wiedijk_100_theorems.friendship_graphs ⟷ Archive.Wiedijk100Theorems.FriendshipGraphs

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

@@ -88,7 +88,7 @@ variable (R)
 theorem adjMatrix_sq_of_ne {v w : V} (hvw : v ≠ w) : (G.adjMatrix R ^ 2) v w = 1 :=
   by
   rw [sq, ← Nat.cast_one, ← hG hvw]
-  simp [common_neighbors, neighbor_finset_eq_filter, Finset.filter_filter, and_comm', ←
+  simp [common_neighbors, neighbor_finset_eq_filter, Finset.filter_filter, and_comm, ←
     neighbor_finset_def]
 #align theorems_100.friendship.adj_matrix_sq_of_ne Theorems100.Friendship.adjMatrix_sq_of_ne
 

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

@@ -244,7 +244,7 @@ theorem false_of_three_le_degree (hd : G.IsRegularOfDegree d) (h : 3 ≤ d) : Fa
   by
   -- get a prime factor of d - 1
   let p : ℕ := (d - 1).minFac
-  have p_dvd_d_pred := (ZMod.nat_cast_zmod_eq_zero_iff_dvd _ _).mpr (d - 1).minFac_dvd
+  have p_dvd_d_pred := (ZMod.natCast_zmod_eq_zero_iff_dvd _ _).mpr (d - 1).minFac_dvd
   have dpos : 0 < d := by linarith
   have d_cast : ↑(d - 1) = (d : ℤ) - 1 := by norm_cast
   haveI : Fact p.prime := ⟨Nat.minFac_prime (by linarith)⟩
@@ -264,7 +264,7 @@ theorem false_of_three_le_degree (hd : G.IsRegularOfDegree d) (h : 3 ≤ d) : Fa
   rw [adj_matrix_pow_mod_p_of_regular hG dmod hd hp2]
   dsimp only [Fintype.card] at Vmod
   simp only [Matrix.trace, Matrix.diag, mul_one, nsmul_eq_mul, LinearMap.coe_mk, sum_const]
-  rw [Vmod, ← Nat.cast_one, ZMod.nat_cast_zmod_eq_zero_iff_dvd, Nat.dvd_one, Nat.minFac_eq_one_iff]
+  rw [Vmod, ← Nat.cast_one, ZMod.natCast_zmod_eq_zero_iff_dvd, Nat.dvd_one, Nat.minFac_eq_one_iff]
   linarith
 #align theorems_100.friendship.false_of_three_le_degree Theorems100.Friendship.false_of_three_le_degree
 

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

@@ -5,8 +5,8 @@ Authors: Aaron Anderson, Jalex Stark, Kyle Miller
 -/
 import Combinatorics.SimpleGraph.AdjMatrix
 import LinearAlgebra.Matrix.Charpoly.FiniteField
-import Data.Int.Modeq
-import Data.Zmod.Basic
+import Data.Int.ModEq
+import Data.ZMod.Basic
 import Tactic.IntervalCases
 
 #align_import wiedijk_100_theorems.friendship_graphs from "leanprover-community/mathlib"@"08b081ea92d80e3a41f899eea36ef6d56e0f1db0"
@@ -97,7 +97,7 @@ theorem adjMatrix_sq_of_ne {v w : V} (hvw : v ≠ w) : (G.adjMatrix R ^ 2) v w =
 theorem adjMatrix_pow_three_of_not_adj {v w : V} (non_adj : ¬G.Adj v w) :
     (G.adjMatrix R ^ 3) v w = degree G v :=
   by
-  rw [pow_succ, mul_eq_mul, adj_matrix_mul_apply, degree, card_eq_sum_ones, Nat.cast_sum]
+  rw [pow_succ', mul_eq_mul, adj_matrix_mul_apply, degree, card_eq_sum_ones, Nat.cast_sum]
   apply sum_congr rfl
   intro x hx
   rw [adj_matrix_sq_of_ne _ hG, Nat.cast_one]
@@ -119,7 +119,7 @@ theorem degree_eq_of_not_adj {v w : V} (hvw : ¬G.Adj v w) : degree G v = degree
     adj_matrix_pow_three_of_not_adj ℕ hG hvw, ←
     adj_matrix_pow_three_of_not_adj ℕ hG fun h => hvw (G.symm h)]
   conv_lhs => rw [← transpose_adj_matrix]
-  simp only [pow_succ, sq, mul_eq_mul, ← transpose_mul, transpose_apply]
+  simp only [pow_succ', sq, mul_eq_mul, ← transpose_mul, transpose_apply]
   simp only [← mul_eq_mul, mul_assoc]
 #align theorems_100.friendship.degree_eq_of_not_adj Theorems100.Friendship.degree_eq_of_not_adj
 
