combinatorics.simple_graph.inc_matrix | Mathlib porting status

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

bb168510

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

75be6b61

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -157,7 +157,7 @@ theorem sum_incMatrix_apply_of_mem_edgeSet : e ∈ G.edgeSetEmbedding → ∑ a,
   classical
   refine' e.ind _
   intro a b h
-  rw [mem_edge_set] at h 
+  rw [mem_edge_set] at h
   rw [← Nat.cast_two, ← card_doubleton h.ne]
   simp only [inc_matrix_apply', sum_boole, mk_mem_incidence_set_iff, h, true_and_iff]
   congr 2

75be6b61

bump to nightly-2024-02-01-06

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

5433bded

Diff

@@ -85,7 +85,9 @@ variable [MulZeroOneClass R] {a b : α} {e : Sym2 α}
 #print SimpleGraph.incMatrix_apply_mul_incMatrix_apply /-
 theorem incMatrix_apply_mul_incMatrix_apply :
     G.incMatrix R a e * G.incMatrix R b e = (G.incidenceSet a ∩ G.incidenceSet b).indicator 1 e :=
-  by classical
+  by
+  classical simp only [inc_matrix, Set.indicator_apply, ← ite_zero_mul_ite_zero, Pi.one_apply,
+    mul_one, Set.mem_inter_iff]
 #align simple_graph.inc_matrix_apply_mul_inc_matrix_apply SimpleGraph.incMatrix_apply_mul_incMatrix_apply
 -/
 
@@ -151,7 +153,16 @@ theorem incMatrix_mul_transpose_diag [DecidableEq α] [DecidableRel G.Adj] :
 
 #print SimpleGraph.sum_incMatrix_apply_of_mem_edgeSet /-
 theorem sum_incMatrix_apply_of_mem_edgeSet : e ∈ G.edgeSetEmbedding → ∑ a, G.incMatrix R a e = 2 :=
-  by classical
+  by
+  classical
+  refine' e.ind _
+  intro a b h
+  rw [mem_edge_set] at h 
+  rw [← Nat.cast_two, ← card_doubleton h.ne]
+  simp only [inc_matrix_apply', sum_boole, mk_mem_incidence_set_iff, h, true_and_iff]
+  congr 2
+  ext e
+  simp only [mem_filter, mem_univ, true_and_iff, mem_insert, mem_singleton]
 #align simple_graph.sum_inc_matrix_apply_of_mem_edge_set SimpleGraph.sum_incMatrix_apply_of_mem_edgeSet
 -/
 
@@ -164,7 +175,23 @@ theorem sum_incMatrix_apply_of_not_mem_edgeSet (h : e ∉ G.edgeSetEmbedding) :
 
 #print SimpleGraph.incMatrix_transpose_mul_diag /-
 theorem incMatrix_transpose_mul_diag [DecidableRel G.Adj] :
-    ((G.incMatrix R)ᵀ ⬝ G.incMatrix R) e e = if e ∈ G.edgeSetEmbedding then 2 else 0 := by classical
+    ((G.incMatrix R)ᵀ ⬝ G.incMatrix R) e e = if e ∈ G.edgeSetEmbedding then 2 else 0 := by
+  classical
+  simp only [Matrix.mul_apply, inc_matrix_apply', transpose_apply, ← ite_zero_mul_ite_zero, one_mul,
+    sum_boole, and_self_iff]
+  split_ifs with h
+  · revert h
+    refine' e.ind _
+    intro v w h
+    rw [← Nat.cast_two, ← card_doubleton (G.ne_of_adj h)]
+    simp [mk_mem_incidence_set_iff, G.mem_edge_set.mp h]
+    congr 2
+    ext u
+    simp
+  · revert h
+    refine' e.ind _
+    intro v w h
+    simp [mk_mem_incidence_set_iff, G.mem_edge_set.not.mp h]
 #align simple_graph.inc_matrix_transpose_mul_diag SimpleGraph.incMatrix_transpose_mul_diag
 -/
 
@@ -176,7 +203,14 @@ variable [Fintype (Sym2 α)] [Semiring R] {a b : α} {e : Sym2 α}
 
 #print SimpleGraph.incMatrix_mul_transpose_apply_of_adj /-
 theorem incMatrix_mul_transpose_apply_of_adj (h : G.Adj a b) :
-    (G.incMatrix R ⬝ (G.incMatrix R)ᵀ) a b = (1 : R) := by classical
+    (G.incMatrix R ⬝ (G.incMatrix R)ᵀ) a b = (1 : R) := by
+  classical
+  simp_rw [Matrix.mul_apply, Matrix.transpose_apply, inc_matrix_apply_mul_inc_matrix_apply,
+    Set.indicator_apply, Pi.one_apply, sum_boole]
+  convert Nat.cast_one
+  convert card_singleton ⟦(a, b)⟧
+  rw [← coe_eq_singleton, coe_filter_univ]
+  exact G.incidence_set_inter_incidence_set_of_adj h
 #align simple_graph.inc_matrix_mul_transpose_apply_of_adj SimpleGraph.incMatrix_mul_transpose_apply_of_adj
 -/

75be6b61

bump to nightly-2024-01-31-06

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

61100fe9

Diff

@@ -85,9 +85,7 @@ variable [MulZeroOneClass R] {a b : α} {e : Sym2 α}
 #print SimpleGraph.incMatrix_apply_mul_incMatrix_apply /-
 theorem incMatrix_apply_mul_incMatrix_apply :
     G.incMatrix R a e * G.incMatrix R b e = (G.incidenceSet a ∩ G.incidenceSet b).indicator 1 e :=
-  by
-  classical simp only [inc_matrix, Set.indicator_apply, ← ite_zero_mul_ite_zero, Pi.one_apply,
-    mul_one, Set.mem_inter_iff]
+  by classical
 #align simple_graph.inc_matrix_apply_mul_inc_matrix_apply SimpleGraph.incMatrix_apply_mul_incMatrix_apply
 -/
 
@@ -153,16 +151,7 @@ theorem incMatrix_mul_transpose_diag [DecidableEq α] [DecidableRel G.Adj] :
 
 #print SimpleGraph.sum_incMatrix_apply_of_mem_edgeSet /-
 theorem sum_incMatrix_apply_of_mem_edgeSet : e ∈ G.edgeSetEmbedding → ∑ a, G.incMatrix R a e = 2 :=
-  by
-  classical
-  refine' e.ind _
-  intro a b h
-  rw [mem_edge_set] at h 
-  rw [← Nat.cast_two, ← card_doubleton h.ne]
-  simp only [inc_matrix_apply', sum_boole, mk_mem_incidence_set_iff, h, true_and_iff]
-  congr 2
-  ext e
-  simp only [mem_filter, mem_univ, true_and_iff, mem_insert, mem_singleton]
+  by classical
 #align simple_graph.sum_inc_matrix_apply_of_mem_edge_set SimpleGraph.sum_incMatrix_apply_of_mem_edgeSet
 -/
 
@@ -175,23 +164,7 @@ theorem sum_incMatrix_apply_of_not_mem_edgeSet (h : e ∉ G.edgeSetEmbedding) :
 
 #print SimpleGraph.incMatrix_transpose_mul_diag /-
 theorem incMatrix_transpose_mul_diag [DecidableRel G.Adj] :
-    ((G.incMatrix R)ᵀ ⬝ G.incMatrix R) e e = if e ∈ G.edgeSetEmbedding then 2 else 0 := by
-  classical
-  simp only [Matrix.mul_apply, inc_matrix_apply', transpose_apply, ← ite_zero_mul_ite_zero, one_mul,
-    sum_boole, and_self_iff]
-  split_ifs with h
-  · revert h
-    refine' e.ind _
-    intro v w h
-    rw [← Nat.cast_two, ← card_doubleton (G.ne_of_adj h)]
-    simp [mk_mem_incidence_set_iff, G.mem_edge_set.mp h]
-    congr 2
-    ext u
-    simp
-  · revert h
-    refine' e.ind _
-    intro v w h
-    simp [mk_mem_incidence_set_iff, G.mem_edge_set.not.mp h]
+    ((G.incMatrix R)ᵀ ⬝ G.incMatrix R) e e = if e ∈ G.edgeSetEmbedding then 2 else 0 := by classical
 #align simple_graph.inc_matrix_transpose_mul_diag SimpleGraph.incMatrix_transpose_mul_diag
 -/
 
@@ -203,14 +176,7 @@ variable [Fintype (Sym2 α)] [Semiring R] {a b : α} {e : Sym2 α}
 
 #print SimpleGraph.incMatrix_mul_transpose_apply_of_adj /-
 theorem incMatrix_mul_transpose_apply_of_adj (h : G.Adj a b) :
-    (G.incMatrix R ⬝ (G.incMatrix R)ᵀ) a b = (1 : R) := by
-  classical
-  simp_rw [Matrix.mul_apply, Matrix.transpose_apply, inc_matrix_apply_mul_inc_matrix_apply,
-    Set.indicator_apply, Pi.one_apply, sum_boole]
-  convert Nat.cast_one
-  convert card_singleton ⟦(a, b)⟧
-  rw [← coe_eq_singleton, coe_filter_univ]
-  exact G.incidence_set_inter_incidence_set_of_adj h
+    (G.incMatrix R ⬝ (G.incMatrix R)ᵀ) a b = (1 : R) := by classical
 #align simple_graph.inc_matrix_mul_transpose_apply_of_adj SimpleGraph.incMatrix_mul_transpose_apply_of_adj
 -/

75be6b61

bump to nightly-2023-12-06-06

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

d09917f6

Diff

@@ -86,8 +86,8 @@ variable [MulZeroOneClass R] {a b : α} {e : Sym2 α}
 theorem incMatrix_apply_mul_incMatrix_apply :
     G.incMatrix R a e * G.incMatrix R b e = (G.incidenceSet a ∩ G.incidenceSet b).indicator 1 e :=
   by
-  classical simp only [inc_matrix, Set.indicator_apply, ← ite_and_mul_zero, Pi.one_apply, mul_one,
-    Set.mem_inter_iff]
+  classical simp only [inc_matrix, Set.indicator_apply, ← ite_zero_mul_ite_zero, Pi.one_apply,
+    mul_one, Set.mem_inter_iff]
 #align simple_graph.inc_matrix_apply_mul_inc_matrix_apply SimpleGraph.incMatrix_apply_mul_incMatrix_apply
 -/
 
@@ -147,7 +147,7 @@ theorem incMatrix_mul_transpose_diag [DecidableEq α] [DecidableRel G.Adj] :
     (G.incMatrix R ⬝ (G.incMatrix R)ᵀ) a a = G.degree a :=
   by
   rw [← sum_inc_matrix_apply]
-  simp [Matrix.mul_apply, inc_matrix_apply', ← ite_and_mul_zero]
+  simp [Matrix.mul_apply, inc_matrix_apply', ← ite_zero_mul_ite_zero]
 #align simple_graph.inc_matrix_mul_transpose_diag SimpleGraph.incMatrix_mul_transpose_diag
 -/
 
@@ -177,7 +177,7 @@ theorem sum_incMatrix_apply_of_not_mem_edgeSet (h : e ∉ G.edgeSetEmbedding) :
 theorem incMatrix_transpose_mul_diag [DecidableRel G.Adj] :
     ((G.incMatrix R)ᵀ ⬝ G.incMatrix R) e e = if e ∈ G.edgeSetEmbedding then 2 else 0 := by
   classical
-  simp only [Matrix.mul_apply, inc_matrix_apply', transpose_apply, ← ite_and_mul_zero, one_mul,
+  simp only [Matrix.mul_apply, inc_matrix_apply', transpose_apply, ← ite_zero_mul_ite_zero, one_mul,
     sum_boole, and_self_iff]
   split_ifs with h
   · revert h

75be6b61

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2021 Gabriel Moise. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Gabriel Moise, Yaël Dillies, Kyle Miller
 -/
-import Mathbin.Combinatorics.SimpleGraph.Basic
-import Mathbin.Data.Matrix.Basic
+import Combinatorics.SimpleGraph.Basic
+import Data.Matrix.Basic
 
 #align_import combinatorics.simple_graph.inc_matrix from "leanprover-community/mathlib"@"75be6b616681ab6ca66d798ead117e75cd64f125"

