Changes since the initial port

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.

Changes in mathlib3

10b4e499

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

cb3ceec8

bump to nightly-2024-03-17-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

22f01ce4

Diff

@@ -148,7 +148,7 @@ theorem exists_odd_minimal {a b c : ℤ} (h : Fermat42 a b c) :
     · exfalso
       have h1 : 2 ∣ (Int.gcd a0 b0 : ℤ) :=
         Int.dvd_gcd (Int.dvd_of_emod_eq_zero hap) (Int.dvd_of_emod_eq_zero hbp)
-      rw [int.gcd_eq_one_iff_coprime.mpr (coprime_of_minimal hf)] at h1 ; revert h1; norm_num
+      rw [int.gcd_eq_one_iff_coprime.mpr (coprime_of_minimal hf)] at h1; revert h1; norm_num
     · exact ⟨b0, ⟨a0, ⟨c0, minimal_comm hf, hbp⟩⟩⟩
   exact ⟨a0, ⟨b0, ⟨c0, hf, hap⟩⟩⟩
 #align fermat_42.exists_odd_minimal Fermat42.exists_odd_minimal
@@ -258,17 +258,17 @@ theorem not_minimal {a b c : ℤ} (h : Minimal a b c) (ha2 : a % 2 = 1) (hc : 0
   have hi' : ¬m = -i ^ 2 := by
     by_contra h1
     have hit : -i ^ 2 ≤ 0; apply neg_nonpos.mpr (sq_nonneg i)
-    rw [← h1] at hit 
+    rw [← h1] at hit
     apply absurd h4 (not_lt.mpr hit)
   replace hi : m = i ^ 2; · apply Or.resolve_right hi hi'
-  rw [mul_comm] at hs 
-  rw [Int.gcd_comm] at hcp 
+  rw [mul_comm] at hs
+  rw [Int.gcd_comm] at hcp
   -- obtain d such that r * s = d ^ 2
   obtain ⟨d, hd⟩ := Int.sq_of_gcd_eq_one hcp hs.symm
   -- (b / 2) ^ 2 and m are positive so r * s is positive
   have hd' : ¬r * s = -d ^ 2 := by
     by_contra h1
-    rw [h1] at hs 
+    rw [h1] at hs
     have h2 : b' ^ 2 ≤ 0 := by
       rw [hs, (by ring : -d ^ 2 * m = -(d ^ 2 * m))]
       exact neg_nonpos.mpr ((mul_nonneg_iff_of_pos_right h4).mpr (sq_nonneg d))
@@ -278,20 +278,20 @@ theorem not_minimal {a b c : ℤ} (h : Minimal a b c) (ha2 : a % 2 = 1) (hc : 0
   -- r = +/- j ^ 2
   obtain ⟨j, hj⟩ := Int.sq_of_gcd_eq_one htt4 hd
   have hj0 : j ≠ 0 := by
-    intro h0; rw [h0, zero_pow zero_lt_two, neg_zero, or_self_iff] at hj 
+    intro h0; rw [h0, zero_pow zero_lt_two, neg_zero, or_self_iff] at hj
     apply left_ne_zero_of_mul hrsz hj
-  rw [mul_comm] at hd 
-  rw [Int.gcd_comm] at htt4 
+  rw [mul_comm] at hd
+  rw [Int.gcd_comm] at htt4
   -- s = +/- k ^ 2
   obtain ⟨k, hk⟩ := Int.sq_of_gcd_eq_one htt4 hd
   have hk0 : k ≠ 0 := by
-    intro h0; rw [h0, zero_pow zero_lt_two, neg_zero, or_self_iff] at hk 
+    intro h0; rw [h0, zero_pow zero_lt_two, neg_zero, or_self_iff] at hk
     apply right_ne_zero_of_mul hrsz hk
   have hj2 : r ^ 2 = j ^ 4 := by cases' hj with hjp hjp <;> · rw [hjp]; ring
   have hk2 : s ^ 2 = k ^ 4 := by cases' hk with hkp hkp <;> · rw [hkp]; ring
   -- from m = r ^ 2 + s ^ 2 we now get a new solution to a ^ 4 + b ^ 4 = c ^ 2:
   have hh : i ^ 2 = j ^ 4 + k ^ 4 := by rw [← hi, htt3, hj2, hk2]
-  have hn : n ≠ 0 := by rw [ht2] at hb20 ; apply right_ne_zero_of_mul hb20
+  have hn : n ≠ 0 := by rw [ht2] at hb20; apply right_ne_zero_of_mul hb20
   -- and it has a smaller c: from c = m ^ 2 + n ^ 2 we see that m is smaller than c, and i ^ 2 = m.
   have hic : Int.natAbs i < Int.natAbs c :=
     by

cb3ceec8

bump to nightly-2023-12-28-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

c30f5587

Diff

@@ -271,7 +271,7 @@ theorem not_minimal {a b c : ℤ} (h : Minimal a b c) (ha2 : a % 2 = 1) (hc : 0
     rw [h1] at hs 
     have h2 : b' ^ 2 ≤ 0 := by
       rw [hs, (by ring : -d ^ 2 * m = -(d ^ 2 * m))]
-      exact neg_nonpos.mpr ((zero_le_mul_right h4).mpr (sq_nonneg d))
+      exact neg_nonpos.mpr ((mul_nonneg_iff_of_pos_right h4).mpr (sq_nonneg d))
     have h2' : 0 ≤ b' ^ 2 := by apply sq_nonneg b'
     exact absurd (lt_of_le_of_ne h2' (Ne.symm (pow_ne_zero _ h2b0))) (not_lt.mpr h2)
   replace hd : r * s = d ^ 2; · apply Or.resolve_right hd hd'

cb3ceec8

bump to nightly-2023-11-06-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

f9f7c90b

Diff

@@ -111,7 +111,7 @@ theorem coprime_of_minimal {a b c : ℤ} (h : Minimal a b c) : IsCoprime a b :=
   obtain ⟨c1, rfl⟩ := hpc
   have hf : Fermat42 a1 b1 c1 :=
     (Fermat42.mul (int.coe_nat_ne_zero.mpr (Nat.Prime.ne_zero hp))).mpr h.1
-  apply Nat.le_lt_antisymm (h.2 _ _ _ hf)
+  apply Nat.le_lt_asymm (h.2 _ _ _ hf)
   rw [Int.natAbs_mul, lt_mul_iff_one_lt_left, Int.natAbs_pow, Int.natAbs_ofNat]
   · exact Nat.one_lt_pow _ _ zero_lt_two (Nat.Prime.one_lt hp)
   · exact Nat.pos_of_ne_zero (Int.natAbs_ne_zero_of_ne_zero (NeZero hf))

cb3ceec8

bump to nightly-2023-09-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

5655435f

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2020 Paul van Wamelen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul van Wamelen
 -/
-import Mathbin.NumberTheory.PythagoreanTriples
-import Mathbin.RingTheory.Coprime.Lemmas
-import Mathbin.Tactic.LinearCombination
+import NumberTheory.PythagoreanTriples
+import RingTheory.Coprime.Lemmas
+import Tactic.LinearCombination
 
 #align_import number_theory.fermat4 from "leanprover-community/mathlib"@"cb3ceec8485239a61ed51d944cb9a95b68c6bafc"

cb3ceec8

bump to nightly-2023-09-14-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/001ffdc42920050657fd45bd2b8bfbec8eaaeb29

4e7aae4f

Diff

@@ -320,12 +320,12 @@ theorem not_fermat_42 {a b c : ℤ} (ha : a ≠ 0) (hb : b ≠ 0) : a ^ 4 + b ^
 #align not_fermat_42 not_fermat_42
 -/
 
-#print not_fermat_4 /-
-theorem not_fermat_4 {a b c : ℤ} (ha : a ≠ 0) (hb : b ≠ 0) : a ^ 4 + b ^ 4 ≠ c ^ 4 :=
+#print fermatLastTheoremFour /-
+theorem fermatLastTheoremFour {a b c : ℤ} (ha : a ≠ 0) (hb : b ≠ 0) : a ^ 4 + b ^ 4 ≠ c ^ 4 :=
   by
   intro heq
   apply @not_fermat_42 _ _ (c ^ 2) ha hb
   rw [HEq]; ring
-#align not_fermat_4 not_fermat_4
+#align not_fermat_4 fermatLastTheoremFour
 -/

cb3ceec8

bump to nightly-2023-08-02-01

mathlib commit https://github.com/leanprover-community/mathlib/commit/63721b2c3eba6c325ecf8ae8cca27155a4f6306f

7aca3f15

Diff

@@ -83,7 +83,7 @@ theorem exists_minimal {a b c : ℤ} (h : Fermat42 a b c) : ∃ a0 b0 c0, Minima
   have S_nonempty : S.nonempty := by
     use Int.natAbs c
     rw [Set.mem_setOf_eq]
-    use ⟨a, ⟨b, c⟩⟩; tauto
+    use⟨a, ⟨b, c⟩⟩; tauto
   let m : ℕ := Nat.find S_nonempty
   have m_mem : m ∈ S := Nat.find_spec S_nonempty
   rcases m_mem with ⟨s0, hs0, hs1⟩
@@ -91,7 +91,7 @@ theorem exists_minimal {a b c : ℤ} (h : Fermat42 a b c) : ∃ a0 b0 c0, Minima
   intro a1 b1 c1 h1
   rw [← hs1]
   apply Nat.find_min'
-  use ⟨a1, ⟨b1, c1⟩⟩; tauto
+  use⟨a1, ⟨b1, c1⟩⟩; tauto
 #align fermat_42.exists_minimal Fermat42.exists_minimal
 -/

cb3ceec8

bump to nightly-2023-07-20-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

9c56d0dd

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Paul van Wamelen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul van Wamelen
-
-! This file was ported from Lean 3 source module number_theory.fermat4
-! leanprover-community/mathlib commit cb3ceec8485239a61ed51d944cb9a95b68c6bafc
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.NumberTheory.PythagoreanTriples
 import Mathbin.RingTheory.Coprime.Lemmas
 import Mathbin.Tactic.LinearCombination
 
+#align_import number_theory.fermat4 from "leanprover-community/mathlib"@"cb3ceec8485239a61ed51d944cb9a95b68c6bafc"
+
 /-!
 # Fermat's Last Theorem for the case n = 4

cb3ceec8

bump to nightly-2023-06-13-21

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

829520ac

Diff

@@ -42,6 +42,7 @@ theorem comm {a b c : ℤ} : Fermat42 a b c ↔ Fermat42 b a c := by delta Ferma
 #align fermat_42.comm Fermat42.comm
 -/
 
+#print Fermat42.mul /-
 theorem mul {a b c k : ℤ} (hk0 : k ≠ 0) : Fermat42 a b c ↔ Fermat42 (k * a) (k * b) (k ^ 2 * c) :=
   by
   delta Fermat42
@@ -57,6 +58,7 @@ theorem mul {a b c k : ℤ} (hk0 : k ≠ 0) : Fermat42 a b c ↔ Fermat42 (k * a
     apply (mul_right_inj' (pow_ne_zero 4 hk0)).mp
     linear_combination f42.2.2
 #align fermat_42.mul Fermat42.mul
+-/
 