@@ -229,7 +229,7 @@ theorem adjMatrix_pow_mod_p_of_regular {p : ℕ} (dmod : (d : ZMod p) = 1)
   iterate 2 cases' k with k; · exfalso; linarith
   induction' k with k hind
   · exact adj_matrix_sq_mod_p_of_regular hG dmod hd
-  rw [pow_succ, hind (Nat.le_add_left 2 k)]
+  rw [pow_succ', hind (Nat.le_add_left 2 k)]
   exact adj_matrix_mul_const_one_mod_p_of_regular dmod hd
 #align theorems_100.friendship.adj_matrix_pow_mod_p_of_regular Theorems100.Friendship.adjMatrix_pow_mod_p_of_regular
 

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

@@ -102,7 +102,7 @@ theorem adjMatrix_pow_three_of_not_adj {v w : V} (non_adj : ¬G.Adj v w) :
   intro x hx
   rw [adj_matrix_sq_of_ne _ hG, Nat.cast_one]
   rintro ⟨rfl⟩
-  rw [mem_neighbor_finset] at hx 
+  rw [mem_neighbor_finset] at hx
   exact non_adj hx
 #align theorems_100.friendship.adj_matrix_pow_three_of_not_adj Theorems100.Friendship.adjMatrix_pow_three_of_not_adj
 
@@ -155,8 +155,8 @@ theorem is_regular_of_not_existsPolitician (hG' : ¬ExistsPolitician G) :
   use G.degree v
   intro x
   by_cases hvx : G.adj v x; swap; · exact (degree_eq_of_not_adj hG hvx).symm
-  dsimp only [Theorems100.ExistsPolitician] at hG' 
-  push_neg at hG' 
+  dsimp only [Theorems100.ExistsPolitician] at hG'
+  push_neg at hG'
   rcases hG' v with ⟨w, hvw', hvw⟩
   rcases hG' x with ⟨y, hxy', hxy⟩
   by_cases hxw : G.adj x w
@@ -172,7 +172,7 @@ theorem is_regular_of_not_existsPolitician (hG' : ¬ExistsPolitician G) :
     by
     intro x hx
     have h' := mem_univ (Subtype.mk x hx)
-    rw [h, mem_singleton] at h' 
+    rw [h, mem_singleton] at h'
     injection h'
   apply hxy'
   rw [key ((mem_common_neighbors G).mpr ⟨hvx, G.symm hxw⟩),
@@ -262,7 +262,7 @@ theorem false_of_three_le_degree (hd : G.IsRegularOfDegree d) (h : 3 ≤ d) : Fa
   rw [trace_adj_matrix, zero_pow (Fact.out p.prime).Pos]
   -- but the trace is 1 mod p when computed the other way
   rw [adj_matrix_pow_mod_p_of_regular hG dmod hd hp2]
-  dsimp only [Fintype.card] at Vmod 
+  dsimp only [Fintype.card] at Vmod
   simp only [Matrix.trace, Matrix.diag, mul_one, nsmul_eq_mul, LinearMap.coe_mk, sum_const]
   rw [Vmod, ← Nat.cast_one, ZMod.nat_cast_zmod_eq_zero_iff_dvd, Nat.dvd_one, Nat.minFac_eq_one_iff]
   linarith
@@ -275,12 +275,12 @@ theorem existsPolitician_of_degree_le_one (hd : G.IsRegularOfDegree d) (hd1 : d
   by
   have sq : d * d = d := by interval_cases <;> norm_num
   have h := card_of_regular hG hd
-  rw [sq] at h 
+  rw [sq] at h
   have : Fintype.card V ≤ 1 := by
     cases' Fintype.card V with n
     · exact zero_le _
     · have : n = 0 := by
-        rw [Nat.succ_sub_succ_eq_sub, tsub_zero] at h 
+        rw [Nat.succ_sub_succ_eq_sub, tsub_zero] at h
         linarith
       subst n
   use Classical.arbitrary V
@@ -304,7 +304,7 @@ theorem neighborFinset_eq_of_degree_eq_two (hd : G.IsRegularOfDegree 2) (v : V)
     · have hfr := card_of_regular hG hd
       linarith
     · exact Finset.card_erase_of_mem (Finset.mem_univ _)
-  · dsimp [is_regular_of_degree, degree] at hd 
+  · dsimp [is_regular_of_degree, degree] at hd
     rw [hd]
 #align theorems_100.friendship.neighbor_finset_eq_of_degree_eq_two Theorems100.Friendship.neighborFinset_eq_of_degree_eq_two
 