75be6b61

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Gabriel Moise. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Gabriel Moise, Yaël Dillies, Kyle Miller
-
-! This file was ported from Lean 3 source module combinatorics.simple_graph.inc_matrix
-! leanprover-community/mathlib commit 75be6b616681ab6ca66d798ead117e75cd64f125
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Combinatorics.SimpleGraph.Basic
 import Mathbin.Data.Matrix.Basic
 
+#align_import combinatorics.simple_graph.inc_matrix from "leanprover-community/mathlib"@"75be6b616681ab6ca66d798ead117e75cd64f125"
+
 /-!
 # Incidence matrix of a simple graph

75be6b61

bump to nightly-2023-06-20-01

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

9b351f8c

Diff

@@ -222,7 +222,7 @@ theorem incMatrix_mul_transpose [Fintype α] [DecidableEq α] [DecidableRel G.Ad
     G.incMatrix R ⬝ (G.incMatrix R)ᵀ = fun a b =>
       if a = b then G.degree a else if G.Adj a b then 1 else 0 :=
   by
-  ext (a b)
+  ext a b
   split_ifs with h h'
   · subst b
     convert G.inc_matrix_mul_transpose_diag

75be6b61

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -67,27 +67,34 @@ noncomputable def incMatrix [Zero R] [One R] : Matrix α (Sym2 α) R := fun a =>
 
 variable {R}
 
+#print SimpleGraph.incMatrix_apply /-
 theorem incMatrix_apply [Zero R] [One R] {a : α} {e : Sym2 α} :
     G.incMatrix R a e = (G.incidenceSet a).indicator 1 e :=
   rfl
 #align simple_graph.inc_matrix_apply SimpleGraph.incMatrix_apply
+-/
 
+#print SimpleGraph.incMatrix_apply' /-
 /-- Entries of the incidence matrix can be computed given additional decidable instances. -/
 theorem incMatrix_apply' [Zero R] [One R] [DecidableEq α] [DecidableRel G.Adj] {a : α}
     {e : Sym2 α} : G.incMatrix R a e = if e ∈ G.incidenceSet a then 1 else 0 := by convert rfl
 #align simple_graph.inc_matrix_apply' SimpleGraph.incMatrix_apply'
+-/
 
 section MulZeroOneClass
 
 variable [MulZeroOneClass R] {a b : α} {e : Sym2 α}
 
+#print SimpleGraph.incMatrix_apply_mul_incMatrix_apply /-
 theorem incMatrix_apply_mul_incMatrix_apply :
     G.incMatrix R a e * G.incMatrix R b e = (G.incidenceSet a ∩ G.incidenceSet b).indicator 1 e :=
   by
   classical simp only [inc_matrix, Set.indicator_apply, ← ite_and_mul_zero, Pi.one_apply, mul_one,
     Set.mem_inter_iff]
 #align simple_graph.inc_matrix_apply_mul_inc_matrix_apply SimpleGraph.incMatrix_apply_mul_incMatrix_apply
+-/
 
+#print SimpleGraph.incMatrix_apply_mul_incMatrix_apply_of_not_adj /-
 theorem incMatrix_apply_mul_incMatrix_apply_of_not_adj (hab : a ≠ b) (h : ¬G.Adj a b) :
     G.incMatrix R a e * G.incMatrix R b e = 0 :=
   by
@@ -95,26 +102,35 @@ theorem incMatrix_apply_mul_incMatrix_apply_of_not_adj (hab : a ≠ b) (h : ¬G.
   rw [G.incidence_set_inter_incidence_set_of_not_adj h hab]
   exact Set.not_mem_empty e
 #align simple_graph.inc_matrix_apply_mul_inc_matrix_apply_of_not_adj SimpleGraph.incMatrix_apply_mul_incMatrix_apply_of_not_adj
+-/
 
+#print SimpleGraph.incMatrix_of_not_mem_incidenceSet /-
 theorem incMatrix_of_not_mem_incidenceSet (h : e ∉ G.incidenceSet a) : G.incMatrix R a e = 0 := by
   rw [inc_matrix_apply, Set.indicator_of_not_mem h]
 #align simple_graph.inc_matrix_of_not_mem_incidence_set SimpleGraph.incMatrix_of_not_mem_incidenceSet
+-/
 
+#print SimpleGraph.incMatrix_of_mem_incidenceSet /-
 theorem incMatrix_of_mem_incidenceSet (h : e ∈ G.incidenceSet a) : G.incMatrix R a e = 1 := by
   rw [inc_matrix_apply, Set.indicator_of_mem h, Pi.one_apply]
 #align simple_graph.inc_matrix_of_mem_incidence_set SimpleGraph.incMatrix_of_mem_incidenceSet
+-/
 
 variable [Nontrivial R]
 
+#print SimpleGraph.incMatrix_apply_eq_zero_iff /-
 theorem incMatrix_apply_eq_zero_iff : G.incMatrix R a e = 0 ↔ e ∉ G.incidenceSet a :=
   by
   simp only [inc_matrix_apply, Set.indicator_apply_eq_zero, Pi.one_apply, one_ne_zero]
   exact Iff.rfl
 #align simple_graph.inc_matrix_apply_eq_zero_iff SimpleGraph.incMatrix_apply_eq_zero_iff
+-/
 
+#print SimpleGraph.incMatrix_apply_eq_one_iff /-
 theorem incMatrix_apply_eq_one_iff : G.incMatrix R a e = 1 ↔ e ∈ G.incidenceSet a := by
   convert one_ne_zero.ite_eq_left_iff; infer_instance
 #align simple_graph.inc_matrix_apply_eq_one_iff SimpleGraph.incMatrix_apply_eq_one_iff
+-/
 
 end MulZeroOneClass
 
@@ -122,18 +138,23 @@ section NonAssocSemiring
 
 variable [Fintype α] [NonAssocSemiring R] {a b : α} {e : Sym2 α}
 
+#print SimpleGraph.sum_incMatrix_apply /-
 theorem sum_incMatrix_apply [DecidableEq α] [DecidableRel G.Adj] :
     ∑ e, G.incMatrix R a e = G.degree a := by
   simp [inc_matrix_apply', sum_boole, Set.filter_mem_univ_eq_toFinset]
 #align simple_graph.sum_inc_matrix_apply SimpleGraph.sum_incMatrix_apply
+-/
 
+#print SimpleGraph.incMatrix_mul_transpose_diag /-
 theorem incMatrix_mul_transpose_diag [DecidableEq α] [DecidableRel G.Adj] :
     (G.incMatrix R ⬝ (G.incMatrix R)ᵀ) a a = G.degree a :=
   by
   rw [← sum_inc_matrix_apply]
   simp [Matrix.mul_apply, inc_matrix_apply', ← ite_and_mul_zero]
 #align simple_graph.inc_matrix_mul_transpose_diag SimpleGraph.incMatrix_mul_transpose_diag
+-/
 
+#print SimpleGraph.sum_incMatrix_apply_of_mem_edgeSet /-
 theorem sum_incMatrix_apply_of_mem_edgeSet : e ∈ G.edgeSetEmbedding → ∑ a, G.incMatrix R a e = 2 :=
   by
   classical
@@ -146,12 +167,16 @@ theorem sum_incMatrix_apply_of_mem_edgeSet : e ∈ G.edgeSetEmbedding → ∑ a,
   ext e
   simp only [mem_filter, mem_univ, true_and_iff, mem_insert, mem_singleton]
 #align simple_graph.sum_inc_matrix_apply_of_mem_edge_set SimpleGraph.sum_incMatrix_apply_of_mem_edgeSet
+-/
 
+#print SimpleGraph.sum_incMatrix_apply_of_not_mem_edgeSet /-
 theorem sum_incMatrix_apply_of_not_mem_edgeSet (h : e ∉ G.edgeSetEmbedding) :
     ∑ a, G.incMatrix R a e = 0 :=
   sum_eq_zero fun a _ => G.incMatrix_of_not_mem_incidenceSet fun he => h he.1
 #align simple_graph.sum_inc_matrix_apply_of_not_mem_edge_set SimpleGraph.sum_incMatrix_apply_of_not_mem_edgeSet
+-/
 
+#print SimpleGraph.incMatrix_transpose_mul_diag /-
 theorem incMatrix_transpose_mul_diag [DecidableRel G.Adj] :
     ((G.incMatrix R)ᵀ ⬝ G.incMatrix R) e e = if e ∈ G.edgeSetEmbedding then 2 else 0 := by
   classical
@@ -171,6 +196,7 @@ theorem incMatrix_transpose_mul_diag [DecidableRel G.Adj] :
     intro v w h
     simp [mk_mem_incidence_set_iff, G.mem_edge_set.not.mp h]
 #align simple_graph.inc_matrix_transpose_mul_diag SimpleGraph.incMatrix_transpose_mul_diag
+-/
 
 end NonAssocSemiring
 
@@ -178,6 +204,7 @@ section Semiring
 
 variable [Fintype (Sym2 α)] [Semiring R] {a b : α} {e : Sym2 α}
 
+#print SimpleGraph.incMatrix_mul_transpose_apply_of_adj /-
 theorem incMatrix_mul_transpose_apply_of_adj (h : G.Adj a b) :
     (G.incMatrix R ⬝ (G.incMatrix R)ᵀ) a b = (1 : R) := by
   classical
@@ -188,7 +215,9 @@ theorem incMatrix_mul_transpose_apply_of_adj (h : G.Adj a b) :
   rw [← coe_eq_singleton, coe_filter_univ]
   exact G.incidence_set_inter_incidence_set_of_adj h
 #align simple_graph.inc_matrix_mul_transpose_apply_of_adj SimpleGraph.incMatrix_mul_transpose_apply_of_adj
+-/
 
+#print SimpleGraph.incMatrix_mul_transpose /-
 theorem incMatrix_mul_transpose [Fintype α] [DecidableEq α] [DecidableRel G.Adj] :
     G.incMatrix R ⬝ (G.incMatrix R)ᵀ = fun a b =>
       if a = b then G.degree a else if G.Adj a b then 1 else 0 :=
@@ -202,6 +231,7 @@ theorem incMatrix_mul_transpose [Fintype α] [DecidableEq α] [DecidableRel G.Ad
     simp only [Matrix.mul_apply, Matrix.transpose_apply,
       G.inc_matrix_apply_mul_inc_matrix_apply_of_not_adj h h', sum_const_zero]
 #align simple_graph.inc_matrix_mul_transpose SimpleGraph.incMatrix_mul_transpose
+-/
 
 end Semiring

75be6b61

bump to nightly-2023-06-10-07

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3

3fdc57bc

Diff

@@ -123,7 +123,7 @@ section NonAssocSemiring
 variable [Fintype α] [NonAssocSemiring R] {a b : α} {e : Sym2 α}
 
 theorem sum_incMatrix_apply [DecidableEq α] [DecidableRel G.Adj] :
-    (∑ e, G.incMatrix R a e) = G.degree a := by
+    ∑ e, G.incMatrix R a e = G.degree a := by
   simp [inc_matrix_apply', sum_boole, Set.filter_mem_univ_eq_toFinset]
 #align simple_graph.sum_inc_matrix_apply SimpleGraph.sum_incMatrix_apply
 
@@ -134,8 +134,8 @@ theorem incMatrix_mul_transpose_diag [DecidableEq α] [DecidableRel G.Adj] :
   simp [Matrix.mul_apply, inc_matrix_apply', ← ite_and_mul_zero]
 #align simple_graph.inc_matrix_mul_transpose_diag SimpleGraph.incMatrix_mul_transpose_diag
 
-theorem sum_incMatrix_apply_of_mem_edgeSet :
-    e ∈ G.edgeSetEmbedding → (∑ a, G.incMatrix R a e) = 2 := by
+theorem sum_incMatrix_apply_of_mem_edgeSet : e ∈ G.edgeSetEmbedding → ∑ a, G.incMatrix R a e = 2 :=
+  by
   classical
   refine' e.ind _
   intro a b h
@@ -148,7 +148,7 @@ theorem sum_incMatrix_apply_of_mem_edgeSet :
 #align simple_graph.sum_inc_matrix_apply_of_mem_edge_set SimpleGraph.sum_incMatrix_apply_of_mem_edgeSet
 
 theorem sum_incMatrix_apply_of_not_mem_edgeSet (h : e ∉ G.edgeSetEmbedding) :
-    (∑ a, G.incMatrix R a e) = 0 :=
+    ∑ a, G.incMatrix R a e = 0 :=
   sum_eq_zero fun a _ => G.incMatrix_of_not_mem_incidenceSet fun he => h he.1
 #align simple_graph.sum_inc_matrix_apply_of_not_mem_edge_set SimpleGraph.sum_incMatrix_apply_of_not_mem_edgeSet