 #print Fermat42.ne_zero /-
 theorem ne_zero {a b c : ℤ} (h : Fermat42 a b c) : c ≠ 0 :=
@@ -96,6 +98,7 @@ theorem exists_minimal {a b c : ℤ} (h : Fermat42 a b c) : ∃ a0 b0 c0, Minima
 #align fermat_42.exists_minimal Fermat42.exists_minimal
 -/
 
+#print Fermat42.coprime_of_minimal /-
 /-- a minimal solution to `a ^ 4 + b ^ 4 = c ^ 2` must have `a` and `b` coprime. -/
 theorem coprime_of_minimal {a b c : ℤ} (h : Minimal a b c) : IsCoprime a b :=
   by
@@ -116,6 +119,7 @@ theorem coprime_of_minimal {a b c : ℤ} (h : Minimal a b c) : IsCoprime a b :=
   · exact Nat.one_lt_pow _ _ zero_lt_two (Nat.Prime.one_lt hp)
   · exact Nat.pos_of_ne_zero (Int.natAbs_ne_zero_of_ne_zero (NeZero hf))
 #align fermat_42.coprime_of_minimal Fermat42.coprime_of_minimal
+-/
 
 #print Fermat42.minimal_comm /-
 /-- We can swap `a` and `b` in a minimal solution to `a ^ 4 + b ^ 4 = c ^ 2`. -/
@@ -170,17 +174,21 @@ theorem exists_pos_odd_minimal {a b c : ℤ} (h : Fermat42 a b c) :
 
 end Fermat42
 
+#print Int.coprime_of_sq_sum /-
 theorem Int.coprime_of_sq_sum {r s : ℤ} (h2 : IsCoprime s r) : IsCoprime (r ^ 2 + s ^ 2) r :=
   by
   rw [sq, sq]
   exact (IsCoprime.mul_left h2 h2).mul_add_left_left r
 #align int.coprime_of_sq_sum Int.coprime_of_sq_sum
+-/
 
+#print Int.coprime_of_sq_sum' /-
 theorem Int.coprime_of_sq_sum' {r s : ℤ} (h : IsCoprime r s) : IsCoprime (r ^ 2 + s ^ 2) (r * s) :=
   by
   apply IsCoprime.mul_right (Int.coprime_of_sq_sum (is_coprime_comm.mp h))
   rw [add_comm]; apply Int.coprime_of_sq_sum h
 #align int.coprime_of_sq_sum' Int.coprime_of_sq_sum'
+-/
 
 namespace Fermat42
 
@@ -305,6 +313,7 @@ theorem not_minimal {a b c : ℤ} (h : Minimal a b c) (ha2 : a % 2 = 1) (hc : 0
 
 end Fermat42
 
+#print not_fermat_42 /-
 theorem not_fermat_42 {a b c : ℤ} (ha : a ≠ 0) (hb : b ≠ 0) : a ^ 4 + b ^ 4 ≠ c ^ 2 :=
   by
   intro h
@@ -312,11 +321,14 @@ theorem not_fermat_42 {a b c : ℤ} (ha : a ≠ 0) (hb : b ≠ 0) : a ^ 4 + b ^
     Fermat42.exists_pos_odd_minimal (And.intro ha (And.intro hb h))
   apply Fermat42.not_minimal hf h2 hp
 #align not_fermat_42 not_fermat_42
+-/
 
+#print not_fermat_4 /-
 theorem not_fermat_4 {a b c : ℤ} (ha : a ≠ 0) (hb : b ≠ 0) : a ^ 4 + b ^ 4 ≠ c ^ 4 :=
   by
   intro heq
   apply @not_fermat_42 _ _ (c ^ 2) ha hb
   rw [HEq]; ring
 #align not_fermat_4 not_fermat_4
+-/

cb3ceec8

bump to nightly-2023-06-04-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

3fb4268b

Diff

@@ -80,7 +80,7 @@ def Minimal (a b c : ℤ) : Prop :=
 /-- if we have a solution to `a ^ 4 + b ^ 4 = c ^ 2` then there must be a minimal one. -/
 theorem exists_minimal {a b c : ℤ} (h : Fermat42 a b c) : ∃ a0 b0 c0, Minimal a0 b0 c0 :=
   by
-  let S : Set ℕ := { n | ∃ s : ℤ × ℤ × ℤ, Fermat42 s.1 s.2.1 s.2.2 ∧ n = Int.natAbs s.2.2 }
+  let S : Set ℕ := {n | ∃ s : ℤ × ℤ × ℤ, Fermat42 s.1 s.2.1 s.2.2 ∧ n = Int.natAbs s.2.2}
   have S_nonempty : S.nonempty := by
     use Int.natAbs c
     rw [Set.mem_setOf_eq]

cb3ceec8

bump to nightly-2023-06-01-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

b9c87c70

Diff

@@ -147,7 +147,7 @@ theorem exists_odd_minimal {a b c : ℤ} (h : Fermat42 a b c) :
     · exfalso
       have h1 : 2 ∣ (Int.gcd a0 b0 : ℤ) :=
         Int.dvd_gcd (Int.dvd_of_emod_eq_zero hap) (Int.dvd_of_emod_eq_zero hbp)
-      rw [int.gcd_eq_one_iff_coprime.mpr (coprime_of_minimal hf)] at h1; revert h1; norm_num
+      rw [int.gcd_eq_one_iff_coprime.mpr (coprime_of_minimal hf)] at h1 ; revert h1; norm_num
     · exact ⟨b0, ⟨a0, ⟨c0, minimal_comm hf, hbp⟩⟩⟩
   exact ⟨a0, ⟨b0, ⟨c0, hf, hap⟩⟩⟩
 #align fermat_42.exists_odd_minimal Fermat42.exists_odd_minimal
@@ -253,17 +253,17 @@ theorem not_minimal {a b c : ℤ} (h : Minimal a b c) (ha2 : a % 2 = 1) (hc : 0
   have hi' : ¬m = -i ^ 2 := by
     by_contra h1
     have hit : -i ^ 2 ≤ 0; apply neg_nonpos.mpr (sq_nonneg i)
-    rw [← h1] at hit
+    rw [← h1] at hit 
     apply absurd h4 (not_lt.mpr hit)
   replace hi : m = i ^ 2; · apply Or.resolve_right hi hi'
-  rw [mul_comm] at hs
-  rw [Int.gcd_comm] at hcp
+  rw [mul_comm] at hs 
+  rw [Int.gcd_comm] at hcp 
   -- obtain d such that r * s = d ^ 2
   obtain ⟨d, hd⟩ := Int.sq_of_gcd_eq_one hcp hs.symm
   -- (b / 2) ^ 2 and m are positive so r * s is positive
   have hd' : ¬r * s = -d ^ 2 := by
     by_contra h1
-    rw [h1] at hs
+    rw [h1] at hs 
     have h2 : b' ^ 2 ≤ 0 := by
       rw [hs, (by ring : -d ^ 2 * m = -(d ^ 2 * m))]
       exact neg_nonpos.mpr ((zero_le_mul_right h4).mpr (sq_nonneg d))
@@ -273,20 +273,20 @@ theorem not_minimal {a b c : ℤ} (h : Minimal a b c) (ha2 : a % 2 = 1) (hc : 0
   -- r = +/- j ^ 2
   obtain ⟨j, hj⟩ := Int.sq_of_gcd_eq_one htt4 hd
   have hj0 : j ≠ 0 := by
-    intro h0; rw [h0, zero_pow zero_lt_two, neg_zero, or_self_iff] at hj
+    intro h0; rw [h0, zero_pow zero_lt_two, neg_zero, or_self_iff] at hj 
     apply left_ne_zero_of_mul hrsz hj
-  rw [mul_comm] at hd
-  rw [Int.gcd_comm] at htt4
+  rw [mul_comm] at hd 
+  rw [Int.gcd_comm] at htt4 
   -- s = +/- k ^ 2
   obtain ⟨k, hk⟩ := Int.sq_of_gcd_eq_one htt4 hd
   have hk0 : k ≠ 0 := by
-    intro h0; rw [h0, zero_pow zero_lt_two, neg_zero, or_self_iff] at hk
+    intro h0; rw [h0, zero_pow zero_lt_two, neg_zero, or_self_iff] at hk 
     apply right_ne_zero_of_mul hrsz hk
   have hj2 : r ^ 2 = j ^ 4 := by cases' hj with hjp hjp <;> · rw [hjp]; ring
   have hk2 : s ^ 2 = k ^ 4 := by cases' hk with hkp hkp <;> · rw [hkp]; ring
   -- from m = r ^ 2 + s ^ 2 we now get a new solution to a ^ 4 + b ^ 4 = c ^ 2:
   have hh : i ^ 2 = j ^ 4 + k ^ 4 := by rw [← hi, htt3, hj2, hk2]
-  have hn : n ≠ 0 := by rw [ht2] at hb20; apply right_ne_zero_of_mul hb20
+  have hn : n ≠ 0 := by rw [ht2] at hb20 ; apply right_ne_zero_of_mul hb20
   -- and it has a smaller c: from c = m ^ 2 + n ^ 2 we see that m is smaller than c, and i ^ 2 = m.
   have hic : Int.natAbs i < Int.natAbs c :=
     by

cb3ceec8

bump to nightly-2023-05-28-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

8d353152

Diff

@@ -23,7 +23,7 @@ There are no non-zero integers `a`, `b` and `c` such that `a ^ 4 + b ^ 4 = c ^ 4
 
 noncomputable section
 
-open Classical
+open scoped Classical
 
 #print Fermat42 /-
 /-- Shorthand for three non-zero integers `a`, `b`, and `c` satisfying `a ^ 4 + b ^ 4 = c ^ 2`.

cb3ceec8

bump to nightly-2023-05-28-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

ba5d8b97

Diff

@@ -42,12 +42,6 @@ theorem comm {a b c : ℤ} : Fermat42 a b c ↔ Fermat42 b a c := by delta Ferma
 #align fermat_42.comm Fermat42.comm
 -/
 
-/- warning: fermat_42.mul -> Fermat42.mul is a dubious translation:
-lean 3 declaration is
-  forall {a : Int} {b : Int} {c : Int} {k : Int}, (Ne.{1} Int k (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))) -> (Iff (Fermat42 a b c) (Fermat42 (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) k a) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) k b) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) k (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) c)))
-but is expected to have type
-  forall {a : Int} {b : Int} {c : Int} {k : Int}, (Ne.{1} Int k (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))) -> (Iff (Fermat42 a b c) (Fermat42 (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) k a) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) k b) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) k (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) c)))
-Case conversion may be inaccurate. Consider using '#align fermat_42.mul Fermat42.mulₓ'. -/
 theorem mul {a b c k : ℤ} (hk0 : k ≠ 0) : Fermat42 a b c ↔ Fermat42 (k * a) (k * b) (k ^ 2 * c) :=
   by
   delta Fermat42
@@ -102,12 +96,6 @@ theorem exists_minimal {a b c : ℤ} (h : Fermat42 a b c) : ∃ a0 b0 c0, Minima
 #align fermat_42.exists_minimal Fermat42.exists_minimal
 -/
 