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

@@ -3,11 +3,11 @@ Copyright (c) 2020 Aaron Anderson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Aaron Anderson, Jalex Stark, Kyle Miller
 -/
-import Mathbin.Combinatorics.SimpleGraph.AdjMatrix
-import Mathbin.LinearAlgebra.Matrix.Charpoly.FiniteField
-import Mathbin.Data.Int.Modeq
-import Mathbin.Data.Zmod.Basic
-import Mathbin.Tactic.IntervalCases
+import Combinatorics.SimpleGraph.AdjMatrix
+import LinearAlgebra.Matrix.Charpoly.FiniteField
+import Data.Int.Modeq
+import Data.Zmod.Basic
+import Tactic.IntervalCases
 
 #align_import wiedijk_100_theorems.friendship_graphs from "leanprover-community/mathlib"@"08b081ea92d80e3a41f899eea36ef6d56e0f1db0"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

@@ -212,14 +212,14 @@ theorem card_mod_p_of_regular {p : ℕ} (dmod : (d : ZMod p) = 1) (hd : G.IsRegu
 
 end Nonempty
 
-theorem adjMatrix_sq_mul_const_one_of_regular (hd : G.IsRegularOfDegree d) :
+theorem adjMatrix_sq_hMul_const_one_of_regular (hd : G.IsRegularOfDegree d) :
     (G.adjMatrix R * fun _ _ => 1) = fun _ _ => d := by ext x; simp [← hd x, degree]
-#align theorems_100.friendship.adj_matrix_sq_mul_const_one_of_regular Theorems100.Friendship.adjMatrix_sq_mul_const_one_of_regular
+#align theorems_100.friendship.adj_matrix_sq_mul_const_one_of_regular Theorems100.Friendship.adjMatrix_sq_hMul_const_one_of_regular
 
-theorem adjMatrix_mul_const_one_mod_p_of_regular {p : ℕ} (dmod : (d : ZMod p) = 1)
+theorem adjMatrix_hMul_const_one_mod_p_of_regular {p : ℕ} (dmod : (d : ZMod p) = 1)
     (hd : G.IsRegularOfDegree d) : (G.adjMatrix (ZMod p) * fun _ _ => 1) = fun _ _ => 1 := by
   rw [adj_matrix_sq_mul_const_one_of_regular hd, dmod]
-#align theorems_100.friendship.adj_matrix_mul_const_one_mod_p_of_regular Theorems100.Friendship.adjMatrix_mul_const_one_mod_p_of_regular
+#align theorems_100.friendship.adj_matrix_mul_const_one_mod_p_of_regular Theorems100.Friendship.adjMatrix_hMul_const_one_mod_p_of_regular
 
 /-- Modulo a factor of `d-1`, the square and all higher powers of the adjacency matrix
   of a `d`-regular friendship graph reduce to the matrix whose entries are all 1. -/

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

@@ -2,11 +2,6 @@
 Copyright (c) 2020 Aaron Anderson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Aaron Anderson, Jalex Stark, Kyle Miller
-
-! This file was ported from Lean 3 source module wiedijk_100_theorems.friendship_graphs
-! leanprover-community/mathlib commit 08b081ea92d80e3a41f899eea36ef6d56e0f1db0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Combinatorics.SimpleGraph.AdjMatrix
 import Mathbin.LinearAlgebra.Matrix.Charpoly.FiniteField
@@ -14,6 +9,8 @@ import Mathbin.Data.Int.Modeq
 import Mathbin.Data.Zmod.Basic
 import Mathbin.Tactic.IntervalCases
 