75be6b61

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -85,7 +85,7 @@ theorem incMatrix_apply_mul_incMatrix_apply :
     G.incMatrix R a e * G.incMatrix R b e = (G.incidenceSet a ∩ G.incidenceSet b).indicator 1 e :=
   by
   classical simp only [inc_matrix, Set.indicator_apply, ← ite_and_mul_zero, Pi.one_apply, mul_one,
-      Set.mem_inter_iff]
+    Set.mem_inter_iff]
 #align simple_graph.inc_matrix_apply_mul_inc_matrix_apply SimpleGraph.incMatrix_apply_mul_incMatrix_apply
 
 theorem incMatrix_apply_mul_incMatrix_apply_of_not_adj (hab : a ≠ b) (h : ¬G.Adj a b) :
@@ -137,14 +137,14 @@ theorem incMatrix_mul_transpose_diag [DecidableEq α] [DecidableRel G.Adj] :
 theorem sum_incMatrix_apply_of_mem_edgeSet :
     e ∈ G.edgeSetEmbedding → (∑ a, G.incMatrix R a e) = 2 := by
   classical
-    refine' e.ind _
-    intro a b h
-    rw [mem_edge_set] at h 
-    rw [← Nat.cast_two, ← card_doubleton h.ne]
-    simp only [inc_matrix_apply', sum_boole, mk_mem_incidence_set_iff, h, true_and_iff]
-    congr 2
-    ext e
-    simp only [mem_filter, mem_univ, true_and_iff, mem_insert, mem_singleton]
+  refine' e.ind _
+  intro a b h
+  rw [mem_edge_set] at h 
+  rw [← Nat.cast_two, ← card_doubleton h.ne]
+  simp only [inc_matrix_apply', sum_boole, mk_mem_incidence_set_iff, h, true_and_iff]
+  congr 2
+  ext e
+  simp only [mem_filter, mem_univ, true_and_iff, mem_insert, mem_singleton]
 #align simple_graph.sum_inc_matrix_apply_of_mem_edge_set SimpleGraph.sum_incMatrix_apply_of_mem_edgeSet
 
 theorem sum_incMatrix_apply_of_not_mem_edgeSet (h : e ∉ G.edgeSetEmbedding) :
@@ -155,21 +155,21 @@ theorem sum_incMatrix_apply_of_not_mem_edgeSet (h : e ∉ G.edgeSetEmbedding) :
 theorem incMatrix_transpose_mul_diag [DecidableRel G.Adj] :
     ((G.incMatrix R)ᵀ ⬝ G.incMatrix R) e e = if e ∈ G.edgeSetEmbedding then 2 else 0 := by
   classical
-    simp only [Matrix.mul_apply, inc_matrix_apply', transpose_apply, ← ite_and_mul_zero, one_mul,
-      sum_boole, and_self_iff]
-    split_ifs with h
-    · revert h
-      refine' e.ind _
-      intro v w h
-      rw [← Nat.cast_two, ← card_doubleton (G.ne_of_adj h)]
-      simp [mk_mem_incidence_set_iff, G.mem_edge_set.mp h]
-      congr 2
-      ext u
-      simp
-    · revert h
-      refine' e.ind _
-      intro v w h
-      simp [mk_mem_incidence_set_iff, G.mem_edge_set.not.mp h]
+  simp only [Matrix.mul_apply, inc_matrix_apply', transpose_apply, ← ite_and_mul_zero, one_mul,
+    sum_boole, and_self_iff]
+  split_ifs with h
+  · revert h
+    refine' e.ind _
+    intro v w h
+    rw [← Nat.cast_two, ← card_doubleton (G.ne_of_adj h)]
+    simp [mk_mem_incidence_set_iff, G.mem_edge_set.mp h]
+    congr 2
+    ext u
+    simp
+  · revert h
+    refine' e.ind _
+    intro v w h
+    simp [mk_mem_incidence_set_iff, G.mem_edge_set.not.mp h]
 #align simple_graph.inc_matrix_transpose_mul_diag SimpleGraph.incMatrix_transpose_mul_diag
 
 end NonAssocSemiring
@@ -181,12 +181,12 @@ variable [Fintype (Sym2 α)] [Semiring R] {a b : α} {e : Sym2 α}
 theorem incMatrix_mul_transpose_apply_of_adj (h : G.Adj a b) :
     (G.incMatrix R ⬝ (G.incMatrix R)ᵀ) a b = (1 : R) := by
   classical
-    simp_rw [Matrix.mul_apply, Matrix.transpose_apply, inc_matrix_apply_mul_inc_matrix_apply,
-      Set.indicator_apply, Pi.one_apply, sum_boole]
-    convert Nat.cast_one
-    convert card_singleton ⟦(a, b)⟧
-    rw [← coe_eq_singleton, coe_filter_univ]
-    exact G.incidence_set_inter_incidence_set_of_adj h
+  simp_rw [Matrix.mul_apply, Matrix.transpose_apply, inc_matrix_apply_mul_inc_matrix_apply,
+    Set.indicator_apply, Pi.one_apply, sum_boole]
+  convert Nat.cast_one
+  convert card_singleton ⟦(a, b)⟧
+  rw [← coe_eq_singleton, coe_filter_univ]
+  exact G.incidence_set_inter_incidence_set_of_adj h
 #align simple_graph.inc_matrix_mul_transpose_apply_of_adj SimpleGraph.incMatrix_mul_transpose_apply_of_adj
 
 theorem incMatrix_mul_transpose [Fintype α] [DecidableEq α] [DecidableRel G.Adj] :

75be6b61

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -139,7 +139,7 @@ theorem sum_incMatrix_apply_of_mem_edgeSet :
   classical
     refine' e.ind _
     intro a b h
-    rw [mem_edge_set] at h
+    rw [mem_edge_set] at h 
     rw [← Nat.cast_two, ← card_doubleton h.ne]
     simp only [inc_matrix_apply', sum_boole, mk_mem_incidence_set_iff, h, true_and_iff]
     congr 2

75be6b61

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -51,7 +51,7 @@ incidence matrix for each `simple_graph α` has the same type.
 
 open Finset Matrix SimpleGraph Sym2
 
-open BigOperators Matrix
+open scoped BigOperators Matrix
 
 namespace SimpleGraph

75be6b61

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -67,23 +67,11 @@ noncomputable def incMatrix [Zero R] [One R] : Matrix α (Sym2 α) R := fun a =>
 
 variable {R}
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align simple_graph.inc_matrix_apply SimpleGraph.incMatrix_applyₓ'. -/
 theorem incMatrix_apply [Zero R] [One R] {a : α} {e : Sym2 α} :
     G.incMatrix R a e = (G.incidenceSet a).indicator 1 e :=
   rfl
 #align simple_graph.inc_matrix_apply SimpleGraph.incMatrix_apply
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align simple_graph.inc_matrix_apply' SimpleGraph.incMatrix_apply'ₓ'. -/
 /-- Entries of the incidence matrix can be computed given additional decidable instances. -/
 theorem incMatrix_apply' [Zero R] [One R] [DecidableEq α] [DecidableRel G.Adj] {a : α}
     {e : Sym2 α} : G.incMatrix R a e = if e ∈ G.incidenceSet a then 1 else 0 := by convert rfl
@@ -93,12 +81,6 @@ section MulZeroOneClass
 
 variable [MulZeroOneClass R] {a b : α} {e : Sym2 α}
 
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-Case conversion may be inaccurate. Consider using '#align simple_graph.inc_matrix_apply_mul_inc_matrix_apply SimpleGraph.incMatrix_apply_mul_incMatrix_applyₓ'. -/
 theorem incMatrix_apply_mul_incMatrix_apply :
     G.incMatrix R a e * G.incMatrix R b e = (G.incidenceSet a ∩ G.incidenceSet b).indicator 1 e :=
   by
@@ -106,12 +88,6 @@ theorem incMatrix_apply_mul_incMatrix_apply :
       Set.mem_inter_iff]
 #align simple_graph.inc_matrix_apply_mul_inc_matrix_apply SimpleGraph.incMatrix_apply_mul_incMatrix_apply
 
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-Case conversion may be inaccurate. Consider using '#align simple_graph.inc_matrix_apply_mul_inc_matrix_apply_of_not_adj SimpleGraph.incMatrix_apply_mul_incMatrix_apply_of_not_adjₓ'. -/
 theorem incMatrix_apply_mul_incMatrix_apply_of_not_adj (hab : a ≠ b) (h : ¬G.Adj a b) :
     G.incMatrix R a e * G.incMatrix R b e = 0 :=
   by
@@ -120,46 +96,22 @@ theorem incMatrix_apply_mul_incMatrix_apply_of_not_adj (hab : a ≠ b) (h : ¬G.
   exact Set.not_mem_empty e
 #align simple_graph.inc_matrix_apply_mul_inc_matrix_apply_of_not_adj SimpleGraph.incMatrix_apply_mul_incMatrix_apply_of_not_adj
 
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 theorem incMatrix_of_not_mem_incidenceSet (h : e ∉ G.incidenceSet a) : G.incMatrix R a e = 0 := by
   rw [inc_matrix_apply, Set.indicator_of_not_mem h]
 #align simple_graph.inc_matrix_of_not_mem_incidence_set SimpleGraph.incMatrix_of_not_mem_incidenceSet
 
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-Case conversion may be inaccurate. Consider using '#align simple_graph.inc_matrix_of_mem_incidence_set SimpleGraph.incMatrix_of_mem_incidenceSetₓ'. -/
 theorem incMatrix_of_mem_incidenceSet (h : e ∈ G.incidenceSet a) : G.incMatrix R a e = 1 := by
   rw [inc_matrix_apply, Set.indicator_of_mem h, Pi.one_apply]
 #align simple_graph.inc_matrix_of_mem_incidence_set SimpleGraph.incMatrix_of_mem_incidenceSet
 
 variable [Nontrivial R]
 
-/- warning: simple_graph.inc_matrix_apply_eq_zero_iff -> SimpleGraph.incMatrix_apply_eq_zero_iff is a dubious translation:
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 theorem incMatrix_apply_eq_zero_iff : G.incMatrix R a e = 0 ↔ e ∉ G.incidenceSet a :=
   by
   simp only [inc_matrix_apply, Set.indicator_apply_eq_zero, Pi.one_apply, one_ne_zero]
   exact Iff.rfl
 #align simple_graph.inc_matrix_apply_eq_zero_iff SimpleGraph.incMatrix_apply_eq_zero_iff
 
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-Case conversion may be inaccurate. Consider using '#align simple_graph.inc_matrix_apply_eq_one_iff SimpleGraph.incMatrix_apply_eq_one_iffₓ'. -/
 theorem incMatrix_apply_eq_one_iff : G.incMatrix R a e = 1 ↔ e ∈ G.incidenceSet a := by
   convert one_ne_zero.ite_eq_left_iff; infer_instance
 #align simple_graph.inc_matrix_apply_eq_one_iff SimpleGraph.incMatrix_apply_eq_one_iff
@@ -170,23 +122,11 @@ section NonAssocSemiring
 
 variable [Fintype α] [NonAssocSemiring R] {a b : α} {e : Sym2 α}
 
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-Case conversion may be inaccurate. Consider using '#align simple_graph.sum_inc_matrix_apply SimpleGraph.sum_incMatrix_applyₓ'. -/
 theorem sum_incMatrix_apply [DecidableEq α] [DecidableRel G.Adj] :
     (∑ e, G.incMatrix R a e) = G.degree a := by
   simp [inc_matrix_apply', sum_boole, Set.filter_mem_univ_eq_toFinset]
 #align simple_graph.sum_inc_matrix_apply SimpleGraph.sum_incMatrix_apply
 
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 theorem incMatrix_mul_transpose_diag [DecidableEq α] [DecidableRel G.Adj] :
     (G.incMatrix R ⬝ (G.incMatrix R)ᵀ) a a = G.degree a :=
   by
@@ -194,12 +134,6 @@ theorem incMatrix_mul_transpose_diag [DecidableEq α] [DecidableRel G.Adj] :
   simp [Matrix.mul_apply, inc_matrix_apply', ← ite_and_mul_zero]
 #align simple_graph.inc_matrix_mul_transpose_diag SimpleGraph.incMatrix_mul_transpose_diag
 