-/- warning: fermat_42.coprime_of_minimal -> Fermat42.coprime_of_minimal is a dubious translation:
-lean 3 declaration is
-  forall {a : Int} {b : Int} {c : Int}, (Fermat42.Minimal a b c) -> (IsCoprime.{0} Int Int.commSemiring a b)
-but is expected to have type
-  forall {a : Int} {b : Int} {c : Int}, (Fermat42.Minimal a b c) -> (IsCoprime.{0} Int Int.instCommSemiringInt a b)
-Case conversion may be inaccurate. Consider using '#align fermat_42.coprime_of_minimal Fermat42.coprime_of_minimalₓ'. -/
 /-- a minimal solution to `a ^ 4 + b ^ 4 = c ^ 2` must have `a` and `b` coprime. -/
 theorem coprime_of_minimal {a b c : ℤ} (h : Minimal a b c) : IsCoprime a b :=
   by
@@ -182,24 +170,12 @@ theorem exists_pos_odd_minimal {a b c : ℤ} (h : Fermat42 a b c) :
 
 end Fermat42
 
-/- warning: int.coprime_of_sq_sum -> Int.coprime_of_sq_sum is a dubious translation:
-lean 3 declaration is
-  forall {r : Int} {s : Int}, (IsCoprime.{0} Int Int.commSemiring s r) -> (IsCoprime.{0} Int Int.commSemiring (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) r (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) s (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) r)
-but is expected to have type
-  forall {r : Int} {s : Int}, (IsCoprime.{0} Int Int.instCommSemiringInt s r) -> (IsCoprime.{0} Int Int.instCommSemiringInt (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) r (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) s (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) r)
-Case conversion may be inaccurate. Consider using '#align int.coprime_of_sq_sum Int.coprime_of_sq_sumₓ'. -/
 theorem Int.coprime_of_sq_sum {r s : ℤ} (h2 : IsCoprime s r) : IsCoprime (r ^ 2 + s ^ 2) r :=
   by
   rw [sq, sq]
   exact (IsCoprime.mul_left h2 h2).mul_add_left_left r
 #align int.coprime_of_sq_sum Int.coprime_of_sq_sum
 
-/- warning: int.coprime_of_sq_sum' -> Int.coprime_of_sq_sum' is a dubious translation:
-lean 3 declaration is
-  forall {r : Int} {s : Int}, (IsCoprime.{0} Int Int.commSemiring r s) -> (IsCoprime.{0} Int Int.commSemiring (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) r (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) s (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) r s))
-but is expected to have type
-  forall {r : Int} {s : Int}, (IsCoprime.{0} Int Int.instCommSemiringInt r s) -> (IsCoprime.{0} Int Int.instCommSemiringInt (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) r (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) s (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) r s))
-Case conversion may be inaccurate. Consider using '#align int.coprime_of_sq_sum' Int.coprime_of_sq_sum'ₓ'. -/
 theorem Int.coprime_of_sq_sum' {r s : ℤ} (h : IsCoprime r s) : IsCoprime (r ^ 2 + s ^ 2) (r * s) :=
   by
   apply IsCoprime.mul_right (Int.coprime_of_sq_sum (is_coprime_comm.mp h))
@@ -329,12 +305,6 @@ theorem not_minimal {a b c : ℤ} (h : Minimal a b c) (ha2 : a % 2 = 1) (hc : 0
 
 end Fermat42
 
-/- warning: not_fermat_42 -> not_fermat_42 is a dubious translation:
-lean 3 declaration is
-  forall {a : Int} {b : Int} {c : Int}, (Ne.{1} Int a (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))) -> (Ne.{1} Int b (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))) -> (Ne.{1} Int (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) a (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) b (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) c (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))
-but is expected to have type
-  forall {a : Int} {b : Int} {c : Int}, (Ne.{1} Int a (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))) -> (Ne.{1} Int b (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))) -> (Ne.{1} Int (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) a (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) b (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) c (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))
-Case conversion may be inaccurate. Consider using '#align not_fermat_42 not_fermat_42ₓ'. -/
 theorem not_fermat_42 {a b c : ℤ} (ha : a ≠ 0) (hb : b ≠ 0) : a ^ 4 + b ^ 4 ≠ c ^ 2 :=
   by
   intro h
@@ -343,12 +313,6 @@ theorem not_fermat_42 {a b c : ℤ} (ha : a ≠ 0) (hb : b ≠ 0) : a ^ 4 + b ^
   apply Fermat42.not_minimal hf h2 hp
 #align not_fermat_42 not_fermat_42
 
-/- warning: not_fermat_4 -> not_fermat_4 is a dubious translation:
-lean 3 declaration is
-  forall {a : Int} {b : Int} {c : Int}, (Ne.{1} Int a (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))) -> (Ne.{1} Int b (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))) -> (Ne.{1} Int (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) a (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) b (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) c (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))
-but is expected to have type
-  forall {a : Int} {b : Int} {c : Int}, (Ne.{1} Int a (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))) -> (Ne.{1} Int b (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))) -> (Ne.{1} Int (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) a (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) b (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) c (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))))
-Case conversion may be inaccurate. Consider using '#align not_fermat_4 not_fermat_4ₓ'. -/
 theorem not_fermat_4 {a b c : ℤ} (ha : a ≠ 0) (hb : b ≠ 0) : a ^ 4 + b ^ 4 ≠ c ^ 4 :=
   by
   intro heq

cb3ceec8

bump to nightly-2023-05-28-04

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

6797a637

Diff

@@ -37,10 +37,7 @@ def Fermat42 (a b c : ℤ) : Prop :=
 namespace Fermat42
 
 #print Fermat42.comm /-
-theorem comm {a b c : ℤ} : Fermat42 a b c ↔ Fermat42 b a c :=
-  by
-  delta Fermat42
-  rw [add_comm]
+theorem comm {a b c : ℤ} : Fermat42 a b c ↔ Fermat42 b a c := by delta Fermat42; rw [add_comm];
   tauto
 #align fermat_42.comm Fermat42.comm
 -/
@@ -56,17 +53,13 @@ theorem mul {a b c k : ℤ} (hk0 : k ≠ 0) : Fermat42 a b c ↔ Fermat42 (k * a
   delta Fermat42
   constructor
   · intro f42
-    constructor
-    · exact mul_ne_zero hk0 f42.1
-    constructor
-    · exact mul_ne_zero hk0 f42.2.1
+    constructor; · exact mul_ne_zero hk0 f42.1
+    constructor; · exact mul_ne_zero hk0 f42.2.1
     · have H : a ^ 4 + b ^ 4 = c ^ 2 := f42.2.2
       linear_combination k ^ 4 * H
   · intro f42
-    constructor
-    · exact right_ne_zero_of_mul f42.1
-    constructor
-    · exact right_ne_zero_of_mul f42.2.1
+    constructor; · exact right_ne_zero_of_mul f42.1
+    constructor; · exact right_ne_zero_of_mul f42.2.1
     apply (mul_right_inj' (pow_ne_zero 4 hk0)).mp
     linear_combination f42.2.2
 #align fermat_42.mul Fermat42.mul
@@ -97,8 +90,7 @@ theorem exists_minimal {a b c : ℤ} (h : Fermat42 a b c) : ∃ a0 b0 c0, Minima
   have S_nonempty : S.nonempty := by
     use Int.natAbs c
     rw [Set.mem_setOf_eq]
-    use ⟨a, ⟨b, c⟩⟩
-    tauto
+    use ⟨a, ⟨b, c⟩⟩; tauto
   let m : ℕ := Nat.find S_nonempty
   have m_mem : m ∈ S := Nat.find_spec S_nonempty
   rcases m_mem with ⟨s0, hs0, hs1⟩
@@ -106,8 +98,7 @@ theorem exists_minimal {a b c : ℤ} (h : Fermat42 a b c) : ∃ a0 b0 c0, Minima
   intro a1 b1 c1 h1
   rw [← hs1]
   apply Nat.find_min'
-  use ⟨a1, ⟨b1, c1⟩⟩
-  tauto
+  use ⟨a1, ⟨b1, c1⟩⟩; tauto
 #align fermat_42.exists_minimal Fermat42.exists_minimal
 -/
 