+#align_import wiedijk_100_theorems.friendship_graphs from "leanprover-community/mathlib"@"08b081ea92d80e3a41f899eea36ef6d56e0f1db0"
+
 /-!
 # The Friendship Theorem
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/bf2428c9486c407ca38b5b3fb10b87dad0bc99fa

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Aaron Anderson, Jalex Stark, Kyle Miller
 
 ! This file was ported from Lean 3 source module wiedijk_100_theorems.friendship_graphs
-! leanprover-community/mathlib commit 5563b1b49e86e135e8c7b556da5ad2f5ff881cad
+! leanprover-community/mathlib commit 08b081ea92d80e3a41f899eea36ef6d56e0f1db0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -17,6 +17,9 @@ import Mathbin.Tactic.IntervalCases
 /-!
 # The Friendship Theorem
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 ## Definitions and Statement
 - A `friendship` graph is one in which any two distinct vertices have exactly one neighbor in common
 - A `politician`, at least in the context of this problem, is a vertex in a graph which is adjacent

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

@@ -130,7 +130,7 @@ theorem degree_eq_of_not_adj {v w : V} (hvw : ¬G.Adj v w) : degree G v = degree
 theorem adjMatrix_sq_of_regular (hd : G.IsRegularOfDegree d) :
     G.adjMatrix R ^ 2 = fun v w => if v = w then d else 1 :=
   by
-  ext (v w); by_cases h : v = w
+  ext v w; by_cases h : v = w
   · rw [h, sq, mul_eq_mul, adj_matrix_mul_self_apply_self, hd]; simp
   · rw [adj_matrix_sq_of_ne R hG h, if_neg h]
 #align theorems_100.friendship.adj_matrix_sq_of_regular Theorems100.Friendship.adjMatrix_sq_of_regular

mathlib commit https://github.com/leanprover-community/mathlib/commit/893964fc28cefbcffc7cb784ed00a2895b4e65cf

@@ -3,8 +3,8 @@ Copyright (c) 2020 Aaron Anderson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Aaron Anderson, Jalex Stark, Kyle Miller
 
-! This file was ported from Lean 3 source module «100-theorems-list».«83_friendship_graphs»
-! leanprover-community/mathlib commit 328375597f2c0dd00522d9c2e5a33b6a6128feeb
+! This file was ported from Lean 3 source module wiedijk_100_theorems.friendship_graphs
+! leanprover-community/mathlib commit 5563b1b49e86e135e8c7b556da5ad2f5ff881cad
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/

Now that I am defining NNRat.cast, I want a definitive answer to this naming issue. Plenty of lemmas in mathlib already use natCast/intCast/ratCast over nat_cast/int_cast/rat_cast, and this matches with the general expectation that underscore-separated name parts correspond to a single declaration.

@@ -240,7 +240,7 @@ variable [Nonempty V]
 theorem false_of_three_le_degree (hd : G.IsRegularOfDegree d) (h : 3 ≤ d) : False := by
   -- get a prime factor of d - 1
   let p : ℕ := (d - 1).minFac
-  have p_dvd_d_pred := (ZMod.nat_cast_zmod_eq_zero_iff_dvd _ _).mpr (d - 1).minFac_dvd
+  have p_dvd_d_pred := (ZMod.natCast_zmod_eq_zero_iff_dvd _ _).mpr (d - 1).minFac_dvd
   have dpos : 1 ≤ d := by linarith
   have d_cast : ↑(d - 1) = (d : ℤ) - 1 := by norm_cast
   haveI : Fact p.Prime := ⟨Nat.minFac_prime (by linarith)⟩
@@ -260,7 +260,7 @@ theorem false_of_three_le_degree (hd : G.IsRegularOfDegree d) (h : 3 ≤ d) : Fa
   dsimp only [Fintype.card] at Vmod
   simp only [Matrix.trace, Matrix.diag, mul_one, nsmul_eq_mul, LinearMap.coe_mk, sum_const,
     of_apply, Ne]
-  rw [Vmod, ← Nat.cast_one (R := ZMod (Nat.minFac (d - 1))), ZMod.nat_cast_zmod_eq_zero_iff_dvd,
+  rw [Vmod, ← Nat.cast_one (R := ZMod (Nat.minFac (d - 1))), ZMod.natCast_zmod_eq_zero_iff_dvd,
     Nat.dvd_one, Nat.minFac_eq_one_iff]
   linarith
 #align theorems_100.friendship.false_of_three_le_degree Theorems100.Friendship.false_of_three_le_degree