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 theorem sum_incMatrix_apply_of_mem_edgeSet :
     e ∈ G.edgeSetEmbedding → (∑ a, G.incMatrix R a e) = 2 := by
   classical
@@ -213,23 +147,11 @@ theorem sum_incMatrix_apply_of_mem_edgeSet :
     simp only [mem_filter, mem_univ, true_and_iff, mem_insert, mem_singleton]
 #align simple_graph.sum_inc_matrix_apply_of_mem_edge_set SimpleGraph.sum_incMatrix_apply_of_mem_edgeSet
 
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 theorem sum_incMatrix_apply_of_not_mem_edgeSet (h : e ∉ G.edgeSetEmbedding) :
     (∑ a, G.incMatrix R a e) = 0 :=
   sum_eq_zero fun a _ => G.incMatrix_of_not_mem_incidenceSet fun he => h he.1
 #align simple_graph.sum_inc_matrix_apply_of_not_mem_edge_set SimpleGraph.sum_incMatrix_apply_of_not_mem_edgeSet
 
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-Case conversion may be inaccurate. Consider using '#align simple_graph.inc_matrix_transpose_mul_diag SimpleGraph.incMatrix_transpose_mul_diagₓ'. -/
 theorem incMatrix_transpose_mul_diag [DecidableRel G.Adj] :
     ((G.incMatrix R)ᵀ ⬝ G.incMatrix R) e e = if e ∈ G.edgeSetEmbedding then 2 else 0 := by
   classical
@@ -256,12 +178,6 @@ section Semiring
 
 variable [Fintype (Sym2 α)] [Semiring R] {a b : α} {e : Sym2 α}
 
-/- warning: simple_graph.inc_matrix_mul_transpose_apply_of_adj -> SimpleGraph.incMatrix_mul_transpose_apply_of_adj is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align simple_graph.inc_matrix_mul_transpose_apply_of_adj SimpleGraph.incMatrix_mul_transpose_apply_of_adjₓ'. -/
 theorem incMatrix_mul_transpose_apply_of_adj (h : G.Adj a b) :
     (G.incMatrix R ⬝ (G.incMatrix R)ᵀ) a b = (1 : R) := by
   classical
@@ -273,12 +189,6 @@ theorem incMatrix_mul_transpose_apply_of_adj (h : G.Adj a b) :
     exact G.incidence_set_inter_incidence_set_of_adj h
 #align simple_graph.inc_matrix_mul_transpose_apply_of_adj SimpleGraph.incMatrix_mul_transpose_apply_of_adj
 
-/- warning: simple_graph.inc_matrix_mul_transpose -> SimpleGraph.incMatrix_mul_transpose is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align simple_graph.inc_matrix_mul_transpose SimpleGraph.incMatrix_mul_transposeₓ'. -/
 theorem incMatrix_mul_transpose [Fintype α] [DecidableEq α] [DecidableRel G.Adj] :
     G.incMatrix R ⬝ (G.incMatrix R)ᵀ = fun a b =>
       if a = b then G.degree a else if G.Adj a b then 1 else 0 :=

75be6b61

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -160,10 +160,8 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u2}} {α : Type.{u1}} (G : SimpleGraph.{u1} α) [_inst_1 : MulZeroOneClass.{u2} R] {a : α} {e : Sym2.{u1} α} [_inst_2 : Nontrivial.{u2} R], Iff (Eq.{succ u2} R (SimpleGraph.incMatrix.{u2, u1} R α G (MulZeroOneClass.toZero.{u2} R _inst_1) (MulOneClass.toOne.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R _inst_1)) a e) (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (MulOneClass.toOne.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R _inst_1))))) (Membership.mem.{u1, u1} (Sym2.{u1} α) (Set.{u1} (Sym2.{u1} α)) (Set.instMembershipSet.{u1} (Sym2.{u1} α)) e (SimpleGraph.incidenceSet.{u1} α G a))
 Case conversion may be inaccurate. Consider using '#align simple_graph.inc_matrix_apply_eq_one_iff SimpleGraph.incMatrix_apply_eq_one_iffₓ'. -/
-theorem incMatrix_apply_eq_one_iff : G.incMatrix R a e = 1 ↔ e ∈ G.incidenceSet a :=
-  by
-  convert one_ne_zero.ite_eq_left_iff
-  infer_instance
+theorem incMatrix_apply_eq_one_iff : G.incMatrix R a e = 1 ↔ e ∈ G.incidenceSet a := by
+  convert one_ne_zero.ite_eq_left_iff; infer_instance
 #align simple_graph.inc_matrix_apply_eq_one_iff SimpleGraph.incMatrix_apply_eq_one_iff
 
 end MulZeroOneClass

75be6b61

bump to nightly-2023-04-07-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/5ec62c8106221a3f9160e4e4fcc3eed79fe213e9

3f979973

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Gabriel Moise, Yaël Dillies, Kyle Miller
 
 ! This file was ported from Lean 3 source module combinatorics.simple_graph.inc_matrix
-! leanprover-community/mathlib commit bb168510ef455e9280a152e7f31673cabd3d7496
+! leanprover-community/mathlib commit 75be6b616681ab6ca66d798ead117e75cd64f125
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Data.Matrix.Basic
 /-!
 # Incidence matrix of a simple graph
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines the unoriented incidence matrix of a simple graph.
 
 ## Main definitions

bb168510

bump to nightly-2023-04-05-10

mathlib commit https://github.com/leanprover-community/mathlib/commit/1a4df69ca1a9a0e5e26bfe12e2b92814216016d0

5fef5172

Diff

@@ -54,19 +54,33 @@ namespace SimpleGraph
 
 variable (R : Type _) {α : Type _} (G : SimpleGraph α)
 
+#print SimpleGraph.incMatrix /-
 /-- `G.inc_matrix R` is the `α × sym2 α` matrix whose `(a, e)`-entry is `1` if `e` is incident to
 `a` and `0` otherwise. -/
 noncomputable def incMatrix [Zero R] [One R] : Matrix α (Sym2 α) R := fun a =>
   (G.incidenceSet a).indicator 1
 #align simple_graph.inc_matrix SimpleGraph.incMatrix
+-/
 
 variable {R}
 
+/- warning: simple_graph.inc_matrix_apply -> SimpleGraph.incMatrix_apply is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {α : Type.{u2}} (G : SimpleGraph.{u2} α) [_inst_1 : Zero.{u1} R] [_inst_2 : One.{u1} R] {a : α} {e : Sym2.{u2} α}, Eq.{succ u1} R (SimpleGraph.incMatrix.{u1, u2} R α G _inst_1 _inst_2 a e) (Set.indicator.{u2, u1} (Sym2.{u2} α) R _inst_1 (SimpleGraph.incidenceSet.{u2} α G a) (OfNat.ofNat.{max u2 u1} ((Sym2.{u2} α) -> R) 1 (OfNat.mk.{max u2 u1} ((Sym2.{u2} α) -> R) 1 (One.one.{max u2 u1} ((Sym2.{u2} α) -> R) (Pi.instOne.{u2, u1} (Sym2.{u2} α) (fun (ᾰ : Sym2.{u2} α) => R) (fun (i : Sym2.{u2} α) => _inst_2))))) e)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align simple_graph.inc_matrix_apply SimpleGraph.incMatrix_applyₓ'. -/
 theorem incMatrix_apply [Zero R] [One R] {a : α} {e : Sym2 α} :
     G.incMatrix R a e = (G.incidenceSet a).indicator 1 e :=
   rfl
 #align simple_graph.inc_matrix_apply SimpleGraph.incMatrix_apply
 
+/- warning: simple_graph.inc_matrix_apply' -> SimpleGraph.incMatrix_apply' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {α : Type.{u2}} (G : SimpleGraph.{u2} α) [_inst_1 : Zero.{u1} R] [_inst_2 : One.{u1} R] [_inst_3 : DecidableEq.{succ u2} α] [_inst_4 : DecidableRel.{succ u2} α (SimpleGraph.Adj.{u2} α G)] {a : α} {e : Sym2.{u2} α}, Eq.{succ u1} R (SimpleGraph.incMatrix.{u1, u2} R α G _inst_1 _inst_2 a e) (ite.{succ u1} R (Membership.Mem.{u2, u2} (Sym2.{u2} α) (Set.{u2} (Sym2.{u2} α)) (Set.hasMem.{u2} (Sym2.{u2} α)) e (SimpleGraph.incidenceSet.{u2} α G a)) (SimpleGraph.decidableMemIncidenceSet.{u2} α G (fun (a : α) (b : α) => _inst_3 a b) (fun (a : α) (b : α) => _inst_4 a b) a e) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R _inst_2))) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R _inst_1))))
+but is expected to have type
+  forall {R : Type.{u2}} {α : Type.{u1}} (G : SimpleGraph.{u1} α) [_inst_1 : Zero.{u2} R] [_inst_2 : One.{u2} R] [_inst_3 : DecidableEq.{succ u1} α] [_inst_4 : DecidableRel.{succ u1} α (SimpleGraph.Adj.{u1} α G)] {a : α} {e : Sym2.{u1} α}, Eq.{succ u2} R (SimpleGraph.incMatrix.{u2, u1} R α G _inst_1 _inst_2 a e) (ite.{succ u2} R (Membership.mem.{u1, u1} (Sym2.{u1} α) (Set.{u1} (Sym2.{u1} α)) (Set.instMembershipSet.{u1} (Sym2.{u1} α)) e (SimpleGraph.incidenceSet.{u1} α G a)) (SimpleGraph.decidableMemIncidenceSet.{u1} α G (fun (a : α) (b : α) => _inst_3 a b) (fun (a : α) (b : α) => _inst_4 a b) a e) (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R _inst_2)) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R _inst_1)))
+Case conversion may be inaccurate. Consider using '#align simple_graph.inc_matrix_apply' SimpleGraph.incMatrix_apply'ₓ'. -/
 /-- Entries of the incidence matrix can be computed given additional decidable instances. -/
 theorem incMatrix_apply' [Zero R] [One R] [DecidableEq α] [DecidableRel G.Adj] {a : α}
     {e : Sym2 α} : G.incMatrix R a e = if e ∈ G.incidenceSet a then 1 else 0 := by convert rfl
@@ -76,6 +90,12 @@ section MulZeroOneClass
 
 variable [MulZeroOneClass R] {a b : α} {e : Sym2 α}
 
+/- warning: simple_graph.inc_matrix_apply_mul_inc_matrix_apply -> SimpleGraph.incMatrix_apply_mul_incMatrix_apply is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {α : Type.{u2}} (G : SimpleGraph.{u2} α) [_inst_1 : MulZeroOneClass.{u1} R] {a : α} {b : α} {e : Sym2.{u2} α}, Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (MulZeroClass.toHasMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R _inst_1))) (SimpleGraph.incMatrix.{u1, u2} R α G (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R _inst_1)) (MulOneClass.toHasOne.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R _inst_1)) a e) (SimpleGraph.incMatrix.{u1, u2} R α G (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R _inst_1)) (MulOneClass.toHasOne.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R _inst_1)) b e)) (Set.indicator.{u2, u1} (Sym2.{u2} α) R (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R _inst_1)) (Inter.inter.{u2} (Set.{u2} (Sym2.{u2} α)) (Set.hasInter.{u2} (Sym2.{u2} α)) (SimpleGraph.incidenceSet.{u2} α G a) (SimpleGraph.incidenceSet.{u2} α G b)) (OfNat.ofNat.{max u2 u1} ((Sym2.{u2} α) -> R) 1 (OfNat.mk.{max u2 u1} ((Sym2.{u2} α) -> R) 1 (One.one.{max u2 u1} ((Sym2.{u2} α) -> R) (Pi.instOne.{u2, u1} (Sym2.{u2} α) (fun (ᾰ : Sym2.{u2} α) => R) (fun (i : Sym2.{u2} α) => MulOneClass.toHasOne.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R _inst_1)))))) e)
+but is expected to have type
+  forall {R : Type.{u2}} {α : Type.{u1}} (G : SimpleGraph.{u1} α) [_inst_1 : MulZeroOneClass.{u2} R] {a : α} {b : α} {e : Sym2.{u1} α}, Eq.{succ u2} R (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (MulZeroClass.toMul.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R _inst_1))) (SimpleGraph.incMatrix.{u2, u1} R α G (MulZeroOneClass.toZero.{u2} R _inst_1) (MulOneClass.toOne.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R _inst_1)) a e) (SimpleGraph.incMatrix.{u2, u1} R α G (MulZeroOneClass.toZero.{u2} R _inst_1) (MulOneClass.toOne.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R _inst_1)) b e)) (Set.indicator.{u1, u2} (Sym2.{u1} α) R (MulZeroOneClass.toZero.{u2} R _inst_1) (Inter.inter.{u1} (Set.{u1} (Sym2.{u1} α)) (Set.instInterSet.{u1} (Sym2.{u1} α)) (SimpleGraph.incidenceSet.{u1} α G a) (SimpleGraph.incidenceSet.{u1} α G b)) (OfNat.ofNat.{max u1 u2} ((Sym2.{u1} α) -> R) 1 (One.toOfNat1.{max u2 u1} ((Sym2.{u1} α) -> R) (Pi.instOne.{u1, u2} (Sym2.{u1} α) (fun (a._@.Mathlib.Algebra.IndicatorFunction._hyg.77 : Sym2.{u1} α) => R) (fun (i : Sym2.{u1} α) => MulOneClass.toOne.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R _inst_1))))) e)
+Case conversion may be inaccurate. Consider using '#align simple_graph.inc_matrix_apply_mul_inc_matrix_apply SimpleGraph.incMatrix_apply_mul_incMatrix_applyₓ'. -/
 theorem incMatrix_apply_mul_incMatrix_apply :
     G.incMatrix R a e * G.incMatrix R b e = (G.incidenceSet a ∩ G.incidenceSet b).indicator 1 e :=
   by
@@ -83,6 +103,12 @@ theorem incMatrix_apply_mul_incMatrix_apply :
       Set.mem_inter_iff]
 #align simple_graph.inc_matrix_apply_mul_inc_matrix_apply SimpleGraph.incMatrix_apply_mul_incMatrix_apply
 
