data.int.sqrt
⟷
Mathlib.Data.Int.Sqrt
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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(last sync)
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -3,7 +3,7 @@ Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
-import Data.Nat.Sqrt
+import Data.Nat.Defs
#align_import data.int.sqrt from "leanprover-community/mathlib"@"c3291da49cfa65f0d43b094750541c0731edc932"
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -44,7 +44,7 @@ theorem exists_mul_self (x : ℤ) : (∃ n, n * n = x) ↔ sqrt x * sqrt x = x :
#print Int.sqrt_nonneg /-
theorem sqrt_nonneg (n : ℤ) : 0 ≤ sqrt n :=
- coe_nat_nonneg _
+ natCast_nonneg _
#align int.sqrt_nonneg Int.sqrt_nonneg
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,7 +3,7 @@ Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
-import Mathbin.Data.Nat.Sqrt
+import Data.Nat.Sqrt
#align_import data.int.sqrt from "leanprover-community/mathlib"@"c3291da49cfa65f0d43b094750541c0731edc932"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,14 +2,11 @@
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-
-! This file was ported from Lean 3 source module data.int.sqrt
-! 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.Data.Nat.Sqrt
+#align_import data.int.sqrt from "leanprover-community/mathlib"@"c3291da49cfa65f0d43b094750541c0731edc932"
+
/-!
# Square root of integers
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
Nat.sqrt
material (#11866)
Move the content of Data.Nat.ForSqrt
and Data.Nat.Sqrt
to Data.Nat.Defs
by using Nat
-specific Std lemmas rather than the mathlib general ones. This makes it ready to move to Std if wanted.
@@ -3,7 +3,9 @@ Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
-import Mathlib.Data.Nat.Sqrt
+import Mathlib.Data.Int.Defs
+import Mathlib.Data.Nat.Defs
+import Mathlib.Tactic.Common
#align_import data.int.sqrt from "leanprover-community/mathlib"@"ba2245edf0c8bb155f1569fd9b9492a9b384cde6"
@@ -37,9 +39,4 @@ theorem sqrt_nonneg (n : ℤ) : 0 ≤ sqrt n :=
natCast_nonneg _
#align int.sqrt_nonneg Int.sqrt_nonneg
-/-- `IsSquare` can be decided on `ℤ` by checking against the square root. -/
-instance : DecidablePred (IsSquare : ℤ → Prop) :=
- fun m => decidable_of_iff' (sqrt m * sqrt m = m) <| by
- simp_rw [← exists_mul_self m, IsSquare, eq_comm]
-
end Int
coe_nat
to natCast
(#11637)
Reduce the diff of #11499
All in the Int
namespace:
ofNat_eq_cast
→ ofNat_eq_natCast
cast_eq_cast_iff_Nat
→ natCast_inj
natCast_eq_ofNat
→ ofNat_eq_natCast
coe_nat_sub
→ natCast_sub
coe_nat_nonneg
→ natCast_nonneg
sign_coe_add_one
→ sign_natCast_add_one
nat_succ_eq_int_succ
→ natCast_succ
succ_neg_nat_succ
→ succ_neg_natCast_succ
coe_pred_of_pos
→ natCast_pred_of_pos
coe_nat_div
→ natCast_div
coe_nat_ediv
→ natCast_ediv
sign_coe_nat_of_nonzero
→ sign_natCast_of_ne_zero
toNat_coe_nat
→ toNat_natCast
toNat_coe_nat_add_one
→ toNat_natCast_add_one
coe_nat_dvd
→ natCast_dvd_natCast
coe_nat_dvd_left
→ natCast_dvd
coe_nat_dvd_right
→ dvd_natCast
le_coe_nat_sub
→ le_natCast_sub
succ_coe_nat_pos
→ succ_natCast_pos
coe_nat_modEq_iff
→ natCast_modEq_iff
coe_natAbs
→ natCast_natAbs
coe_nat_eq_zero
→ natCast_eq_zero
coe_nat_ne_zero
→ natCast_ne_zero
coe_nat_ne_zero_iff_pos
→ natCast_ne_zero_iff_pos
abs_coe_nat
→ abs_natCast
coe_nat_nonpos_iff
→ natCast_nonpos_iff
Also rename Nat.coe_nat_dvd
to Nat.cast_dvd_cast
@@ -26,7 +26,7 @@ def sqrt (z : ℤ) : ℤ :=
#align int.sqrt Int.sqrt
theorem sqrt_eq (n : ℤ) : sqrt (n * n) = n.natAbs := by
- rw [sqrt, ← natAbs_mul_self, toNat_coe_nat, Nat.sqrt_eq]
+ rw [sqrt, ← natAbs_mul_self, toNat_natCast, Nat.sqrt_eq]
#align int.sqrt_eq Int.sqrt_eq
theorem exists_mul_self (x : ℤ) : (∃ n, n * n = x) ↔ sqrt x * sqrt x = x :=
@@ -34,7 +34,7 @@ theorem exists_mul_self (x : ℤ) : (∃ n, n * n = x) ↔ sqrt x * sqrt x = x :
#align int.exists_mul_self Int.exists_mul_self
theorem sqrt_nonneg (n : ℤ) : 0 ≤ sqrt n :=
- coe_nat_nonneg _
+ natCast_nonneg _
#align int.sqrt_nonneg Int.sqrt_nonneg
/-- `IsSquare` can be decided on `ℤ` by checking against the square root. -/
@@ -40,6 +40,6 @@ theorem sqrt_nonneg (n : ℤ) : 0 ≤ sqrt n :=
/-- `IsSquare` can be decided on `ℤ` by checking against the square root. -/
instance : DecidablePred (IsSquare : ℤ → Prop) :=
fun m => decidable_of_iff' (sqrt m * sqrt m = m) <| by
- simp_rw [←exists_mul_self m, IsSquare, eq_comm]
+ simp_rw [← exists_mul_self m, IsSquare, eq_comm]
end Int
IsSquare
(#7935)
@@ -37,4 +37,9 @@ theorem sqrt_nonneg (n : ℤ) : 0 ≤ sqrt n :=
coe_nat_nonneg _
#align int.sqrt_nonneg Int.sqrt_nonneg
+/-- `IsSquare` can be decided on `ℤ` by checking against the square root. -/
+instance : DecidablePred (IsSquare : ℤ → Prop) :=
+ fun m => decidable_of_iff' (sqrt m * sqrt m = m) <| by
+ simp_rw [←exists_mul_self m, IsSquare, eq_comm]
+
end Int
@@ -2,14 +2,11 @@
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-
-! This file was ported from Lean 3 source module data.int.sqrt
-! leanprover-community/mathlib commit ba2245edf0c8bb155f1569fd9b9492a9b384cde6
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Data.Nat.Sqrt
+#align_import data.int.sqrt from "leanprover-community/mathlib"@"ba2245edf0c8bb155f1569fd9b9492a9b384cde6"
+
/-!
# Square root of integers
The unported dependencies are