@@ -181,7 +181,7 @@ theorem card_of_regular (hd : G.IsRegularOfDegree d) : d + (Fintype.card V - 1)
   trans ((G.adjMatrix ℕ ^ 2) *ᵥ (fun _ => 1)) v
   · rw [adjMatrix_sq_of_regular hG hd, mulVec, dotProduct, ← insert_erase (mem_univ v)]
     simp only [sum_insert, mul_one, if_true, Nat.cast_id, eq_self_iff_true, mem_erase, not_true,
-      Ne.def, not_false_iff, add_right_inj, false_and_iff, of_apply]
+      Ne, not_false_iff, add_right_inj, false_and_iff, of_apply]
     rw [Finset.sum_const_nat, card_erase_of_mem (mem_univ v), mul_one]; · rfl
     intro x hx; simp [(ne_of_mem_erase hx).symm]
   · rw [sq, ← mulVec_mulVec]
@@ -259,7 +259,7 @@ theorem false_of_three_le_degree (hd : G.IsRegularOfDegree d) (h : 3 ≤ d) : Fa
   rw [adjMatrix_pow_mod_p_of_regular hG dmod hd hp2]
   dsimp only [Fintype.card] at Vmod
   simp only [Matrix.trace, Matrix.diag, mul_one, nsmul_eq_mul, LinearMap.coe_mk, sum_const,
-    of_apply, Ne.def]
+    of_apply, Ne]
   rw [Vmod, ← Nat.cast_one (R := ZMod (Nat.minFac (d - 1))), ZMod.nat_cast_zmod_eq_zero_iff_dvd,
     Nat.dvd_one, Nat.minFac_eq_one_iff]
   linarith

We change the following field in the definition of an additive commutative monoid:

 nsmul_succ : ∀ (n : ℕ) (x : G),
-  AddMonoid.nsmul (n + 1) x = x + AddMonoid.nsmul n x
+  AddMonoid.nsmul (n + 1) x = AddMonoid.nsmul n x + x

where the latter is more natural

We adjust the definitions of ^ in monoids, groups, etc. Originally there was a warning comment about why this natural order was preferred

use x * npowRec n x and not npowRec n x * x in the definition to make sure that definitional unfolding of npowRec is blocked, to avoid deep recursion issues.

but it seems to no longer apply.

Remarks on the PR :

• pow_succ and pow_succ' have switched their meanings.
• Most of the time, the proofs were adjusted by priming/unpriming one lemma, or exchanging left and right; a few proofs were more complicated to adjust.
• In particular, [Mathlib/NumberTheory/RamificationInertia.lean] used Ideal.IsPrime.mul_mem_pow which is defined in [Mathlib/RingTheory/DedekindDomain/Ideal.lean]. Changing the order of operation forced me to add the symmetric lemma Ideal.IsPrime.mem_pow_mul.
• the docstring for Cauchy condensation test in [Mathlib/Analysis/PSeries.lean] was mathematically incorrect, I added the mention that the function is antitone.