@@ -128,8 +119,7 @@ theorem coprime_of_minimal {a b c : ℤ} (h : Minimal a b c) : IsCoprime a b :=
   have hpc : (p : ℤ) ^ 2 ∣ c :=
     by
     rw [← Int.pow_dvd_pow_iff zero_lt_two, ← h.1.2.2]
-    apply Dvd.intro (a1 ^ 4 + b1 ^ 4)
-    ring
+    apply Dvd.intro (a1 ^ 4 + b1 ^ 4); ring
   obtain ⟨c1, rfl⟩ := hpc
   have hf : Fermat42 a1 b1 c1 :=
     (Fermat42.mul (int.coe_nat_ne_zero.mpr (Nat.Prime.ne_zero hp))).mpr h.1
@@ -153,8 +143,7 @@ theorem neg_of_minimal {a b c : ℤ} : Minimal a b c → Minimal a b (-c) :=
   rintro ⟨⟨ha, hb, heq⟩, h2⟩
   constructor
   · apply And.intro ha (And.intro hb _)
-    rw [HEq]
-    exact (neg_sq c).symm
+    rw [HEq]; exact (neg_sq c).symm
   rwa [Int.natAbs_neg c]
 #align fermat_42.neg_of_minimal Fermat42.neg_of_minimal
 -/
@@ -170,9 +159,7 @@ theorem exists_odd_minimal {a b c : ℤ} (h : Fermat42 a b c) :
     · exfalso
       have h1 : 2 ∣ (Int.gcd a0 b0 : ℤ) :=
         Int.dvd_gcd (Int.dvd_of_emod_eq_zero hap) (Int.dvd_of_emod_eq_zero hbp)
-      rw [int.gcd_eq_one_iff_coprime.mpr (coprime_of_minimal hf)] at h1
-      revert h1
-      norm_num
+      rw [int.gcd_eq_one_iff_coprime.mpr (coprime_of_minimal hf)] at h1; revert h1; norm_num
     · exact ⟨b0, ⟨a0, ⟨c0, minimal_comm hf, hbp⟩⟩⟩
   exact ⟨a0, ⟨b0, ⟨c0, hf, hap⟩⟩⟩
 #align fermat_42.exists_odd_minimal Fermat42.exists_odd_minimal
@@ -186,10 +173,8 @@ theorem exists_pos_odd_minimal {a b c : ℤ} (h : Fermat42 a b c) :
   by
   obtain ⟨a0, b0, c0, hf, hc⟩ := exists_odd_minimal h
   rcases lt_trichotomy 0 c0 with (h1 | rfl | h1)
-  · use a0, b0, c0
-    tauto
-  · exfalso
-    exact NeZero hf.1 rfl
+  · use a0, b0, c0; tauto
+  · exfalso; exact NeZero hf.1 rfl
   · use a0, b0, -c0, neg_of_minimal hf, hc
     exact neg_pos.mpr h1
 #align fermat_42.exists_pos_odd_minimal Fermat42.exists_pos_odd_minimal
@@ -239,9 +224,7 @@ theorem not_minimal {a b c : ℤ} (h : Minimal a b c) (ha2 : a % 2 = 1) (hc : 0
   have h2 : Int.gcd (a ^ 2) (b ^ 2) = 1 := int.gcd_eq_one_iff_coprime.mpr (coprime_of_minimal h).pow
   -- in order to reduce the possibilities we get from the classification of pythagorean triples
   -- it helps if we know the parity of a ^ 2 (and the sign of c):
-  have ha22 : a ^ 2 % 2 = 1 := by
-    rw [sq, Int.mul_emod, ha2]
-    norm_num
+  have ha22 : a ^ 2 % 2 = 1 := by rw [sq, Int.mul_emod, ha2]; norm_num
   obtain ⟨m, n, ht1, ht2, ht3, ht4, ht5, ht6⟩ := ht.coprime_classification' h2 ha22 hc
   -- Now a, n, m form a pythagorean triple and so we can obtain r and s such that
   -- a = r ^ 2 - s ^ 2, n = 2 * r * s and m = r ^ 2 + s ^ 2
@@ -262,8 +245,7 @@ theorem not_minimal {a b c : ℤ} (h : Minimal a b c) (ha2 : a % 2 = 1) (hc : 0
     apply lt_of_le_of_ne ht6
     rintro rfl
     revert hb20
-    rw [ht2]
-    simp
+    rw [ht2]; simp
   obtain ⟨r, s, htt1, htt2, htt3, htt4, htt5, htt6⟩ := htt.coprime_classification' h3 ha2 h4
   -- Now use the fact that (b / 2) ^ 2 = m * r * s, and m, r and s are pairwise coprime to obtain
   -- i, j and k such that m = i ^ 2, r = j ^ 2 and s = k ^ 2.
@@ -275,8 +257,7 @@ theorem not_minimal {a b c : ℤ} (h : Minimal a b c) (ha2 : a % 2 = 1) (hc : 0
   -- b is even because b ^ 2 = 2 * m * n.
   have hb2 : 2 ∣ b := by
     apply @Int.Prime.dvd_pow' _ 2 _ Nat.prime_two
-    rw [ht2, mul_assoc]
-    exact dvd_mul_right 2 (m * n)
+    rw [ht2, mul_assoc]; exact dvd_mul_right 2 (m * n)
   cases' hb2 with b' hb2'
   have hs : b' ^ 2 = m * (r * s) :=
     by
@@ -286,25 +267,19 @@ theorem not_minimal {a b c : ℤ} (h : Minimal a b c) (ha2 : a % 2 = 1) (hc : 0
     by
     -- because b ^ 2 is not zero and (b / 2) ^ 2 = m * (r * s)
     by_contra hrsz
-    revert hb20
-    rw [ht2, htt2, mul_assoc, @mul_assoc _ _ _ r s, hrsz]
+    revert hb20; rw [ht2, htt2, mul_assoc, @mul_assoc _ _ _ r s, hrsz]
     simp
   have h2b0 : b' ≠ 0 := by
     apply ne_zero_pow two_ne_zero
-    rw [hs]
-    apply mul_ne_zero
-    · exact ne_of_gt h4
-    · exact hrsz
+    rw [hs]; apply mul_ne_zero; · exact ne_of_gt h4; · exact hrsz
   obtain ⟨i, hi⟩ := Int.sq_of_gcd_eq_one hcp hs.symm
   -- use m is positive to exclude m = - i ^ 2
   have hi' : ¬m = -i ^ 2 := by
     by_contra h1
-    have hit : -i ^ 2 ≤ 0
-    apply neg_nonpos.mpr (sq_nonneg i)
+    have hit : -i ^ 2 ≤ 0; apply neg_nonpos.mpr (sq_nonneg i)
     rw [← h1] at hit
     apply absurd h4 (not_lt.mpr hit)
-  replace hi : m = i ^ 2
-  · apply Or.resolve_right hi hi'
+  replace hi : m = i ^ 2; · apply Or.resolve_right hi hi'
   rw [mul_comm] at hs
   rw [Int.gcd_comm] at hcp
   -- obtain d such that r * s = d ^ 2
@@ -318,40 +293,28 @@ theorem not_minimal {a b c : ℤ} (h : Minimal a b c) (ha2 : a % 2 = 1) (hc : 0
       exact neg_nonpos.mpr ((zero_le_mul_right h4).mpr (sq_nonneg d))
     have h2' : 0 ≤ b' ^ 2 := by apply sq_nonneg b'
     exact absurd (lt_of_le_of_ne h2' (Ne.symm (pow_ne_zero _ h2b0))) (not_lt.mpr h2)
-  replace hd : r * s = d ^ 2
-  · apply Or.resolve_right hd hd'
+  replace hd : r * s = d ^ 2; · apply Or.resolve_right hd hd'
   -- r = +/- j ^ 2
   obtain ⟨j, hj⟩ := Int.sq_of_gcd_eq_one htt4 hd
   have hj0 : j ≠ 0 := by
-    intro h0
-    rw [h0, zero_pow zero_lt_two, neg_zero, or_self_iff] at hj
+    intro h0; rw [h0, zero_pow zero_lt_two, neg_zero, or_self_iff] at hj
     apply left_ne_zero_of_mul hrsz hj
   rw [mul_comm] at hd
   rw [Int.gcd_comm] at htt4
   -- s = +/- k ^ 2
   obtain ⟨k, hk⟩ := Int.sq_of_gcd_eq_one htt4 hd
   have hk0 : k ≠ 0 := by
-    intro h0
-    rw [h0, zero_pow zero_lt_two, neg_zero, or_self_iff] at hk
+    intro h0; rw [h0, zero_pow zero_lt_two, neg_zero, or_self_iff] at hk
     apply right_ne_zero_of_mul hrsz hk
-  have hj2 : r ^ 2 = j ^ 4 := by
-    cases' hj with hjp hjp <;>
-      · rw [hjp]
-        ring
-  have hk2 : s ^ 2 = k ^ 4 := by
-    cases' hk with hkp hkp <;>
-      · rw [hkp]
-        ring
+  have hj2 : r ^ 2 = j ^ 4 := by cases' hj with hjp hjp <;> · rw [hjp]; ring
+  have hk2 : s ^ 2 = k ^ 4 := by cases' hk with hkp hkp <;> · rw [hkp]; ring
   -- from m = r ^ 2 + s ^ 2 we now get a new solution to a ^ 4 + b ^ 4 = c ^ 2:
   have hh : i ^ 2 = j ^ 4 + k ^ 4 := by rw [← hi, htt3, hj2, hk2]
-  have hn : n ≠ 0 := by
-    rw [ht2] at hb20
-    apply right_ne_zero_of_mul hb20
+  have hn : n ≠ 0 := by rw [ht2] at hb20; apply right_ne_zero_of_mul hb20
   -- and it has a smaller c: from c = m ^ 2 + n ^ 2 we see that m is smaller than c, and i ^ 2 = m.
   have hic : Int.natAbs i < Int.natAbs c :=
     by
-    apply int.coe_nat_lt.mp
-    rw [← Int.eq_natAbs_of_zero_le (le_of_lt hc)]
+    apply int.coe_nat_lt.mp; rw [← Int.eq_natAbs_of_zero_le (le_of_lt hc)]
     apply gt_of_gt_of_ge _ (Int.natAbs_le_self_sq i)
     rw [← hi, ht3]
     apply gt_of_gt_of_ge _ (Int.le_self_sq m)

cb3ceec8

bump to nightly-2023-03-26-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/55d771df074d0dd020139ee1cd4b95521422df9f

ca5de00c

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul van Wamelen
 
 ! This file was ported from Lean 3 source module number_theory.fermat4
-! leanprover-community/mathlib commit 10b4e499f43088dd3bb7b5796184ad5216648ab1
+! leanprover-community/mathlib commit cb3ceec8485239a61ed51d944cb9a95b68c6bafc
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Tactic.LinearCombination
 
 /-!
 # Fermat's Last Theorem for the case n = 4
+
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
 There are no non-zero integers `a`, `b` and `c` such that `a ^ 4 + b ^ 4 = c ^ 4`.
 -/

10b4e499

bump to nightly-2023-03-24-14

mathlib commit https://github.com/leanprover-community/mathlib/commit/b19481deb571022990f1baa9cbf9172e6757a479

4fed16d5

Diff

@@ -22,22 +22,32 @@ noncomputable section
 
 open Classical
 
+#print Fermat42 /-
 /-- Shorthand for three non-zero integers `a`, `b`, and `c` satisfying `a ^ 4 + b ^ 4 = c ^ 2`.
 We will show that no integers satisfy this equation. Clearly Fermat's Last theorem for n = 4
 follows. -/
 def Fermat42 (a b c : ℤ) : Prop :=
   a ≠ 0 ∧ b ≠ 0 ∧ a ^ 4 + b ^ 4 = c ^ 2
 #align fermat_42 Fermat42
+-/
 
 namespace Fermat42
 
+#print Fermat42.comm /-
 theorem comm {a b c : ℤ} : Fermat42 a b c ↔ Fermat42 b a c :=
   by
   delta Fermat42
   rw [add_comm]
   tauto
 #align fermat_42.comm Fermat42.comm
+-/
 
+/- warning: fermat_42.mul -> Fermat42.mul is a dubious translation:
+lean 3 declaration is
+  forall {a : Int} {b : Int} {c : Int} {k : Int}, (Ne.{1} Int k (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))) -> (Iff (Fermat42 a b c) (Fermat42 (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) k a) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) k b) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) k (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) c)))
+but is expected to have type
+  forall {a : Int} {b : Int} {c : Int} {k : Int}, (Ne.{1} Int k (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))) -> (Iff (Fermat42 a b c) (Fermat42 (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) k a) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) k b) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) k (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) c)))
+Case conversion may be inaccurate. Consider using '#align fermat_42.mul Fermat42.mulₓ'. -/
 theorem mul {a b c k : ℤ} (hk0 : k ≠ 0) : Fermat42 a b c ↔ Fermat42 (k * a) (k * b) (k ^ 2 * c) :=
   by
   delta Fermat42
@@ -58,6 +68,7 @@ theorem mul {a b c k : ℤ} (hk0 : k ≠ 0) : Fermat42 a b c ↔ Fermat42 (k * a
     linear_combination f42.2.2
 #align fermat_42.mul Fermat42.mul
 
+#print Fermat42.ne_zero /-
 theorem ne_zero {a b c : ℤ} (h : Fermat42 a b c) : c ≠ 0 :=
   by
   apply ne_zero_pow two_ne_zero _; apply ne_of_gt
@@ -65,13 +76,17 @@ theorem ne_zero {a b c : ℤ} (h : Fermat42 a b c) : c ≠ 0 :=
   exact
     add_pos (sq_pos_of_ne_zero _ (pow_ne_zero 2 h.1)) (sq_pos_of_ne_zero _ (pow_ne_zero 2 h.2.1))
 #align fermat_42.ne_zero Fermat42.ne_zero
+-/
 
