLEInt (OfNat.ofNat.{0} Int 0 (instOfNatInt 0)) d), (forall (n : Int), Ne.{1} Int d (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) n n)) -> (Function.Injective.{1, 1} (Zsqrtd d) Real (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} (Zsqrtd d) Real (NonAssocRing.toNonAssocSemiring.{0} (Zsqrtd d) (Ring.toNonAssocRing.{0} (Zsqrtd d) (Zsqrtd.instRingZsqrtd d))) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (Zsqrtd d) (fun (_x : Zsqrtd d) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Zsqrtd d) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} (Zsqrtd d) Real (NonAssocRing.toNonAssocSemiring.{0} (Zsqrtd d) (Ring.toNonAssocRing.{0} (Zsqrtd d) (Zsqrtd.instRingZsqrtd d))) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (Zsqrtd d) Real (NonUnitalNonAssocSemiring.toMul.{0} (Zsqrtd d) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} (Zsqrtd d) (NonAssocRing.toNonAssocSemiring.{0} (Zsqrtd d) (Ring.toNonAssocRing.{0} (Zsqrtd d) (Zsqrtd.instRingZsqrtd d))))) (NonUnitalNonAssocSemiring.toMul.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} (Zsqrtd d) Real (NonAssocRing.toNonAssocSemiring.{0} (Zsqrtd d) (Ring.toNonAssocRing.{0} (Zsqrtd d) (Zsqrtd.instRingZsqrtd d))) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (Zsqrtd d) Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} (Zsqrtd d) (NonAssocRing.toNonAssocSemiring.{0} (Zsqrtd d) (Ring.toNonAssocRing.{0} (Zsqrtd d) (Zsqrtd.instRingZsqrtd d)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} (Zsqrtd d) Real (NonAssocRing.toNonAssocSemiring.{0} (Zsqrtd d) (Ring.toNonAssocRing.{0} (Zsqrtd d) (Zsqrtd.instRingZsqrtd d))) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (Zsqrtd d) Real (NonAssocRing.toNonAssocSemiring.{0} (Zsqrtd d) (Ring.toNonAssocRing.{0} (Zsqrtd d) (Zsqrtd.instRingZsqrtd d))) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) (RingHom.instRingHomClassRingHom.{0, 0} (Zsqrtd d) Real (NonAssocRing.toNonAssocSemiring.{0} (Zsqrtd d) (Ring.toNonAssocRing.{0} (Zsqrtd d) (Zsqrtd.instRingZsqrtd d))) (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))))) (Zsqrtd.toReal d h0d)))
+Case conversion may be inaccurate. Consider using '#align zsqrtd.to_real_injective Zsqrtd.toReal_injectiveₓ'. -/
theorem toReal_injective {d : ℤ} (h0d : 0 ≤ d) (hd : ∀ n : ℤ, d ≠ n * n) :
Function.Injective (toReal h0d) :=
lift_injective _ hd
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
This adds the notation √r
for Real.sqrt r
. The precedence is such that √x⁻¹
is parsed as √(x⁻¹)
; not because this is particularly desirable, but because it's the default and the choice doesn't really matter.
This is extracted from #7907, which adds a more general nth root typeclass.
The idea is to perform all the boring substitutions downstream quickly, so that we can play around with custom elaborators with a much slower rate of code-rot.
This PR also won't rot as quickly, as it does not forbid writing x.sqrt
as that PR does.
While perhaps claiming √
for Real.sqrt
is greedy; it:
NNReal.sqrt
and Nat.sqrt
sqrt
on Float
Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>
@@ -23,7 +23,7 @@ namespace Zsqrtd
If the negative root is desired, use `toReal h (star a)`. -/
@[simps!]
noncomputable def toReal {d : ℤ} (h : 0 ≤ d) : ℤ√d →+* ℝ :=
- lift ⟨Real.sqrt d, Real.mul_self_sqrt (Int.cast_nonneg.mpr h)⟩
+ lift ⟨√↑d, Real.mul_self_sqrt (Int.cast_nonneg.mpr h)⟩
#align zsqrtd.to_real Zsqrtd.toReal
theorem toReal_injective {d : ℤ} (h0d : 0 ≤ d) (hd : ∀ n : ℤ, d ≠ n * n) :
@@ -2,15 +2,12 @@
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-
-! This file was ported from Lean 3 source module number_theory.zsqrtd.to_real
-! leanprover-community/mathlib commit e59154361202a34b26176e0de9267ef8e2dcd446
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Data.Real.Sqrt
import Mathlib.NumberTheory.Zsqrtd.Basic
+#align_import number_theory.zsqrtd.to_real from "leanprover-community/mathlib"@"e59154361202a34b26176e0de9267ef8e2dcd446"
+
/-!
# Image of `Zsqrtd` in `ℝ`
@@ -12,7 +12,7 @@ import Mathlib.Data.Real.Sqrt
import Mathlib.NumberTheory.Zsqrtd.Basic
/-!
-# Image of `zsqrtd` in `ℝ`
+# Image of `Zsqrtd` in `ℝ`
This file defines `Zsqrtd.toReal` and related lemmas.
It is in a separate file to avoid pulling in all of `Data.Real` into `Data.Zsqrtd`.
@@ -23,7 +23,7 @@ namespace Zsqrtd
/-- The image of `Zsqrtd` in `ℝ`, using `Real.sqrt` which takes the positive root of `d`.
-If the negative root is desired, use `toReal h a.conj`. -/
+If the negative root is desired, use `toReal h (star a)`. -/
@[simps!]
noncomputable def toReal {d : ℤ} (h : 0 ≤ d) : ℤ√d →+* ℝ :=
lift ⟨Real.sqrt d, Real.mul_self_sqrt (Int.cast_nonneg.mpr h)⟩
The unported dependencies are
algebra.order.module
init.core
algebra.order.monoid.cancel.defs
algebra.abs
algebra.group_power.lemmas
init.data.list.basic
algebra.order.monoid.cancel.basic
init.data.list.default
topology.subset_properties
init.logic
The following 1 dependencies have changed in mathlib3 since they were ported, which may complicate porting this file