+/- warning: simple_graph.inc_matrix_apply_mul_inc_matrix_apply_of_not_adj -> SimpleGraph.incMatrix_apply_mul_incMatrix_apply_of_not_adj is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {α : Type.{u2}} (G : SimpleGraph.{u2} α) [_inst_1 : MulZeroOneClass.{u1} R] {a : α} {b : α} {e : Sym2.{u2} α}, (Ne.{succ u2} α a b) -> (Not (SimpleGraph.Adj.{u2} α G a b)) -> (Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (MulZeroClass.toHasMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R _inst_1))) (SimpleGraph.incMatrix.{u1, u2} R α G (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R _inst_1)) (MulOneClass.toHasOne.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R _inst_1)) a e) (SimpleGraph.incMatrix.{u1, u2} R α G (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R _inst_1)) (MulOneClass.toHasOne.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R _inst_1)) b e)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R _inst_1))))))
+but is expected to have type
+  forall {R : Type.{u1}} {α : Type.{u2}} (G : SimpleGraph.{u2} α) [_inst_1 : MulZeroOneClass.{u1} R] {a : α} {b : α} {e : Sym2.{u2} α}, (Ne.{succ u2} α a b) -> (Not (SimpleGraph.Adj.{u2} α G a b)) -> (Eq.{succ u1} R (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (MulZeroClass.toMul.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R _inst_1))) (SimpleGraph.incMatrix.{u1, u2} R α G (MulZeroOneClass.toZero.{u1} R _inst_1) (MulOneClass.toOne.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R _inst_1)) a e) (SimpleGraph.incMatrix.{u1, u2} R α G (MulZeroOneClass.toZero.{u1} R _inst_1) (MulOneClass.toOne.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R _inst_1)) b e)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MulZeroOneClass.toZero.{u1} R _inst_1))))
+Case conversion may be inaccurate. Consider using '#align simple_graph.inc_matrix_apply_mul_inc_matrix_apply_of_not_adj SimpleGraph.incMatrix_apply_mul_incMatrix_apply_of_not_adjₓ'. -/
 theorem incMatrix_apply_mul_incMatrix_apply_of_not_adj (hab : a ≠ b) (h : ¬G.Adj a b) :
     G.incMatrix R a e * G.incMatrix R b e = 0 :=
   by
@@ -91,22 +117,46 @@ theorem incMatrix_apply_mul_incMatrix_apply_of_not_adj (hab : a ≠ b) (h : ¬G.
   exact Set.not_mem_empty e
 #align simple_graph.inc_matrix_apply_mul_inc_matrix_apply_of_not_adj SimpleGraph.incMatrix_apply_mul_incMatrix_apply_of_not_adj
 
+/- warning: simple_graph.inc_matrix_of_not_mem_incidence_set -> SimpleGraph.incMatrix_of_not_mem_incidenceSet is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {α : Type.{u2}} (G : SimpleGraph.{u2} α) [_inst_1 : MulZeroOneClass.{u1} R] {a : α} {e : Sym2.{u2} α}, (Not (Membership.Mem.{u2, u2} (Sym2.{u2} α) (Set.{u2} (Sym2.{u2} α)) (Set.hasMem.{u2} (Sym2.{u2} α)) e (SimpleGraph.incidenceSet.{u2} α G a))) -> (Eq.{succ u1} R (SimpleGraph.incMatrix.{u1, u2} R α G (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R _inst_1)) (MulOneClass.toHasOne.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R _inst_1)) a e) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R _inst_1))))))
+but is expected to have type
+  forall {R : Type.{u1}} {α : Type.{u2}} (G : SimpleGraph.{u2} α) [_inst_1 : MulZeroOneClass.{u1} R] {a : α} {e : Sym2.{u2} α}, (Not (Membership.mem.{u2, u2} (Sym2.{u2} α) (Set.{u2} (Sym2.{u2} α)) (Set.instMembershipSet.{u2} (Sym2.{u2} α)) e (SimpleGraph.incidenceSet.{u2} α G a))) -> (Eq.{succ u1} R (SimpleGraph.incMatrix.{u1, u2} R α G (MulZeroOneClass.toZero.{u1} R _inst_1) (MulOneClass.toOne.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R _inst_1)) a e) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MulZeroOneClass.toZero.{u1} R _inst_1))))
+Case conversion may be inaccurate. Consider using '#align simple_graph.inc_matrix_of_not_mem_incidence_set SimpleGraph.incMatrix_of_not_mem_incidenceSetₓ'. -/
 theorem incMatrix_of_not_mem_incidenceSet (h : e ∉ G.incidenceSet a) : G.incMatrix R a e = 0 := by
   rw [inc_matrix_apply, Set.indicator_of_not_mem h]
 #align simple_graph.inc_matrix_of_not_mem_incidence_set SimpleGraph.incMatrix_of_not_mem_incidenceSet
 
+/- warning: simple_graph.inc_matrix_of_mem_incidence_set -> SimpleGraph.incMatrix_of_mem_incidenceSet is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {α : Type.{u2}} (G : SimpleGraph.{u2} α) [_inst_1 : MulZeroOneClass.{u1} R] {a : α} {e : Sym2.{u2} α}, (Membership.Mem.{u2, u2} (Sym2.{u2} α) (Set.{u2} (Sym2.{u2} α)) (Set.hasMem.{u2} (Sym2.{u2} α)) e (SimpleGraph.incidenceSet.{u2} α G a)) -> (Eq.{succ u1} R (SimpleGraph.incMatrix.{u1, u2} R α G (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R _inst_1)) (MulOneClass.toHasOne.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R _inst_1)) a e) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (MulOneClass.toHasOne.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R _inst_1))))))
+but is expected to have type
+  forall {R : Type.{u1}} {α : Type.{u2}} (G : SimpleGraph.{u2} α) [_inst_1 : MulZeroOneClass.{u1} R] {a : α} {e : Sym2.{u2} α}, (Membership.mem.{u2, u2} (Sym2.{u2} α) (Set.{u2} (Sym2.{u2} α)) (Set.instMembershipSet.{u2} (Sym2.{u2} α)) e (SimpleGraph.incidenceSet.{u2} α G a)) -> (Eq.{succ u1} R (SimpleGraph.incMatrix.{u1, u2} R α G (MulZeroOneClass.toZero.{u1} R _inst_1) (MulOneClass.toOne.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R _inst_1)) a e) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (MulOneClass.toOne.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R _inst_1)))))
+Case conversion may be inaccurate. Consider using '#align simple_graph.inc_matrix_of_mem_incidence_set SimpleGraph.incMatrix_of_mem_incidenceSetₓ'. -/
 theorem incMatrix_of_mem_incidenceSet (h : e ∈ G.incidenceSet a) : G.incMatrix R a e = 1 := by
   rw [inc_matrix_apply, Set.indicator_of_mem h, Pi.one_apply]
 #align simple_graph.inc_matrix_of_mem_incidence_set SimpleGraph.incMatrix_of_mem_incidenceSet
 
 variable [Nontrivial R]
 
+/- warning: simple_graph.inc_matrix_apply_eq_zero_iff -> SimpleGraph.incMatrix_apply_eq_zero_iff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {α : Type.{u2}} (G : SimpleGraph.{u2} α) [_inst_1 : MulZeroOneClass.{u1} R] {a : α} {e : Sym2.{u2} α} [_inst_2 : Nontrivial.{u1} R], Iff (Eq.{succ u1} R (SimpleGraph.incMatrix.{u1, u2} R α G (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R _inst_1)) (MulOneClass.toHasOne.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R _inst_1)) a e) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R _inst_1)))))) (Not (Membership.Mem.{u2, u2} (Sym2.{u2} α) (Set.{u2} (Sym2.{u2} α)) (Set.hasMem.{u2} (Sym2.{u2} α)) e (SimpleGraph.incidenceSet.{u2} α G a)))
+but is expected to have type
+  forall {R : Type.{u2}} {α : Type.{u1}} (G : SimpleGraph.{u1} α) [_inst_1 : MulZeroOneClass.{u2} R] {a : α} {e : Sym2.{u1} α} [_inst_2 : Nontrivial.{u2} R], Iff (Eq.{succ u2} R (SimpleGraph.incMatrix.{u2, u1} R α G (MulZeroOneClass.toZero.{u2} R _inst_1) (MulOneClass.toOne.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R _inst_1)) a e) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MulZeroOneClass.toZero.{u2} R _inst_1)))) (Not (Membership.mem.{u1, u1} (Sym2.{u1} α) (Set.{u1} (Sym2.{u1} α)) (Set.instMembershipSet.{u1} (Sym2.{u1} α)) e (SimpleGraph.incidenceSet.{u1} α G a)))
+Case conversion may be inaccurate. Consider using '#align simple_graph.inc_matrix_apply_eq_zero_iff SimpleGraph.incMatrix_apply_eq_zero_iffₓ'. -/
 theorem incMatrix_apply_eq_zero_iff : G.incMatrix R a e = 0 ↔ e ∉ G.incidenceSet a :=
   by
   simp only [inc_matrix_apply, Set.indicator_apply_eq_zero, Pi.one_apply, one_ne_zero]
   exact Iff.rfl
 #align simple_graph.inc_matrix_apply_eq_zero_iff SimpleGraph.incMatrix_apply_eq_zero_iff
 