@@ -93,7 +93,7 @@ theorem adjMatrix_sq_of_ne {v w : V} (hvw : v ≠ w) :
   We use it to show that nonadjacent vertices have equal degrees. -/
 theorem adjMatrix_pow_three_of_not_adj {v w : V} (non_adj : ¬G.Adj v w) :
     (G.adjMatrix R ^ 3 : Matrix V V R) v w = degree G v := by
-  rw [pow_succ, adjMatrix_mul_apply, degree, card_eq_sum_ones, Nat.cast_sum]
+  rw [pow_succ', adjMatrix_mul_apply, degree, card_eq_sum_ones, Nat.cast_sum]
   apply sum_congr rfl
   intro x hx
   rw [adjMatrix_sq_of_ne _ hG, Nat.cast_one]
@@ -226,7 +226,7 @@ theorem adjMatrix_pow_mod_p_of_regular {p : ℕ} (dmod : (d : ZMod p) = 1)
   | k + 2 =>
     induction' k with k hind
     · exact adjMatrix_sq_mod_p_of_regular hG dmod hd
-    rw [pow_succ, hind (Nat.le_add_left 2 k)]
+    rw [pow_succ', hind (Nat.le_add_left 2 k)]
     exact adjMatrix_mul_const_one_mod_p_of_regular dmod hd
 #align theorems_100.friendship.adj_matrix_pow_mod_p_of_regular Theorems100.Friendship.adjMatrix_pow_mod_p_of_regular
 

Zulip discussion: https://leanprover.zulipchat.com/#narrow/stream/113488-general/topic/Notation.20for.20mul_vec.20and.20vec_mul

Co-authored-by: Martin Dvorak <mdvorak@ista.ac.at>

@@ -178,7 +178,7 @@ theorem isRegularOf_not_existsPolitician (hG' : ¬ExistsPolitician G) :
   This essentially means that the graph has `d ^ 2 - d + 1` vertices. -/
 theorem card_of_regular (hd : G.IsRegularOfDegree d) : d + (Fintype.card V - 1) = d * d := by
   have v := Classical.arbitrary V
-  trans (G.adjMatrix ℕ ^ 2).mulVec (fun _ => 1) v
+  trans ((G.adjMatrix ℕ ^ 2) *ᵥ (fun _ => 1)) v
   · rw [adjMatrix_sq_of_regular hG hd, mulVec, dotProduct, ← insert_erase (mem_univ v)]
     simp only [sum_insert, mul_one, if_true, Nat.cast_id, eq_self_iff_true, mem_erase, not_true,
       Ne.def, not_false_iff, add_right_inj, false_and_iff, of_apply]

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

From LeanAPAP

@@ -254,7 +254,7 @@ theorem false_of_three_le_degree (hd : G.IsRegularOfDegree d) (h : 3 ≤ d) : Fa
   have := ZMod.trace_pow_card (G.adjMatrix (ZMod p))
   contrapose! this; clear this
   -- the trace is 0 mod p when computed one way
-  rw [trace_adjMatrix, zero_pow (Fact.out (p := p.Prime)).pos]
+  rw [trace_adjMatrix, zero_pow this.out.ne_zero]
   -- but the trace is 1 mod p when computed the other way
   rw [adjMatrix_pow_mod_p_of_regular hG dmod hd hp2]
   dsimp only [Fintype.card] at Vmod

The main difficulty here is that * has a slightly difference precedence to ⬝. notably around smul and neg.

The other annoyance is that ↑U ⬝ A ⬝ ↑U⁻¹ : Matrix m m 𝔸 now has to be written U.val * A * (U⁻¹).val in order to typecheck.

A downside of this change to consider: if you have a goal of A * (B * C) = (A * B) * C, mul_assoc now gives the illusion of matching, when in fact Matrix.mul_assoc is needed. Previously the distinct symbol made it easy to avoid this mistake.

On the flipside, there is now no need to rewrite by Matrix.mul_eq_mul all the time (indeed, the lemma is now removed).

@@ -93,7 +93,7 @@ theorem adjMatrix_sq_of_ne {v w : V} (hvw : v ≠ w) :
   We use it to show that nonadjacent vertices have equal degrees. -/
 theorem adjMatrix_pow_three_of_not_adj {v w : V} (non_adj : ¬G.Adj v w) :
     (G.adjMatrix R ^ 3 : Matrix V V R) v w = degree G v := by
-  rw [pow_succ, mul_eq_mul, adjMatrix_mul_apply, degree, card_eq_sum_ones, Nat.cast_sum]
+  rw [pow_succ, adjMatrix_mul_apply, degree, card_eq_sum_ones, Nat.cast_sum]
   apply sum_congr rfl
   intro x hx
   rw [adjMatrix_sq_of_ne _ hG, Nat.cast_one]
@@ -114,8 +114,8 @@ theorem degree_eq_of_not_adj {v w : V} (hvw : ¬G.Adj v w) : degree G v = degree
     ← adjMatrix_pow_three_of_not_adj ℕ hG hvw,
     ← adjMatrix_pow_three_of_not_adj ℕ hG fun h => hvw (G.symm h)]
   conv_lhs => rw [← transpose_adjMatrix]
-  simp only [pow_succ _ 2, sq, mul_eq_mul, ← transpose_mul, transpose_apply]
-  simp only [← mul_eq_mul, mul_assoc]
+  simp only [pow_succ _ 2, sq, ← transpose_mul, transpose_apply]
+  simp only [mul_assoc]
 #align theorems_100.friendship.degree_eq_of_not_adj Theorems100.Friendship.degree_eq_of_not_adj
 