+#print Fermat42.Minimal /-
 /-- We say a solution to `a ^ 4 + b ^ 4 = c ^ 2` is minimal if there is no other solution with
 a smaller `c` (in absolute value). -/
 def Minimal (a b c : ℤ) : Prop :=
   Fermat42 a b c ∧ ∀ a1 b1 c1 : ℤ, Fermat42 a1 b1 c1 → Int.natAbs c ≤ Int.natAbs c1
 #align fermat_42.minimal Fermat42.Minimal
+-/
 
+#print Fermat42.exists_minimal /-
 /-- if we have a solution to `a ^ 4 + b ^ 4 = c ^ 2` then there must be a minimal one. -/
 theorem exists_minimal {a b c : ℤ} (h : Fermat42 a b c) : ∃ a0 b0 c0, Minimal a0 b0 c0 :=
   by
@@ -91,7 +106,14 @@ theorem exists_minimal {a b c : ℤ} (h : Fermat42 a b c) : ∃ a0 b0 c0, Minima
   use ⟨a1, ⟨b1, c1⟩⟩
   tauto
 #align fermat_42.exists_minimal Fermat42.exists_minimal
+-/
 
+/- warning: fermat_42.coprime_of_minimal -> Fermat42.coprime_of_minimal is a dubious translation:
+lean 3 declaration is
+  forall {a : Int} {b : Int} {c : Int}, (Fermat42.Minimal a b c) -> (IsCoprime.{0} Int Int.commSemiring a b)
+but is expected to have type
+  forall {a : Int} {b : Int} {c : Int}, (Fermat42.Minimal a b c) -> (IsCoprime.{0} Int Int.instCommSemiringInt a b)
+Case conversion may be inaccurate. Consider using '#align fermat_42.coprime_of_minimal Fermat42.coprime_of_minimalₓ'. -/
 /-- a minimal solution to `a ^ 4 + b ^ 4 = c ^ 2` must have `a` and `b` coprime. -/
 theorem coprime_of_minimal {a b c : ℤ} (h : Minimal a b c) : IsCoprime a b :=
   by
@@ -114,11 +136,14 @@ theorem coprime_of_minimal {a b c : ℤ} (h : Minimal a b c) : IsCoprime a b :=
   · exact Nat.pos_of_ne_zero (Int.natAbs_ne_zero_of_ne_zero (NeZero hf))
 #align fermat_42.coprime_of_minimal Fermat42.coprime_of_minimal
 
+#print Fermat42.minimal_comm /-
 /-- We can swap `a` and `b` in a minimal solution to `a ^ 4 + b ^ 4 = c ^ 2`. -/
 theorem minimal_comm {a b c : ℤ} : Minimal a b c → Minimal b a c := fun ⟨h1, h2⟩ =>
   ⟨Fermat42.comm.mp h1, h2⟩
 #align fermat_42.minimal_comm Fermat42.minimal_comm
+-/
 
+#print Fermat42.neg_of_minimal /-
 /-- We can assume that a minimal solution to `a ^ 4 + b ^ 4 = c ^ 2` has positive `c`. -/
 theorem neg_of_minimal {a b c : ℤ} : Minimal a b c → Minimal a b (-c) :=
   by
@@ -129,7 +154,9 @@ theorem neg_of_minimal {a b c : ℤ} : Minimal a b c → Minimal a b (-c) :=
     exact (neg_sq c).symm
   rwa [Int.natAbs_neg c]
 #align fermat_42.neg_of_minimal Fermat42.neg_of_minimal
+-/
 
+#print Fermat42.exists_odd_minimal /-
 /-- We can assume that a minimal solution to `a ^ 4 + b ^ 4 = c ^ 2` has `a` odd. -/
 theorem exists_odd_minimal {a b c : ℤ} (h : Fermat42 a b c) :
     ∃ a0 b0 c0, Minimal a0 b0 c0 ∧ a0 % 2 = 1 :=
@@ -146,7 +173,9 @@ theorem exists_odd_minimal {a b c : ℤ} (h : Fermat42 a b c) :
     · exact ⟨b0, ⟨a0, ⟨c0, minimal_comm hf, hbp⟩⟩⟩
   exact ⟨a0, ⟨b0, ⟨c0, hf, hap⟩⟩⟩
 #align fermat_42.exists_odd_minimal Fermat42.exists_odd_minimal
+-/
 
+#print Fermat42.exists_pos_odd_minimal /-
 /-- We can assume that a minimal solution to `a ^ 4 + b ^ 4 = c ^ 2` has
 `a` odd and `c` positive. -/
 theorem exists_pos_odd_minimal {a b c : ℤ} (h : Fermat42 a b c) :
@@ -161,15 +190,28 @@ theorem exists_pos_odd_minimal {a b c : ℤ} (h : Fermat42 a b c) :
   · use a0, b0, -c0, neg_of_minimal hf, hc
     exact neg_pos.mpr h1
 #align fermat_42.exists_pos_odd_minimal Fermat42.exists_pos_odd_minimal
+-/
 
 end Fermat42
 
+/- warning: int.coprime_of_sq_sum -> Int.coprime_of_sq_sum is a dubious translation:
+lean 3 declaration is
+  forall {r : Int} {s : Int}, (IsCoprime.{0} Int Int.commSemiring s r) -> (IsCoprime.{0} Int Int.commSemiring (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) r (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) s (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) r)
+but is expected to have type
+  forall {r : Int} {s : Int}, (IsCoprime.{0} Int Int.instCommSemiringInt s r) -> (IsCoprime.{0} Int Int.instCommSemiringInt (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) r (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) s (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) r)
+Case conversion may be inaccurate. Consider using '#align int.coprime_of_sq_sum Int.coprime_of_sq_sumₓ'. -/
 theorem Int.coprime_of_sq_sum {r s : ℤ} (h2 : IsCoprime s r) : IsCoprime (r ^ 2 + s ^ 2) r :=
   by
   rw [sq, sq]
   exact (IsCoprime.mul_left h2 h2).mul_add_left_left r
 #align int.coprime_of_sq_sum Int.coprime_of_sq_sum
 
+/- warning: int.coprime_of_sq_sum' -> Int.coprime_of_sq_sum' is a dubious translation:
+lean 3 declaration is
+  forall {r : Int} {s : Int}, (IsCoprime.{0} Int Int.commSemiring r s) -> (IsCoprime.{0} Int Int.commSemiring (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) r (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) s (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) r s))
+but is expected to have type
+  forall {r : Int} {s : Int}, (IsCoprime.{0} Int Int.instCommSemiringInt r s) -> (IsCoprime.{0} Int Int.instCommSemiringInt (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) r (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) s (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) r s))
+Case conversion may be inaccurate. Consider using '#align int.coprime_of_sq_sum' Int.coprime_of_sq_sum'ₓ'. -/
 theorem Int.coprime_of_sq_sum' {r s : ℤ} (h : IsCoprime r s) : IsCoprime (r ^ 2 + s ^ 2) (r * s) :=
   by
   apply IsCoprime.mul_right (Int.coprime_of_sq_sum (is_coprime_comm.mp h))
@@ -178,6 +220,7 @@ theorem Int.coprime_of_sq_sum' {r s : ℤ} (h : IsCoprime r s) : IsCoprime (r ^
 
 namespace Fermat42
 
+#print Fermat42.not_minimal /-
 -- If we have a solution to a ^ 4 + b ^ 4 = c ^ 2, we can construct a smaller one. This
 -- implies there can't be a smallest solution.
 theorem not_minimal {a b c : ℤ} (h : Minimal a b c) (ha2 : a % 2 = 1) (hc : 0 < c) : False :=
@@ -316,9 +359,16 @@ theorem not_minimal {a b c : ℤ} (h : Minimal a b c) (ha2 : a % 2 = 1) (hc : 0
     exact ⟨hj0, hk0, hh.symm⟩
   apply absurd (not_le_of_lt hic) (not_not.mpr hic')
 #align fermat_42.not_minimal Fermat42.not_minimal
+-/
 
 end Fermat42
 
+/- warning: not_fermat_42 -> not_fermat_42 is a dubious translation:
+lean 3 declaration is
+  forall {a : Int} {b : Int} {c : Int}, (Ne.{1} Int a (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))) -> (Ne.{1} Int b (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))) -> (Ne.{1} Int (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) a (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) b (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) c (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))
+but is expected to have type
+  forall {a : Int} {b : Int} {c : Int}, (Ne.{1} Int a (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))) -> (Ne.{1} Int b (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))) -> (Ne.{1} Int (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) a (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) b (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) c (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))
+Case conversion may be inaccurate. Consider using '#align not_fermat_42 not_fermat_42ₓ'. -/
 theorem not_fermat_42 {a b c : ℤ} (ha : a ≠ 0) (hb : b ≠ 0) : a ^ 4 + b ^ 4 ≠ c ^ 2 :=
   by
   intro h
@@ -327,6 +377,12 @@ theorem not_fermat_42 {a b c : ℤ} (ha : a ≠ 0) (hb : b ≠ 0) : a ^ 4 + b ^
   apply Fermat42.not_minimal hf h2 hp
 #align not_fermat_42 not_fermat_42
 
+/- warning: not_fermat_4 -> not_fermat_4 is a dubious translation:
+lean 3 declaration is
+  forall {a : Int} {b : Int} {c : Int}, (Ne.{1} Int a (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))) -> (Ne.{1} Int b (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))) -> (Ne.{1} Int (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) a (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) b (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) c (OfNat.ofNat.{0} Nat 4 (OfNat.mk.{0} Nat 4 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))
+but is expected to have type
+  forall {a : Int} {b : Int} {c : Int}, (Ne.{1} Int a (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))) -> (Ne.{1} Int b (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))) -> (Ne.{1} Int (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) a (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) b (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4)))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.instMonoidInt)) c (OfNat.ofNat.{0} Nat 4 (instOfNatNat 4))))
+Case conversion may be inaccurate. Consider using '#align not_fermat_4 not_fermat_4ₓ'. -/
 theorem not_fermat_4 {a b c : ℤ} (ha : a ≠ 0) (hb : b ≠ 0) : a ^ 4 + b ^ 4 ≠ c ^ 4 :=
   by
   intro heq

10b4e499

bump to nightly-2023-02-21-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

1107b979

Changes in mathlib4

mathlib3

mathlib4

10b4e499

chore: make argument to sq_pos_of_ne_zero/sq_pos_iff implicit (#12288)

This matches our general policy and zpow_two_pos_of_ne_zero.