+/- warning: simple_graph.inc_matrix_apply_eq_one_iff -> SimpleGraph.incMatrix_apply_eq_one_iff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {α : Type.{u2}} (G : SimpleGraph.{u2} α) [_inst_1 : MulZeroOneClass.{u1} R] {a : α} {e : Sym2.{u2} α} [_inst_2 : Nontrivial.{u1} R], Iff (Eq.{succ u1} R (SimpleGraph.incMatrix.{u1, u2} R α G (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R _inst_1)) (MulOneClass.toHasOne.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R _inst_1)) a e) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (MulOneClass.toHasOne.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R _inst_1)))))) (Membership.Mem.{u2, u2} (Sym2.{u2} α) (Set.{u2} (Sym2.{u2} α)) (Set.hasMem.{u2} (Sym2.{u2} α)) e (SimpleGraph.incidenceSet.{u2} α G a))
+but is expected to have type
+  forall {R : Type.{u2}} {α : Type.{u1}} (G : SimpleGraph.{u1} α) [_inst_1 : MulZeroOneClass.{u2} R] {a : α} {e : Sym2.{u1} α} [_inst_2 : Nontrivial.{u2} R], Iff (Eq.{succ u2} R (SimpleGraph.incMatrix.{u2, u1} R α G (MulZeroOneClass.toZero.{u2} R _inst_1) (MulOneClass.toOne.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R _inst_1)) a e) (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (MulOneClass.toOne.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R _inst_1))))) (Membership.mem.{u1, u1} (Sym2.{u1} α) (Set.{u1} (Sym2.{u1} α)) (Set.instMembershipSet.{u1} (Sym2.{u1} α)) e (SimpleGraph.incidenceSet.{u1} α G a))
+Case conversion may be inaccurate. Consider using '#align simple_graph.inc_matrix_apply_eq_one_iff SimpleGraph.incMatrix_apply_eq_one_iffₓ'. -/
 theorem incMatrix_apply_eq_one_iff : G.incMatrix R a e = 1 ↔ e ∈ G.incidenceSet a :=
   by
   convert one_ne_zero.ite_eq_left_iff
@@ -119,11 +169,23 @@ section NonAssocSemiring
 
 variable [Fintype α] [NonAssocSemiring R] {a b : α} {e : Sym2 α}
 
+/- warning: simple_graph.sum_inc_matrix_apply -> SimpleGraph.sum_incMatrix_apply is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {α : Type.{u2}} (G : SimpleGraph.{u2} α) [_inst_1 : Fintype.{u2} α] [_inst_2 : NonAssocSemiring.{u1} R] {a : α} [_inst_3 : DecidableEq.{succ u2} α] [_inst_4 : DecidableRel.{succ u2} α (SimpleGraph.Adj.{u2} α G)], Eq.{succ u1} R (Finset.sum.{u1, u2} R (Sym2.{u2} α) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_2)) (Finset.univ.{u2} (Sym2.{u2} α) (Quotient.fintype.{u2} (Prod.{u2, u2} α α) (Prod.fintype.{u2, u2} α α _inst_1 _inst_1) (Sym2.Rel.setoid.{u2} α) (fun (a : Prod.{u2, u2} α α) (b : Prod.{u2, u2} α α) => Sym2.Rel.decidableRel.{u2} α (fun (a : α) (b : α) => _inst_3 a b) a b))) (fun (e : Sym2.{u2} α) => SimpleGraph.incMatrix.{u1, u2} R α G (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_2))) (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R _inst_2))) a e)) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R _inst_2)))))) (SimpleGraph.degree.{u2} α G a (SimpleGraph.neighborSetFintype.{u2} α G _inst_1 (fun (a : α) (b : α) => _inst_4 a b) a)))
+but is expected to have type
+  forall {R : Type.{u1}} {α : Type.{u2}} (G : SimpleGraph.{u2} α) [_inst_1 : Fintype.{u2} α] [_inst_2 : NonAssocSemiring.{u1} R] {a : α} [_inst_3 : DecidableEq.{succ u2} α] [_inst_4 : DecidableRel.{succ u2} α (SimpleGraph.Adj.{u2} α G)], Eq.{succ u1} R (Finset.sum.{u1, u2} R (Sym2.{u2} α) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_2)) (Finset.univ.{u2} (Sym2.{u2} α) (Quotient.fintype.{u2} (Prod.{u2, u2} α α) (instFintypeProd.{u2, u2} α α _inst_1 _inst_1) (Sym2.Rel.setoid.{u2} α) (fun (a : Prod.{u2, u2} α α) (b : Prod.{u2, u2} α α) => Sym2.instRelDecidable'.{u2} α (fun (a : α) (b : α) => _inst_3 a b) a b))) (fun (e : Sym2.{u2} α) => SimpleGraph.incMatrix.{u1, u2} R α G (MulZeroOneClass.toZero.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R _inst_2)) (NonAssocSemiring.toOne.{u1} R _inst_2) a e)) (Nat.cast.{u1} R (NonAssocSemiring.toNatCast.{u1} R _inst_2) (SimpleGraph.degree.{u2} α G a (SimpleGraph.neighborSetFintype.{u2} α G _inst_1 (fun (a : α) (b : α) => _inst_4 a b) a)))
+Case conversion may be inaccurate. Consider using '#align simple_graph.sum_inc_matrix_apply SimpleGraph.sum_incMatrix_applyₓ'. -/
 theorem sum_incMatrix_apply [DecidableEq α] [DecidableRel G.Adj] :
     (∑ e, G.incMatrix R a e) = G.degree a := by
   simp [inc_matrix_apply', sum_boole, Set.filter_mem_univ_eq_toFinset]
 #align simple_graph.sum_inc_matrix_apply SimpleGraph.sum_incMatrix_apply
 
+/- warning: simple_graph.inc_matrix_mul_transpose_diag -> SimpleGraph.incMatrix_mul_transpose_diag is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {α : Type.{u2}} (G : SimpleGraph.{u2} α) [_inst_1 : Fintype.{u2} α] [_inst_2 : NonAssocSemiring.{u1} R] {a : α} [_inst_3 : DecidableEq.{succ u2} α] [_inst_4 : DecidableRel.{succ u2} α (SimpleGraph.Adj.{u2} α G)], Eq.{succ u1} R (Matrix.mul.{u1, u2, u2, u2} α (Sym2.{u2} α) α R (Quotient.fintype.{u2} (Prod.{u2, u2} α α) (Prod.fintype.{u2, u2} α α _inst_1 _inst_1) (Sym2.Rel.setoid.{u2} α) (fun (a : Prod.{u2, u2} α α) (b : Prod.{u2, u2} α α) => Sym2.Rel.decidableRel.{u2} α (fun (a : α) (b : α) => _inst_3 a b) a b)) (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_2)) (SimpleGraph.incMatrix.{u1, u2} R α G (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_2))) (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R _inst_2)))) (Matrix.transpose.{u1, u2, u2} α (Sym2.{u2} α) R (SimpleGraph.incMatrix.{u1, u2} R α G (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_2))) (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R _inst_2))))) a a) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R _inst_2)))))) (SimpleGraph.degree.{u2} α G a (SimpleGraph.neighborSetFintype.{u2} α G _inst_1 (fun (a : α) (b : α) => _inst_4 a b) a)))
+but is expected to have type
+  forall {R : Type.{u1}} {α : Type.{u2}} (G : SimpleGraph.{u2} α) [_inst_1 : Fintype.{u2} α] [_inst_2 : NonAssocSemiring.{u1} R] {a : α} [_inst_3 : DecidableEq.{succ u2} α] [_inst_4 : DecidableRel.{succ u2} α (SimpleGraph.Adj.{u2} α G)], Eq.{succ u1} R (Matrix.mul.{u1, u2, u2, u2} α (Sym2.{u2} α) α R (Quotient.fintype.{u2} (Prod.{u2, u2} α α) (instFintypeProd.{u2, u2} α α _inst_1 _inst_1) (Sym2.Rel.setoid.{u2} α) (fun (a : Prod.{u2, u2} α α) (b : Prod.{u2, u2} α α) => Sym2.instRelDecidable'.{u2} α (fun (a : α) (b : α) => _inst_3 a b) a b)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_2)) (SimpleGraph.incMatrix.{u1, u2} R α G (MulZeroOneClass.toZero.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R _inst_2)) (NonAssocSemiring.toOne.{u1} R _inst_2)) (Matrix.transpose.{u1, u2, u2} α (Sym2.{u2} α) R (SimpleGraph.incMatrix.{u1, u2} R α G (MulZeroOneClass.toZero.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R _inst_2)) (NonAssocSemiring.toOne.{u1} R _inst_2))) a a) (Nat.cast.{u1} R (NonAssocSemiring.toNatCast.{u1} R _inst_2) (SimpleGraph.degree.{u2} α G a (SimpleGraph.neighborSetFintype.{u2} α G _inst_1 (fun (a : α) (b : α) => _inst_4 a b) a)))
+Case conversion may be inaccurate. Consider using '#align simple_graph.inc_matrix_mul_transpose_diag SimpleGraph.incMatrix_mul_transpose_diagₓ'. -/
 theorem incMatrix_mul_transpose_diag [DecidableEq α] [DecidableRel G.Adj] :
     (G.incMatrix R ⬝ (G.incMatrix R)ᵀ) a a = G.degree a :=
   by
@@ -131,7 +193,13 @@ theorem incMatrix_mul_transpose_diag [DecidableEq α] [DecidableRel G.Adj] :
   simp [Matrix.mul_apply, inc_matrix_apply', ← ite_and_mul_zero]
 #align simple_graph.inc_matrix_mul_transpose_diag SimpleGraph.incMatrix_mul_transpose_diag
 