 /-- Let `A` be the adjacency matrix of a graph `G`.
@@ -125,7 +125,7 @@ theorem degree_eq_of_not_adj {v w : V} (hvw : ¬G.Adj v w) : degree G v = degree
 theorem adjMatrix_sq_of_regular (hd : G.IsRegularOfDegree d) :
     G.adjMatrix R ^ 2 = of fun v w => if v = w then (d : R) else (1 : R) := by
   ext (v w); by_cases h : v = w
-  · rw [h, sq, mul_eq_mul, adjMatrix_mul_self_apply_self, hd]; simp
+  · rw [h, sq, adjMatrix_mul_self_apply_self, hd]; simp
   · rw [adjMatrix_sq_of_ne R hG h, of_apply, if_neg h]
 #align theorems_100.friendship.adj_matrix_sq_of_regular Theorems100.Friendship.adjMatrix_sq_of_regular
 
@@ -184,7 +184,7 @@ theorem card_of_regular (hd : G.IsRegularOfDegree d) : d + (Fintype.card V - 1)
       Ne.def, not_false_iff, add_right_inj, false_and_iff, of_apply]
     rw [Finset.sum_const_nat, card_erase_of_mem (mem_univ v), mul_one]; · rfl
     intro x hx; simp [(ne_of_mem_erase hx).symm]
-  · rw [sq, mul_eq_mul, ← mulVec_mulVec]
+  · rw [sq, ← mulVec_mulVec]
     simp only [adjMatrix_mulVec_const_apply_of_regular hd, neighborFinset,
       card_neighborSet_eq_degree, hd v, Function.const_def, adjMatrix_mulVec_apply _ _ (mulVec _ _),
       mul_one, sum_const, Set.toFinset_card, Algebra.id.smul_eq_mul, Nat.cast_id]
@@ -206,7 +206,7 @@ end Nonempty
 theorem adjMatrix_sq_mul_const_one_of_regular (hd : G.IsRegularOfDegree d) :
     G.adjMatrix R * of (fun _ _ => 1) = of (fun _ _ => (d : R)) := by
   ext x
-  simp only [← hd x, degree, mul_eq_mul, adjMatrix_mul_apply, sum_const, Nat.smul_one_eq_coe,
+  simp only [← hd x, degree, adjMatrix_mul_apply, sum_const, Nat.smul_one_eq_coe,
     of_apply]
 #align theorems_100.friendship.adj_matrix_sq_mul_const_one_of_regular Theorems100.Friendship.adjMatrix_sq_mul_const_one_of_regular
 

• depends on: #5966

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

@@ -2,11 +2,6 @@
 Copyright (c) 2020 Aaron Anderson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Aaron Anderson, Jalex Stark, Kyle Miller
-
-! This file was ported from Lean 3 source module wiedijk_100_theorems.friendship_graphs
-! leanprover-community/mathlib commit 5563b1b49e86e135e8c7b556da5ad2f5ff881cad
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Combinatorics.SimpleGraph.AdjMatrix
 import Mathlib.LinearAlgebra.Matrix.Charpoly.FiniteField
@@ -14,6 +9,8 @@ import Mathlib.Data.Int.ModEq
 import Mathlib.Data.ZMod.Basic
 import Mathlib.Tactic.IntervalCases
 
+#align_import wiedijk_100_theorems.friendship_graphs from "leanprover-community/mathlib"@"5563b1b49e86e135e8c7b556da5ad2f5ff881cad"
+
 /-!
 # The Friendship Theorem