Also define sq_pos_of_ne_zero as an alias.

ff9ef348

Diff

@@ -59,7 +59,7 @@ theorem ne_zero {a b c : ℤ} (h : Fermat42 a b c) : c ≠ 0 := by
   apply ne_zero_pow two_ne_zero _; apply ne_of_gt
   rw [← h.2.2, (by ring : a ^ 4 + b ^ 4 = (a ^ 2) ^ 2 + (b ^ 2) ^ 2)]
   exact
-    add_pos (sq_pos_of_ne_zero _ (pow_ne_zero 2 h.1)) (sq_pos_of_ne_zero _ (pow_ne_zero 2 h.2.1))
+    add_pos (sq_pos_of_ne_zero (pow_ne_zero 2 h.1)) (sq_pos_of_ne_zero (pow_ne_zero 2 h.2.1))
 #align fermat_42.ne_zero Fermat42.ne_zero
 
 /-- We say a solution to `a ^ 4 + b ^ 4 = c ^ 2` is minimal if there is no other solution with
@@ -286,7 +286,7 @@ theorem not_minimal {a b c : ℤ} (h : Minimal a b c) (ha2 : a % 2 = 1) (hc : 0
     apply gt_of_gt_of_ge _ (Int.natAbs_le_self_sq i)
     rw [← hi, ht3]
     apply gt_of_gt_of_ge _ (Int.le_self_sq m)
-    exact lt_add_of_pos_right (m ^ 2) (sq_pos_of_ne_zero n hn)
+    exact lt_add_of_pos_right (m ^ 2) (sq_pos_of_ne_zero hn)
   have hic' : Int.natAbs c ≤ Int.natAbs i := by
     apply h.2 j k i
     exact ⟨hj0, hk0, hh.symm⟩

10b4e499

Feat: add fermatLastTheoremThree_of_three_dvd_only_c (#11767)

We add fermatLastTheoremThree_of_three_dvd_only_c: To prove FermatLastTheoremFor 3, we may assume that ¬ 3 ∣ a, ¬ 3 ∣ b, a and b are coprime and 3 ∣ c.

From the flt3 project in LFTCM2024.

Co-authored-by: Pietro Monticone <38562595+pitmonticone@users.noreply.github.com>

fcf5d484

Diff

@@ -93,7 +93,7 @@ theorem coprime_of_minimal {a b c : ℤ} (h : Minimal a b c) : IsCoprime a b :=
   obtain ⟨a1, rfl⟩ := Int.natCast_dvd.mpr hpa
   obtain ⟨b1, rfl⟩ := Int.natCast_dvd.mpr hpb
   have hpc : (p : ℤ) ^ 2 ∣ c := by
-    rw [← Int.pow_dvd_pow_iff zero_lt_two, ← h.1.2.2]
+    rw [← Int.pow_dvd_pow_iff two_ne_zero, ← h.1.2.2]
     apply Dvd.intro (a1 ^ 4 + b1 ^ 4)
     ring
   obtain ⟨c1, rfl⟩ := hpc

10b4e499

chore(Data/Int): Rename coe_nat to natCast (#11637)

Reduce the diff of #11499

Renames

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

392a24a9

Diff

@@ -90,15 +90,15 @@ theorem coprime_of_minimal {a b c : ℤ} (h : Minimal a b c) : IsCoprime a b :=
   apply Int.gcd_eq_one_iff_coprime.mp
   by_contra hab
   obtain ⟨p, hp, hpa, hpb⟩ := Nat.Prime.not_coprime_iff_dvd.mp hab
-  obtain ⟨a1, rfl⟩ := Int.coe_nat_dvd_left.mpr hpa
-  obtain ⟨b1, rfl⟩ := Int.coe_nat_dvd_left.mpr hpb
+  obtain ⟨a1, rfl⟩ := Int.natCast_dvd.mpr hpa
+  obtain ⟨b1, rfl⟩ := Int.natCast_dvd.mpr hpb
   have hpc : (p : ℤ) ^ 2 ∣ c := by
     rw [← Int.pow_dvd_pow_iff zero_lt_two, ← h.1.2.2]
     apply Dvd.intro (a1 ^ 4 + b1 ^ 4)
     ring
   obtain ⟨c1, rfl⟩ := hpc
   have hf : Fermat42 a1 b1 c1 :=
-    (Fermat42.mul (Int.coe_nat_ne_zero.mpr (Nat.Prime.ne_zero hp))).mpr h.1
+    (Fermat42.mul (Int.natCast_ne_zero.mpr (Nat.Prime.ne_zero hp))).mpr h.1
   apply Nat.le_lt_asymm (h.2 _ _ _ hf)
   rw [Int.natAbs_mul, lt_mul_iff_one_lt_left, Int.natAbs_pow, Int.natAbs_ofNat]
   · exact Nat.one_lt_pow two_ne_zero (Nat.Prime.one_lt hp)

10b4e499

chore(Data/Nat): Use Std lemmas (#11661)

Move basic Nat lemmas from Data.Nat.Order.Basic and Data.Nat.Pow to Data.Nat.Defs. Most proofs need adapting, but that's easily solved by replacing the general mathlib lemmas by the new Std Nat-specific lemmas and using omega.

Other changes

Move the last few lemmas left in Data.Nat.Pow to Algebra.GroupPower.Order
Move the deprecated aliases from Data.Nat.Pow to Algebra.GroupPower.Order
Move the bit/bit0/bit1 lemmas from Data.Nat.Order.Basic to Data.Nat.Bits
Fix some fallout from not importing Data.Nat.Order.Basic anymore
Add a few Nat-specific lemmas to help fix the fallout (look for nolint simpNF)
Turn Nat.mul_self_le_mul_self_iff and Nat.mul_self_lt_mul_self_iff around (they were misnamed)
Make more arguments to Nat.one_lt_pow implicit

5bc68d9f

Diff

@@ -101,7 +101,7 @@ theorem coprime_of_minimal {a b c : ℤ} (h : Minimal a b c) : IsCoprime a b :=
     (Fermat42.mul (Int.coe_nat_ne_zero.mpr (Nat.Prime.ne_zero hp))).mpr h.1
   apply Nat.le_lt_asymm (h.2 _ _ _ hf)
   rw [Int.natAbs_mul, lt_mul_iff_one_lt_left, Int.natAbs_pow, Int.natAbs_ofNat]
-  · exact Nat.one_lt_pow _ _ two_ne_zero (Nat.Prime.one_lt hp)
+  · exact Nat.one_lt_pow two_ne_zero (Nat.Prime.one_lt hp)
   · exact Nat.pos_of_ne_zero (Int.natAbs_ne_zero.2 (ne_zero hf))
 #align fermat_42.coprime_of_minimal Fermat42.coprime_of_minimal

10b4e499

chore: scope open Classical (#11199)

We remove all but one open Classicals, instead preferring to use open scoped Classical. The only real side-effect this led to is moving a couple declarations to use Exists.choose instead of Classical.choose.

The first few commits are explicitly labelled regex replaces for ease of review.

c747be0a

Diff

@@ -18,7 +18,7 @@ There are no non-zero integers `a`, `b` and `c` such that `a ^ 4 + b ^ 4 = c ^ 4
 
 noncomputable section
 
-open Classical
+open scoped Classical
 
 /-- Shorthand for three non-zero integers `a`, `b`, and `c` satisfying `a ^ 4 + b ^ 4 = c ^ 2`.
 We will show that no integers satisfy this equation. Clearly Fermat's Last theorem for n = 4

10b4e499

chore: remove stream-of-consciousness uses of have, replace and suffices (#10640)

No changes to tactic file, it's just boring fixes throughout the library.

This follows on from #6964.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

a13e8040

Diff

@@ -234,12 +234,10 @@ theorem not_minimal {a b c : ℤ} (h : Minimal a b c) (ha2 : a % 2 = 1) (hc : 0
   -- use m is positive to exclude m = - i ^ 2
   have hi' : ¬m = -i ^ 2 := by
     by_contra h1
-    have hit : -i ^ 2 ≤ 0
-    apply neg_nonpos.mpr (sq_nonneg i)
+    have hit : -i ^ 2 ≤ 0 := neg_nonpos.mpr (sq_nonneg i)
     rw [← h1] at hit
     apply absurd h4 (not_lt.mpr hit)
-  replace hi : m = i ^ 2
-  · apply Or.resolve_right hi hi'
+  replace hi : m = i ^ 2 := Or.resolve_right hi hi'
   rw [mul_comm] at hs
   rw [Int.gcd_comm] at hcp
   -- obtain d such that r * s = d ^ 2
@@ -253,8 +251,7 @@ theorem not_minimal {a b c : ℤ} (h : Minimal a b c) (ha2 : a % 2 = 1) (hc : 0
       exact neg_nonpos.mpr ((mul_nonneg_iff_of_pos_right h4).mpr (sq_nonneg d))
     have h2' : 0 ≤ b' ^ 2 := by apply sq_nonneg b'
     exact absurd (lt_of_le_of_ne h2' (Ne.symm (pow_ne_zero _ h2b0))) (not_lt.mpr h2)
-  replace hd : r * s = d ^ 2
-  · apply Or.resolve_right hd hd'
+  replace hd : r * s = d ^ 2 := Or.resolve_right hd hd'
   -- r = +/- j ^ 2
   obtain ⟨j, hj⟩ := Int.sq_of_gcd_eq_one htt4 hd
   have hj0 : j ≠ 0 := by

10b4e499

feat: The support of f ^ n (#9617)

This involves moving lemmas from Algebra.GroupPower.Ring to Algebra.GroupWithZero.Basic and changing some 0 < n assumptions to n ≠ 0.

From LeanAPAP

9d1a7d26

Diff

@@ -259,7 +259,7 @@ theorem not_minimal {a b c : ℤ} (h : Minimal a b c) (ha2 : a % 2 = 1) (hc : 0
   obtain ⟨j, hj⟩ := Int.sq_of_gcd_eq_one htt4 hd
   have hj0 : j ≠ 0 := by
     intro h0
-    rw [h0, zero_pow zero_lt_two, neg_zero, or_self_iff] at hj
+    rw [h0, zero_pow two_ne_zero, neg_zero, or_self_iff] at hj
     apply left_ne_zero_of_mul hrsz hj
   rw [mul_comm] at hd
   rw [Int.gcd_comm] at htt4
@@ -267,7 +267,7 @@ theorem not_minimal {a b c : ℤ} (h : Minimal a b c) (ha2 : a % 2 = 1) (hc : 0
   obtain ⟨k, hk⟩ := Int.sq_of_gcd_eq_one htt4 hd
   have hk0 : k ≠ 0 := by
     intro h0
-    rw [h0, zero_pow zero_lt_two, neg_zero, or_self_iff] at hk
+    rw [h0, zero_pow two_ne_zero, neg_zero, or_self_iff] at hk
     apply right_ne_zero_of_mul hrsz hk
   have hj2 : r ^ 2 = j ^ 4 := by
     cases' hj with hjp hjp <;>

10b4e499

refactor: Delete Algebra.GroupPower.Lemmas (#9411)

Algebra.GroupPower.Lemmas used to be a big bag of lemmas that made it there on the criterion that they needed "more imports". This was completely untrue, as all lemmas could be moved to earlier files in PRs:

There are several reasons for this:

Necessary lemmas have been moved to earlier files since lemmas were dumped in Algebra.GroupPower.Lemmas
In the Lean 3 → Lean 4 transition, Std acquired basic Int and Nat lemmas which let us shortcircuit the part of the algebraic order hierarchy on which the corresponding general lemmas rest
Some proofs were overpowered
Some earlier files were tangled and I have untangled them

This PR finishes the job by moving the last few lemmas out of Algebra.GroupPower.Lemmas, which is therefore deleted.