-theorem sum_incMatrix_apply_of_mem_edgeSetEmbedding :
+/- warning: simple_graph.sum_inc_matrix_apply_of_mem_edge_set -> SimpleGraph.sum_incMatrix_apply_of_mem_edgeSet is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {α : Type.{u2}} (G : SimpleGraph.{u2} α) [_inst_1 : Fintype.{u2} α] [_inst_2 : NonAssocSemiring.{u1} R] {e : Sym2.{u2} α}, (Membership.Mem.{u2, u2} (Sym2.{u2} α) (Set.{u2} (Sym2.{u2} α)) (Set.hasMem.{u2} (Sym2.{u2} α)) e (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (SimpleGraph.{u2} α) (Set.{u2} (Sym2.{u2} α)) (SimpleGraph.hasLe.{u2} α) (Set.hasLe.{u2} (Sym2.{u2} α))) (fun (_x : RelEmbedding.{u2, u2} (SimpleGraph.{u2} α) (Set.{u2} (Sym2.{u2} α)) (LE.le.{u2} (SimpleGraph.{u2} α) (SimpleGraph.hasLe.{u2} α)) (LE.le.{u2} (Set.{u2} (Sym2.{u2} α)) (Set.hasLe.{u2} (Sym2.{u2} α)))) => (SimpleGraph.{u2} α) -> (Set.{u2} (Sym2.{u2} α))) (RelEmbedding.hasCoeToFun.{u2, u2} (SimpleGraph.{u2} α) (Set.{u2} (Sym2.{u2} α)) (LE.le.{u2} (SimpleGraph.{u2} α) (SimpleGraph.hasLe.{u2} α)) (LE.le.{u2} (Set.{u2} (Sym2.{u2} α)) (Set.hasLe.{u2} (Sym2.{u2} α)))) (SimpleGraph.edgeSetEmbedding.{u2} α) G)) -> (Eq.{succ u1} R (Finset.sum.{u1, u2} R α (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_2)) (Finset.univ.{u2} α _inst_1) (fun (a : α) => SimpleGraph.incMatrix.{u1, u2} R α G (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_2))) (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R _inst_2))) a e)) (OfNat.ofNat.{u1} R 2 (OfNat.mk.{u1} R 2 (bit0.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_2))) (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R _inst_2))))))))
+but is expected to have type
+  forall {R : Type.{u1}} {α : Type.{u2}} (G : SimpleGraph.{u2} α) [_inst_1 : Fintype.{u2} α] [_inst_2 : NonAssocSemiring.{u1} R] {e : Sym2.{u2} α}, (Membership.mem.{u2, u2} (Sym2.{u2} α) (Set.{u2} (Sym2.{u2} α)) (Set.instMembershipSet.{u2} (Sym2.{u2} α)) e (SimpleGraph.edgeSet.{u2} α G)) -> (Eq.{succ u1} R (Finset.sum.{u1, u2} R α (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_2)) (Finset.univ.{u2} α _inst_1) (fun (a : α) => SimpleGraph.incMatrix.{u1, u2} R α G (MulZeroOneClass.toZero.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R _inst_2)) (NonAssocSemiring.toOne.{u1} R _inst_2) a e)) (OfNat.ofNat.{u1} R 2 (instOfNat.{u1} R 2 (NonAssocSemiring.toNatCast.{u1} R _inst_2) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))
+Case conversion may be inaccurate. Consider using '#align simple_graph.sum_inc_matrix_apply_of_mem_edge_set SimpleGraph.sum_incMatrix_apply_of_mem_edgeSetₓ'. -/
+theorem sum_incMatrix_apply_of_mem_edgeSet :
     e ∈ G.edgeSetEmbedding → (∑ a, G.incMatrix R a e) = 2 := by
   classical
     refine' e.ind _
@@ -142,13 +210,25 @@ theorem sum_incMatrix_apply_of_mem_edgeSetEmbedding :
     congr 2
     ext e
     simp only [mem_filter, mem_univ, true_and_iff, mem_insert, mem_singleton]
-#align simple_graph.sum_inc_matrix_apply_of_mem_edge_set SimpleGraph.sum_incMatrix_apply_of_mem_edgeSetEmbedding
-
-theorem sum_incMatrix_apply_of_not_mem_edgeSetEmbedding (h : e ∉ G.edgeSetEmbedding) :
+#align simple_graph.sum_inc_matrix_apply_of_mem_edge_set SimpleGraph.sum_incMatrix_apply_of_mem_edgeSet
+
+/- warning: simple_graph.sum_inc_matrix_apply_of_not_mem_edge_set -> SimpleGraph.sum_incMatrix_apply_of_not_mem_edgeSet is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {α : Type.{u2}} (G : SimpleGraph.{u2} α) [_inst_1 : Fintype.{u2} α] [_inst_2 : NonAssocSemiring.{u1} R] {e : Sym2.{u2} α}, (Not (Membership.Mem.{u2, u2} (Sym2.{u2} α) (Set.{u2} (Sym2.{u2} α)) (Set.hasMem.{u2} (Sym2.{u2} α)) e (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (SimpleGraph.{u2} α) (Set.{u2} (Sym2.{u2} α)) (SimpleGraph.hasLe.{u2} α) (Set.hasLe.{u2} (Sym2.{u2} α))) (fun (_x : RelEmbedding.{u2, u2} (SimpleGraph.{u2} α) (Set.{u2} (Sym2.{u2} α)) (LE.le.{u2} (SimpleGraph.{u2} α) (SimpleGraph.hasLe.{u2} α)) (LE.le.{u2} (Set.{u2} (Sym2.{u2} α)) (Set.hasLe.{u2} (Sym2.{u2} α)))) => (SimpleGraph.{u2} α) -> (Set.{u2} (Sym2.{u2} α))) (RelEmbedding.hasCoeToFun.{u2, u2} (SimpleGraph.{u2} α) (Set.{u2} (Sym2.{u2} α)) (LE.le.{u2} (SimpleGraph.{u2} α) (SimpleGraph.hasLe.{u2} α)) (LE.le.{u2} (Set.{u2} (Sym2.{u2} α)) (Set.hasLe.{u2} (Sym2.{u2} α)))) (SimpleGraph.edgeSetEmbedding.{u2} α) G))) -> (Eq.{succ u1} R (Finset.sum.{u1, u2} R α (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_2)) (Finset.univ.{u2} α _inst_1) (fun (a : α) => SimpleGraph.incMatrix.{u1, u2} R α G (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_2))) (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R _inst_2))) a e)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_2)))))))
+but is expected to have type
+  forall {R : Type.{u1}} {α : Type.{u2}} (G : SimpleGraph.{u2} α) [_inst_1 : Fintype.{u2} α] [_inst_2 : NonAssocSemiring.{u1} R] {e : Sym2.{u2} α}, (Not (Membership.mem.{u2, u2} (Sym2.{u2} α) (Set.{u2} (Sym2.{u2} α)) (Set.instMembershipSet.{u2} (Sym2.{u2} α)) e (SimpleGraph.edgeSet.{u2} α G))) -> (Eq.{succ u1} R (Finset.sum.{u1, u2} R α (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_2)) (Finset.univ.{u2} α _inst_1) (fun (a : α) => SimpleGraph.incMatrix.{u1, u2} R α G (MulZeroOneClass.toZero.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R _inst_2)) (NonAssocSemiring.toOne.{u1} R _inst_2) a e)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MulZeroOneClass.toZero.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R _inst_2)))))
+Case conversion may be inaccurate. Consider using '#align simple_graph.sum_inc_matrix_apply_of_not_mem_edge_set SimpleGraph.sum_incMatrix_apply_of_not_mem_edgeSetₓ'. -/
+theorem sum_incMatrix_apply_of_not_mem_edgeSet (h : e ∉ G.edgeSetEmbedding) :
     (∑ a, G.incMatrix R a e) = 0 :=
   sum_eq_zero fun a _ => G.incMatrix_of_not_mem_incidenceSet fun he => h he.1
-#align simple_graph.sum_inc_matrix_apply_of_not_mem_edge_set SimpleGraph.sum_incMatrix_apply_of_not_mem_edgeSetEmbedding
-
+#align simple_graph.sum_inc_matrix_apply_of_not_mem_edge_set SimpleGraph.sum_incMatrix_apply_of_not_mem_edgeSet
+
+/- warning: simple_graph.inc_matrix_transpose_mul_diag -> SimpleGraph.incMatrix_transpose_mul_diag is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {α : Type.{u2}} (G : SimpleGraph.{u2} α) [_inst_1 : Fintype.{u2} α] [_inst_2 : NonAssocSemiring.{u1} R] {e : Sym2.{u2} α} [_inst_3 : DecidableRel.{succ u2} α (SimpleGraph.Adj.{u2} α G)], Eq.{succ u1} R (Matrix.mul.{u1, u2, u2, u2} (Sym2.{u2} α) α (Sym2.{u2} α) R _inst_1 (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_2)) (Matrix.transpose.{u1, u2, u2} α (Sym2.{u2} α) R (SimpleGraph.incMatrix.{u1, u2} R α G (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_2))) (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R _inst_2))))) (SimpleGraph.incMatrix.{u1, u2} R α G (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_2))) (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R _inst_2)))) e e) (ite.{succ u1} R (Membership.Mem.{u2, u2} (Sym2.{u2} α) (Set.{u2} (Sym2.{u2} α)) (Set.hasMem.{u2} (Sym2.{u2} α)) e (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (SimpleGraph.{u2} α) (Set.{u2} (Sym2.{u2} α)) (SimpleGraph.hasLe.{u2} α) (Set.hasLe.{u2} (Sym2.{u2} α))) (fun (_x : RelEmbedding.{u2, u2} (SimpleGraph.{u2} α) (Set.{u2} (Sym2.{u2} α)) (LE.le.{u2} (SimpleGraph.{u2} α) (SimpleGraph.hasLe.{u2} α)) (LE.le.{u2} (Set.{u2} (Sym2.{u2} α)) (Set.hasLe.{u2} (Sym2.{u2} α)))) => (SimpleGraph.{u2} α) -> (Set.{u2} (Sym2.{u2} α))) (RelEmbedding.hasCoeToFun.{u2, u2} (SimpleGraph.{u2} α) (Set.{u2} (Sym2.{u2} α)) (LE.le.{u2} (SimpleGraph.{u2} α) (SimpleGraph.hasLe.{u2} α)) (LE.le.{u2} (Set.{u2} (Sym2.{u2} α)) (Set.hasLe.{u2} (Sym2.{u2} α)))) (SimpleGraph.edgeSetEmbedding.{u2} α) G)) (SimpleGraph.decidableMemEdgeSet.{u2} α G (fun (a : α) (b : α) => _inst_3 a b) e) (OfNat.ofNat.{u1} R 2 (OfNat.mk.{u1} R 2 (bit0.{u1} R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_2))) (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R _inst_2))))))) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_2)))))))
+but is expected to have type
+  forall {R : Type.{u1}} {α : Type.{u2}} (G : SimpleGraph.{u2} α) [_inst_1 : Fintype.{u2} α] [_inst_2 : NonAssocSemiring.{u1} R] {e : Sym2.{u2} α} [_inst_3 : DecidableRel.{succ u2} α (SimpleGraph.Adj.{u2} α G)], Eq.{succ u1} R (Matrix.mul.{u1, u2, u2, u2} (Sym2.{u2} α) α (Sym2.{u2} α) R _inst_1 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R _inst_2)) (Matrix.transpose.{u1, u2, u2} α (Sym2.{u2} α) R (SimpleGraph.incMatrix.{u1, u2} R α G (MulZeroOneClass.toZero.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R _inst_2)) (NonAssocSemiring.toOne.{u1} R _inst_2))) (SimpleGraph.incMatrix.{u1, u2} R α G (MulZeroOneClass.toZero.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R _inst_2)) (NonAssocSemiring.toOne.{u1} R _inst_2)) e e) (ite.{succ u1} R (Membership.mem.{u2, u2} (Sym2.{u2} α) (Set.{u2} (Sym2.{u2} α)) (Set.instMembershipSet.{u2} (Sym2.{u2} α)) e (SimpleGraph.edgeSet.{u2} α G)) (SimpleGraph.decidableMemEdgeSet.{u2} α G (fun (a : α) (b : α) => _inst_3 a b) e) (OfNat.ofNat.{u1} R 2 (instOfNat.{u1} R 2 (NonAssocSemiring.toNatCast.{u1} R _inst_2) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MulZeroOneClass.toZero.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R _inst_2)))))
+Case conversion may be inaccurate. Consider using '#align simple_graph.inc_matrix_transpose_mul_diag SimpleGraph.incMatrix_transpose_mul_diagₓ'. -/
 theorem incMatrix_transpose_mul_diag [DecidableRel G.Adj] :
     ((G.incMatrix R)ᵀ ⬝ G.incMatrix R) e e = if e ∈ G.edgeSetEmbedding then 2 else 0 := by
   classical
@@ -175,6 +255,12 @@ section Semiring
 
 variable [Fintype (Sym2 α)] [Semiring R] {a b : α} {e : Sym2 α}
 
+/- warning: simple_graph.inc_matrix_mul_transpose_apply_of_adj -> SimpleGraph.incMatrix_mul_transpose_apply_of_adj is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {α : Type.{u2}} (G : SimpleGraph.{u2} α) [_inst_1 : Fintype.{u2} (Sym2.{u2} α)] [_inst_2 : Semiring.{u1} R] {a : α} {b : α}, (SimpleGraph.Adj.{u2} α G a b) -> (Eq.{succ u1} R (Matrix.mul.{u1, u2, u2, u2} α (Sym2.{u2} α) α R _inst_1 (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2))) (SimpleGraph.incMatrix.{u1, u2} R α G (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)))) (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2))))) (Matrix.transpose.{u1, u2, u2} α (Sym2.{u2} α) R (SimpleGraph.incMatrix.{u1, u2} R α G (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)))) (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)))))) a b) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2))))))))
+but is expected to have type
+  forall {R : Type.{u1}} {α : Type.{u2}} (G : SimpleGraph.{u2} α) [_inst_1 : Fintype.{u2} (Sym2.{u2} α)] [_inst_2 : Semiring.{u1} R] {a : α} {b : α}, (SimpleGraph.Adj.{u2} α G a b) -> (Eq.{succ u1} R (Matrix.mul.{u1, u2, u2, u2} α (Sym2.{u2} α) α R _inst_1 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2))) (SimpleGraph.incMatrix.{u1, u2} R α G (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_2)) (Semiring.toOne.{u1} R _inst_2)) (Matrix.transpose.{u1, u2, u2} α (Sym2.{u2} α) R (SimpleGraph.incMatrix.{u1, u2} R α G (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_2)) (Semiring.toOne.{u1} R _inst_2))) a b) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_2))))
+Case conversion may be inaccurate. Consider using '#align simple_graph.inc_matrix_mul_transpose_apply_of_adj SimpleGraph.incMatrix_mul_transpose_apply_of_adjₓ'. -/
 theorem incMatrix_mul_transpose_apply_of_adj (h : G.Adj a b) :
     (G.incMatrix R ⬝ (G.incMatrix R)ᵀ) a b = (1 : R) := by
   classical
@@ -186,6 +272,12 @@ theorem incMatrix_mul_transpose_apply_of_adj (h : G.Adj a b) :
     exact G.incidence_set_inter_incidence_set_of_adj h
 #align simple_graph.inc_matrix_mul_transpose_apply_of_adj SimpleGraph.incMatrix_mul_transpose_apply_of_adj
 