6eb43dc3

Diff

@@ -3,7 +3,6 @@ Copyright (c) 2020 Paul van Wamelen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul van Wamelen
 -/
-import Mathlib.Algebra.GroupPower.Lemmas
 import Mathlib.NumberTheory.FLT.Basic
 import Mathlib.NumberTheory.PythagoreanTriples
 import Mathlib.RingTheory.Coprime.Lemmas

10b4e499

chore: reduce imports (#9830)

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

f4c4ca61

Diff

@@ -3,6 +3,7 @@ Copyright (c) 2020 Paul van Wamelen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul van Wamelen
 -/
+import Mathlib.Algebra.GroupPower.Lemmas
 import Mathlib.NumberTheory.FLT.Basic
 import Mathlib.NumberTheory.PythagoreanTriples
 import Mathlib.RingTheory.Coprime.Lemmas

10b4e499

feat: 0 ≤ a * b ↔ (0 < a → 0 ≤ b) ∧ (0 < b → 0 ≤ a) (#9219)

I had a slightly logic-heavy argument that was nicely simplified by stating this lemma. Also fix a few lemma names.

From LeanAPAP and LeanCamCombi

23429eb2

Diff

@@ -250,7 +250,7 @@ theorem not_minimal {a b c : ℤ} (h : Minimal a b c) (ha2 : a % 2 = 1) (hc : 0
     rw [h1] at hs
     have h2 : b' ^ 2 ≤ 0 := by
       rw [hs, (by ring : -d ^ 2 * m = -(d ^ 2 * m))]
-      exact neg_nonpos.mpr ((zero_le_mul_right h4).mpr (sq_nonneg d))
+      exact neg_nonpos.mpr ((mul_nonneg_iff_of_pos_right h4).mpr (sq_nonneg d))
     have h2' : 0 ≤ b' ^ 2 := by apply sq_nonneg b'
     exact absurd (lt_of_le_of_ne h2' (Ne.symm (pow_ne_zero _ h2b0))) (not_lt.mpr h2)
   replace hd : r * s = d ^ 2

10b4e499

chore: Rename pow monotonicity lemmas (#9095)

The names for lemmas about monotonicity of (a ^ ·) and (· ^ n) were a mess. This PR tidies up everything related by following the naming convention for (a * ·) and (· * b). Namely, (a ^ ·) is pow_right and (· ^ n) is pow_left in lemma names. All lemma renames follow the corresponding multiplication lemma names closely.

Renames

`Algebra.GroupPower.Order`

pow_mono → pow_right_mono
pow_le_pow → pow_le_pow_right
pow_le_pow_of_le_left → pow_le_pow_left
pow_lt_pow_of_lt_left → pow_lt_pow_left
strictMonoOn_pow → pow_left_strictMonoOn
pow_strictMono_right → pow_right_strictMono
pow_lt_pow → pow_lt_pow_right
pow_lt_pow_iff → pow_lt_pow_iff_right
pow_le_pow_iff → pow_le_pow_iff_right
self_lt_pow → lt_self_pow
strictAnti_pow → pow_right_strictAnti
pow_lt_pow_iff_of_lt_one → pow_lt_pow_iff_right_of_lt_one
pow_lt_pow_of_lt_one → pow_lt_pow_right_of_lt_one
lt_of_pow_lt_pow → lt_of_pow_lt_pow_left
le_of_pow_le_pow → le_of_pow_le_pow_left
pow_lt_pow₀ → pow_lt_pow_right₀

`Algebra.GroupPower.CovariantClass`

pow_le_pow_of_le_left' → pow_le_pow_left'
nsmul_le_nsmul_of_le_right → nsmul_le_nsmul_right
pow_lt_pow' → pow_lt_pow_right'
nsmul_lt_nsmul → nsmul_lt_nsmul_left
pow_strictMono_left → pow_right_strictMono'
nsmul_strictMono_right → nsmul_left_strictMono
StrictMono.pow_right' → StrictMono.pow_const
StrictMono.nsmul_left → StrictMono.const_nsmul
pow_strictMono_right' → pow_left_strictMono
nsmul_strictMono_left → nsmul_right_strictMono
Monotone.pow_right → Monotone.pow_const
Monotone.nsmul_left → Monotone.const_nsmul
lt_of_pow_lt_pow' → lt_of_pow_lt_pow_left'
lt_of_nsmul_lt_nsmul → lt_of_nsmul_lt_nsmul_right
pow_le_pow' → pow_le_pow_right'
nsmul_le_nsmul → nsmul_le_nsmul_left
pow_le_pow_of_le_one' → pow_le_pow_right_of_le_one'
nsmul_le_nsmul_of_nonpos → nsmul_le_nsmul_left_of_nonpos
le_of_pow_le_pow' → le_of_pow_le_pow_left'
le_of_nsmul_le_nsmul' → le_of_nsmul_le_nsmul_right'
pow_le_pow_iff' → pow_le_pow_iff_right'
nsmul_le_nsmul_iff → nsmul_le_nsmul_iff_left
pow_lt_pow_iff' → pow_lt_pow_iff_right'
nsmul_lt_nsmul_iff → nsmul_lt_nsmul_iff_left

`Data.Nat.Pow`

Nat.pow_lt_pow_of_lt_left → Nat.pow_lt_pow_left
Nat.pow_le_iff_le_left → Nat.pow_le_pow_iff_left
Nat.pow_lt_iff_lt_left → Nat.pow_lt_pow_iff_left

Lemmas added

pow_le_pow_iff_left
pow_lt_pow_iff_left
pow_right_injective
pow_right_inj
Nat.pow_le_pow_left to have the correct name since Nat.pow_le_pow_of_le_left is in Std.
Nat.pow_le_pow_right to have the correct name since Nat.pow_le_pow_of_le_right is in Std.

Lemmas removed

self_le_pow was a duplicate of le_self_pow.
Nat.pow_lt_pow_of_lt_right is defeq to pow_lt_pow_right.
Nat.pow_right_strictMono is defeq to pow_right_strictMono.
Nat.pow_le_iff_le_right is defeq to pow_le_pow_iff_right.
Nat.pow_lt_iff_lt_right is defeq to pow_lt_pow_iff_right.

Other changes

A bunch of proofs have been golfed.
Some lemma assumptions have been turned from 0 < n or 1 ≤ n to n ≠ 0.
A few Nat lemmas have been protected.
One docstring has been fixed.

d61c95e1

Diff

@@ -101,7 +101,7 @@ theorem coprime_of_minimal {a b c : ℤ} (h : Minimal a b c) : IsCoprime a b :=
     (Fermat42.mul (Int.coe_nat_ne_zero.mpr (Nat.Prime.ne_zero hp))).mpr h.1
   apply Nat.le_lt_asymm (h.2 _ _ _ hf)
   rw [Int.natAbs_mul, lt_mul_iff_one_lt_left, Int.natAbs_pow, Int.natAbs_ofNat]
-  · exact Nat.one_lt_pow _ _ zero_lt_two (Nat.Prime.one_lt hp)
+  · exact Nat.one_lt_pow _ _ two_ne_zero (Nat.Prime.one_lt hp)
   · exact Nat.pos_of_ne_zero (Int.natAbs_ne_zero.2 (ne_zero hf))
 #align fermat_42.coprime_of_minimal Fermat42.coprime_of_minimal

10b4e499

doc: add/edit some FLT docstrings (#8910)

Fix two arguably incorrect docstrings, clarify one, add one more.

3d06b091

Diff

@@ -305,6 +305,10 @@ theorem not_fermat_42 {a b c : ℤ} (ha : a ≠ 0) (hb : b ≠ 0) : a ^ 4 + b ^
   apply Fermat42.not_minimal hf h2 hp
 #align not_fermat_42 not_fermat_42
 
+/--
+Fermat's Last Theorem for $n=4$: if `a b c : ℕ` are all non-zero
+then `a ^ 4 + b ^ 4 ≠ c ^ 4`.
+-/
 theorem fermatLastTheoremFour : FermatLastTheoremFor 4 := by
   rw [fermatLastTheoremFor_iff_int]
   intro a b c ha hb _ heq
@@ -313,8 +317,7 @@ theorem fermatLastTheoremFour : FermatLastTheoremFor 4 := by
 #align not_fermat_4 fermatLastTheoremFour
 
 /--
-To prove Fermat's Last Theorem, it suffices to prove it for odd prime exponents, and the case of
-exponent 4 proved above.
+To prove Fermat's Last Theorem, it suffices to prove it for odd prime exponents.
 -/
 theorem FermatLastTheorem.of_odd_primes
     (hprimes : ∀ p : ℕ, Nat.Prime p → Odd p → FermatLastTheoremFor p) : FermatLastTheorem := by

10b4e499

chore: bump to v4.3.0-rc2 (#8366)

PR contents

This is the supremum of

#8284
#8056
#8023
#8332
#8226 (already approved)
#7834 (already approved)

along with some minor fixes from failures on nightly-testing as Mathlib master is merged into it.

Note that some PRs for changes that are already compatible with the current toolchain and will be necessary have already been split out: #8380.

I am hopeful that in future we will be able to progressively merge adaptation PRs into a bump/v4.X.0 branch, so we never end up with a "big merge" like this. However one of these adaptation PRs (#8056) predates my new scheme for combined CI, and it wasn't possible to keep that PR viable in the meantime.

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

leanprover/lean4#2778

We can get rid of all the

local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)

macros across Mathlib (and in any projects that want to write natural number powers of reals).

leanprover/lean4#2722

Changes the default behaviour of simp to (config := {decide := false}). This makes simp (and consequentially norm_num) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp or norm_num to decide or rfl, or adding (config := {decide := true}).

leanprover/lean4#2783

This changed the behaviour of simp so that simp [f] will only unfold "fully applied" occurrences of f. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true }). We may in future add a syntax for this, e.g. simp [!f]; please provide feedback! In the meantime, we have made the following changes:

switching to using explicit lemmas that have the intended level of application
(config := { unfoldPartialApp := true }) in some places, to recover the old behaviour
Using @[eqns] to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp and Function.flip.

This change in Lean may require further changes down the line (e.g. adding the !f syntax, and/or upstreaming the special treatment for Function.comp and Function.flip, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>

40b64f79

Diff

@@ -131,7 +131,7 @@ theorem exists_odd_minimal {a b c : ℤ} (h : Fermat42 a b c) :
         Int.dvd_gcd (Int.dvd_of_emod_eq_zero hap) (Int.dvd_of_emod_eq_zero hbp)
       rw [Int.gcd_eq_one_iff_coprime.mpr (coprime_of_minimal hf)] at h1
       revert h1
-      norm_num
+      decide
     · exact ⟨b0, ⟨a0, ⟨c0, minimal_comm hf, hbp⟩⟩⟩
   exact ⟨a0, ⟨b0, ⟨c0, hf, hap⟩⟩⟩
 #align fermat_42.exists_odd_minimal Fermat42.exists_odd_minimal
@@ -179,7 +179,7 @@ theorem not_minimal {a b c : ℤ} (h : Minimal a b c) (ha2 : a % 2 = 1) (hc : 0
   -- it helps if we know the parity of a ^ 2 (and the sign of c):
   have ha22 : a ^ 2 % 2 = 1 := by
     rw [sq, Int.mul_emod, ha2]
-    norm_num
+    decide
   obtain ⟨m, n, ht1, ht2, ht3, ht4, ht5, ht6⟩ := ht.coprime_classification' h2 ha22 hc
   -- Now a, n, m form a pythagorean triple and so we can obtain r and s such that
   -- a = r ^ 2 - s ^ 2, n = 2 * r * s and m = r ^ 2 + s ^ 2

10b4e499

fix: patch for std4#194 (more order lemmas for Nat) (#8077)

5f84b04f

Diff

@@ -99,7 +99,7 @@ theorem coprime_of_minimal {a b c : ℤ} (h : Minimal a b c) : IsCoprime a b :=
   obtain ⟨c1, rfl⟩ := hpc
   have hf : Fermat42 a1 b1 c1 :=
     (Fermat42.mul (Int.coe_nat_ne_zero.mpr (Nat.Prime.ne_zero hp))).mpr h.1
-  apply Nat.le_lt_antisymm (h.2 _ _ _ hf)
+  apply Nat.le_lt_asymm (h.2 _ _ _ hf)
   rw [Int.natAbs_mul, lt_mul_iff_one_lt_left, Int.natAbs_pow, Int.natAbs_ofNat]
   · exact Nat.one_lt_pow _ _ zero_lt_two (Nat.Prime.one_lt hp)
   · exact Nat.pos_of_ne_zero (Int.natAbs_ne_zero.2 (ne_zero hf))

10b4e499

feat: reduce FLT to odd primes (#7485)

37079e5a

Diff

@@ -311,3 +311,16 @@ theorem fermatLastTheoremFour : FermatLastTheoremFor 4 := by
   apply @not_fermat_42 _ _ (c ^ 2) ha hb
   rw [heq]; ring
 #align not_fermat_4 fermatLastTheoremFour
+
+/--
+To prove Fermat's Last Theorem, it suffices to prove it for odd prime exponents, and the case of
+exponent 4 proved above.
+-/
+theorem FermatLastTheorem.of_odd_primes
+    (hprimes : ∀ p : ℕ, Nat.Prime p → Odd p → FermatLastTheoremFor p) : FermatLastTheorem := by
+  intro n h
+  rw [ge_iff_le, Nat.succ_le_iff] at h
+  obtain hdvd|⟨p, hpprime, hdvd, hpodd⟩ := Nat.four_dvd_or_exists_odd_prime_and_dvd_of_two_lt h <;>
+    apply FermatLastTheoremWith.mono hdvd
+  · exact fermatLastTheoremFour
+  · exact hprimes p hpprime hpodd

10b4e499

refactor(NumberTheory/FLT): Define Fermat's Last Theorem for fixed exponent (#7494)

This PR adds a definition of Fermat's Last Theorem for fixed exponent. The motivation for this is that FermatLastTheoremWith ℕ n, FermatLastTheoremWith ℤ n, and FermatLastTheoremWith ℚ n are all equivalent, so it would be nice to have a canonical name, rather than sometimes referring to one and sometimes referring to another.

423fc25e

Diff

@@ -305,7 +305,8 @@ theorem not_fermat_42 {a b c : ℤ} (ha : a ≠ 0) (hb : b ≠ 0) : a ^ 4 + b ^
   apply Fermat42.not_minimal hf h2 hp
 #align not_fermat_42 not_fermat_42
 
-theorem fermatLastTheoremFour : FermatLastTheoremWith ℤ 4 := by
+theorem fermatLastTheoremFour : FermatLastTheoremFor 4 := by
+  rw [fermatLastTheoremFor_iff_int]
   intro a b c ha hb _ heq
   apply @not_fermat_42 _ _ (c ^ 2) ha hb
   rw [heq]; ring

10b4e499

feat: statement of Fermat's Last Theorem (#6508)

Co-authored-by: Yaël Dillies <yael.dillies@gmail.com> Co-authored-by: Oliver Nash <github@olivernash.org>

ca73a84a

Diff

@@ -3,6 +3,7 @@ Copyright (c) 2020 Paul van Wamelen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul van Wamelen
 -/
+import Mathlib.NumberTheory.FLT.Basic
 import Mathlib.NumberTheory.PythagoreanTriples
 import Mathlib.RingTheory.Coprime.Lemmas
 import Mathlib.Tactic.LinearCombination
@@ -304,8 +305,8 @@ theorem not_fermat_42 {a b c : ℤ} (ha : a ≠ 0) (hb : b ≠ 0) : a ^ 4 + b ^
   apply Fermat42.not_minimal hf h2 hp
 #align not_fermat_42 not_fermat_42
 
-theorem not_fermat_4 {a b c : ℤ} (ha : a ≠ 0) (hb : b ≠ 0) : a ^ 4 + b ^ 4 ≠ c ^ 4 := by
-  intro heq
+theorem fermatLastTheoremFour : FermatLastTheoremWith ℤ 4 := by
+  intro a b c ha hb _ heq
   apply @not_fermat_42 _ _ (c ^ 2) ha hb
   rw [heq]; ring
-#align not_fermat_4 not_fermat_4
+#align not_fermat_4 fermatLastTheoremFour

10b4e499

fix: let use provide last constructor argument, introduce mathlib3-like flattening use! (#5350)

Changes:

use now by default discharges with try with_reducible use_discharger with a custom discharger tactic rather than try with_reducible rfl, which makes it be closer to exists and the use in mathlib3. It doesn't go so far as to do try with_reducible trivial since that involves the contradiction tactic.
this discharger is configurable with use (discharger := tacticSeq...)
the use evaluation loop will try refining after constructor failure, so it can be used to fill in all arguments rather than all but the last, like in mathlib3 (closes #5072) but with the caveat that it only works so long as the last argument is not an inductive type (like Eq).
adds use!, which is nearly the same as the mathlib3 use and fills in constructor arguments along the nodes and leaves of the nested constructor expressions. This version tries refining before applying constructors, so it can be used like exact for the last argument.

The difference between mathlib3 use and this use! is that (1) use! uses a different tactic to discharge goals (mathlib3 used trivial', which did reducible refl, but also contradiction, which we don't emulate) (2) it does not rewrite using exists_prop. Regarding 2, this feature seems to be less useful now that bounded existentials encode the bound using a conjunction rather than with nested existentials. We do have exists_prop as part of use_discharger however.

Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com>

c8417221

Diff

@@ -74,7 +74,6 @@ theorem exists_minimal {a b c : ℤ} (h : Fermat42 a b c) : ∃ a0 b0 c0, Minima
     use Int.natAbs c
     rw [Set.mem_setOf_eq]
     use ⟨a, ⟨b, c⟩⟩
-    tauto
   let m : ℕ := Nat.find S_nonempty
   have m_mem : m ∈ S := Nat.find_spec S_nonempty
   rcases m_mem with ⟨s0, hs0, hs1⟩
@@ -83,7 +82,6 @@ theorem exists_minimal {a b c : ℤ} (h : Fermat42 a b c) : ∃ a0 b0 c0, Minima
   rw [← hs1]
   apply Nat.find_min'
   use ⟨a1, ⟨b1, c1⟩⟩
-  tauto
 #align fermat_42.exists_minimal Fermat42.exists_minimal
 
 /-- a minimal solution to `a ^ 4 + b ^ 4 = c ^ 2` must have `a` and `b` coprime. -/
@@ -144,7 +142,6 @@ theorem exists_pos_odd_minimal {a b c : ℤ} (h : Fermat42 a b c) :
   obtain ⟨a0, b0, c0, hf, hc⟩ := exists_odd_minimal h
   rcases lt_trichotomy 0 c0 with (h1 | h1 | h1)
   · use a0, b0, c0
-    tauto
   · exfalso
     exact ne_zero hf.1 h1.symm
   · use a0, b0, -c0, neg_of_minimal hf, hc

10b4e499

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

89aa3a3b

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Paul van Wamelen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Paul van Wamelen
-
-! This file was ported from Lean 3 source module number_theory.fermat4
-! leanprover-community/mathlib commit 10b4e499f43088dd3bb7b5796184ad5216648ab1
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.NumberTheory.PythagoreanTriples
 import Mathlib.RingTheory.Coprime.Lemmas
 import Mathlib.Tactic.LinearCombination
 
+#align_import number_theory.fermat4 from "leanprover-community/mathlib"@"10b4e499f43088dd3bb7b5796184ad5216648ab1"
+
 /-!
 # Fermat's Last Theorem for the case n = 4
 There are no non-zero integers `a`, `b` and `c` such that `a ^ 4 + b ^ 4 = c ^ 4`.

10b4e499

chore: bye-bye, solo bys! (#3825)

This PR puts, with one exception, every single remaining by that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh. The exception is when the by begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.

Essentially this is s/\n *by$/ by/g, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated bys".

14167e48

Diff

@@ -161,8 +161,8 @@ theorem Int.coprime_of_sq_sum {r s : ℤ} (h2 : IsCoprime s r) : IsCoprime (r ^
   exact (IsCoprime.mul_left h2 h2).mul_add_left_left r
 #align int.coprime_of_sq_sum Int.coprime_of_sq_sum
 
-theorem Int.coprime_of_sq_sum' {r s : ℤ} (h : IsCoprime r s) : IsCoprime (r ^ 2 + s ^ 2) (r * s) :=
-  by
+theorem Int.coprime_of_sq_sum' {r s : ℤ} (h : IsCoprime r s) :
+    IsCoprime (r ^ 2 + s ^ 2) (r * s) := by
   apply IsCoprime.mul_right (Int.coprime_of_sq_sum (isCoprime_comm.mp h))
   rw [add_comm]; apply Int.coprime_of_sq_sum h
 #align int.coprime_of_sq_sum' Int.coprime_of_sq_sum'

10b4e499

feat: port NumberTheory.Fermat4 (#3064)

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

ebf7fac2

`number_theory.fermat4` ⟷ `Mathlib.NumberTheory.FLT.Four`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Other changes

Renames

`Algebra.GroupPower.Order`

`Algebra.GroupPower.CovariantClass`

`Data.Nat.Pow`

Lemmas added

Lemmas removed

Other changes

PR contents

Lean PRs involved in this bump

leanprover/lean4#2778

leanprover/lean4#2722

leanprover/lean4#2783

Dependencies 8 + 500

number_theory.fermat4 ⟷ Mathlib.NumberTheory.FLT.Four

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Other changes

Renames

Algebra.GroupPower.Order

Algebra.GroupPower.CovariantClass

Data.Nat.Pow

Lemmas added

Lemmas removed

Other changes

PR contents

Lean PRs involved in this bump

leanprover/lean4#2778

leanprover/lean4#2722

leanprover/lean4#2783

Dependencies 8 + 500

`number_theory.fermat4` ⟷ `Mathlib.NumberTheory.FLT.Four`

`Algebra.GroupPower.Order`

`Algebra.GroupPower.CovariantClass`

`Data.Nat.Pow`