+/- warning: simple_graph.inc_matrix_mul_transpose -> SimpleGraph.incMatrix_mul_transpose is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {α : Type.{u2}} (G : SimpleGraph.{u2} α) [_inst_1 : Fintype.{u2} (Sym2.{u2} α)] [_inst_2 : Semiring.{u1} R] [_inst_3 : Fintype.{u2} α] [_inst_4 : DecidableEq.{succ u2} α] [_inst_5 : DecidableRel.{succ u2} α (SimpleGraph.Adj.{u2} α G)], Eq.{succ (max u2 u1)} (Matrix.{u2, u2, u1} α α R) (Matrix.mul.{u1, u2, u2, u2} α (Sym2.{u2} α) α R _inst_1 (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2))) (SimpleGraph.incMatrix.{u1, u2} R α G (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)))) (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2))))) (Matrix.transpose.{u1, u2, u2} α (Sym2.{u2} α) R (SimpleGraph.incMatrix.{u1, u2} R α G (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)))) (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2))))))) (fun (a : α) (b : α) => ite.{succ u1} R (Eq.{succ u2} α a b) (_inst_4 a b) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2))))))) (SimpleGraph.degree.{u2} α G a (SimpleGraph.neighborSetFintype.{u2} α G _inst_3 (fun (a : α) (b : α) => _inst_5 a b) a))) (ite.{succ u1} R (SimpleGraph.Adj.{u2} α G a b) (_inst_5 a b) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2))))))) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2)))))))))
+but is expected to have type
+  forall {R : Type.{u1}} {α : Type.{u2}} (G : SimpleGraph.{u2} α) [_inst_1 : Fintype.{u2} (Sym2.{u2} α)] [_inst_2 : Semiring.{u1} R] [_inst_3 : Fintype.{u2} α] [_inst_4 : DecidableEq.{succ u2} α] [_inst_5 : DecidableRel.{succ u2} α (SimpleGraph.Adj.{u2} α G)], Eq.{max (succ u1) (succ u2)} (Matrix.{u2, u2, u1} α α R) (Matrix.mul.{u1, u2, u2, u2} α (Sym2.{u2} α) α R _inst_1 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_2))) (SimpleGraph.incMatrix.{u1, u2} R α G (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_2)) (Semiring.toOne.{u1} R _inst_2)) (Matrix.transpose.{u1, u2, u2} α (Sym2.{u2} α) R (SimpleGraph.incMatrix.{u1, u2} R α G (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_2)) (Semiring.toOne.{u1} R _inst_2)))) (fun (a : α) (b : α) => ite.{succ u1} R (Eq.{succ u2} α a b) (_inst_4 a b) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R _inst_2) (SimpleGraph.degree.{u2} α G a (SimpleGraph.neighborSetFintype.{u2} α G _inst_3 (fun (a : α) (b : α) => _inst_5 a b) a))) (ite.{succ u1} R (SimpleGraph.Adj.{u2} α G a b) (_inst_5 a b) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_2))) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_2))))))
+Case conversion may be inaccurate. Consider using '#align simple_graph.inc_matrix_mul_transpose SimpleGraph.incMatrix_mul_transposeₓ'. -/
 theorem incMatrix_mul_transpose [Fintype α] [DecidableEq α] [DecidableRel G.Adj] :
     G.incMatrix R ⬝ (G.incMatrix R)ᵀ = fun a b =>
       if a = b then G.degree a else if G.Adj a b then 1 else 0 :=

bb168510

bump to nightly-2023-02-25-00

mathlib commit https://github.com/leanprover-community/mathlib/commit/22131150f88a2d125713ffa0f4693e3355b1eb49

aca219f8

Diff

@@ -131,7 +131,8 @@ theorem incMatrix_mul_transpose_diag [DecidableEq α] [DecidableRel G.Adj] :
   simp [Matrix.mul_apply, inc_matrix_apply', ← ite_and_mul_zero]
 #align simple_graph.inc_matrix_mul_transpose_diag SimpleGraph.incMatrix_mul_transpose_diag
 
-theorem sum_incMatrix_apply_of_mem_edgeSet : e ∈ G.edgeSet → (∑ a, G.incMatrix R a e) = 2 := by
+theorem sum_incMatrix_apply_of_mem_edgeSetEmbedding :
+    e ∈ G.edgeSetEmbedding → (∑ a, G.incMatrix R a e) = 2 := by
   classical
     refine' e.ind _
     intro a b h
@@ -141,14 +142,15 @@ theorem sum_incMatrix_apply_of_mem_edgeSet : e ∈ G.edgeSet → (∑ a, G.incMa
     congr 2
     ext e
     simp only [mem_filter, mem_univ, true_and_iff, mem_insert, mem_singleton]
-#align simple_graph.sum_inc_matrix_apply_of_mem_edge_set SimpleGraph.sum_incMatrix_apply_of_mem_edgeSet
+#align simple_graph.sum_inc_matrix_apply_of_mem_edge_set SimpleGraph.sum_incMatrix_apply_of_mem_edgeSetEmbedding
 
-theorem sum_incMatrix_apply_of_not_mem_edgeSet (h : e ∉ G.edgeSet) : (∑ a, G.incMatrix R a e) = 0 :=
+theorem sum_incMatrix_apply_of_not_mem_edgeSetEmbedding (h : e ∉ G.edgeSetEmbedding) :
+    (∑ a, G.incMatrix R a e) = 0 :=
   sum_eq_zero fun a _ => G.incMatrix_of_not_mem_incidenceSet fun he => h he.1
-#align simple_graph.sum_inc_matrix_apply_of_not_mem_edge_set SimpleGraph.sum_incMatrix_apply_of_not_mem_edgeSet
+#align simple_graph.sum_inc_matrix_apply_of_not_mem_edge_set SimpleGraph.sum_incMatrix_apply_of_not_mem_edgeSetEmbedding
 
 theorem incMatrix_transpose_mul_diag [DecidableRel G.Adj] :
-    ((G.incMatrix R)ᵀ ⬝ G.incMatrix R) e e = if e ∈ G.edgeSet then 2 else 0 := by
+    ((G.incMatrix R)ᵀ ⬝ G.incMatrix R) e e = if e ∈ G.edgeSetEmbedding then 2 else 0 := by
   classical
     simp only [Matrix.mul_apply, inc_matrix_apply', transpose_apply, ← ite_and_mul_zero, one_mul,
       sum_boole, and_self_iff]

bb168510

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

bb168510

chore(SimpleGraph/IncMatrix): review Decidable*/Fintype _ assumptions (#10445)

Drop unneeded assumptions, modify other assumptions to match exactly what's required to formulate the theorems.

9db90fd7

Diff

@@ -116,21 +116,22 @@ end MulZeroOneClass
 
 section NonAssocSemiring
 
-variable [Fintype α] [NonAssocSemiring R] {a b : α} {e : Sym2 α}
+variable [Fintype (Sym2 α)] [NonAssocSemiring R] {a b : α} {e : Sym2 α}
 
-theorem sum_incMatrix_apply [DecidableEq α] [DecidableRel G.Adj] :
+theorem sum_incMatrix_apply [Fintype (neighborSet G a)] :
     ∑ e, G.incMatrix R a e = G.degree a := by
-  simp [incMatrix_apply', sum_boole, Set.filter_mem_univ_eq_toFinset]
+  classical simp [incMatrix_apply', sum_boole, Set.filter_mem_univ_eq_toFinset]
 #align simple_graph.sum_inc_matrix_apply SimpleGraph.sum_incMatrix_apply
 
-theorem incMatrix_mul_transpose_diag [DecidableEq α] [DecidableRel G.Adj] :
+theorem incMatrix_mul_transpose_diag [Fintype (neighborSet G a)] :
     (G.incMatrix R * (G.incMatrix R)ᵀ) a a = G.degree a := by
+  classical
   rw [← sum_incMatrix_apply]
   simp only [mul_apply, incMatrix_apply', transpose_apply, mul_ite, mul_one, mul_zero]
   simp_all only [ite_true, sum_boole]
 #align simple_graph.inc_matrix_mul_transpose_diag SimpleGraph.incMatrix_mul_transpose_diag
 
-theorem sum_incMatrix_apply_of_mem_edgeSet :
+theorem sum_incMatrix_apply_of_mem_edgeSet [Fintype α] :
     e ∈ G.edgeSet → ∑ a, G.incMatrix R a e = 2 := by
   classical
     refine' e.ind _
@@ -143,12 +144,12 @@ theorem sum_incMatrix_apply_of_mem_edgeSet :
     simp only [mem_filter, mem_univ, true_and_iff, mem_insert, mem_singleton]
 #align simple_graph.sum_inc_matrix_apply_of_mem_edge_set SimpleGraph.sum_incMatrix_apply_of_mem_edgeSet
 
-theorem sum_incMatrix_apply_of_not_mem_edgeSet (h : e ∉ G.edgeSet) :
+theorem sum_incMatrix_apply_of_not_mem_edgeSet [Fintype α] (h : e ∉ G.edgeSet) :
     ∑ a, G.incMatrix R a e = 0 :=
   sum_eq_zero fun _ _ => G.incMatrix_of_not_mem_incidenceSet fun he => h he.1
 #align simple_graph.sum_inc_matrix_apply_of_not_mem_edge_set SimpleGraph.sum_incMatrix_apply_of_not_mem_edgeSet
 
-theorem incMatrix_transpose_mul_diag [DecidableRel G.Adj] :
+theorem incMatrix_transpose_mul_diag [Fintype α] [Decidable (e ∈ G.edgeSet)] :
     ((G.incMatrix R)ᵀ * G.incMatrix R) e e = if e ∈ G.edgeSet then 2 else 0 := by
   classical
     simp only [Matrix.mul_apply, incMatrix_apply', transpose_apply, ite_zero_mul_ite_zero, one_mul,
@@ -186,14 +187,14 @@ theorem incMatrix_mul_transpose_apply_of_adj (h : G.Adj a b) :
     exact G.incidenceSet_inter_incidenceSet_of_adj h
 #align simple_graph.inc_matrix_mul_transpose_apply_of_adj SimpleGraph.incMatrix_mul_transpose_apply_of_adj
 
-theorem incMatrix_mul_transpose [Fintype α] [DecidableEq α] [DecidableRel G.Adj] :
+theorem incMatrix_mul_transpose
+    [∀ a, Fintype (neighborSet G a)] [DecidableEq α] [DecidableRel G.Adj] :
     G.incMatrix R * (G.incMatrix R)ᵀ = fun a b =>
       if a = b then (G.degree a : R) else if G.Adj a b then 1 else 0 := by
   ext a b
   split_ifs with h h'
   · subst b
-    rename Semiring R => sr
-    convert @incMatrix_mul_transpose_diag _ _ _ _ sr.toNonAssocSemiring _ _ _
+    exact incMatrix_mul_transpose_diag (R := R) G
   · exact G.incMatrix_mul_transpose_apply_of_adj h'
   · simp only [Matrix.mul_apply, Matrix.transpose_apply,
       G.incMatrix_apply_mul_incMatrix_apply_of_not_adj h h', sum_const_zero]

bb168510

refactor: split out finiteness properties for simple graphs (#10123)

620df7c2

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2021 Gabriel Moise. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Gabriel Moise, Yaël Dillies, Kyle Miller
 -/
-import Mathlib.Combinatorics.SimpleGraph.Basic
+import Mathlib.Combinatorics.SimpleGraph.Finite
 import Mathlib.Data.Finset.Sym
 import Mathlib.Data.Matrix.Basic

bb168510

chore: rename Finset.card_doubleton to Finset.card_pair (#9379)

570a85ce

Diff

@@ -136,7 +136,7 @@ theorem sum_incMatrix_apply_of_mem_edgeSet :
     refine' e.ind _
     intro a b h
     rw [mem_edgeSet] at h
-    rw [← Nat.cast_two, ← card_doubleton h.ne]
+    rw [← Nat.cast_two, ← card_pair h.ne]
     simp only [incMatrix_apply', sum_boole, mk'_mem_incidenceSet_iff, h, true_and_iff]
     congr 2
     ext e
@@ -157,7 +157,7 @@ theorem incMatrix_transpose_mul_diag [DecidableRel G.Adj] :
     · revert h
       refine' e.ind _
       intro v w h
-      rw [← Nat.cast_two, ← card_doubleton (G.ne_of_adj h)]
+      rw [← Nat.cast_two, ← card_pair (G.ne_of_adj h)]
       simp only [mk'_mem_incidenceSet_iff, G.mem_edgeSet.mp h, true_and, mem_univ, forall_true_left,
         forall_eq_or_imp, forall_eq, and_self, mem_singleton, ne_eq]
       congr 2

bb168510

refactor: remove Sym2's global Prod setoid instance, use s(x, y) notation for unordered pairs (#8729)

The Sym2 type used a global setoid instance on α × α so that ⟦(x, y)⟧ could stand for an unordered pair using standard Quotient syntax. This commit refactors Sym2 to not use Quotient and instead use its own s(x, y) notation. One benefit to this is that this notation produces a term with type Sym2 rather than Quotient.

The Fintype instance for Sym2 is in Mathlib.Data.Finset.Sym. We switch from using the one for Quotient because it does not require DecidableEq.

9ed6b90f

Diff

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Gabriel Moise, Yaël Dillies, Kyle Miller
 -/
 import Mathlib.Combinatorics.SimpleGraph.Basic
+import Mathlib.Data.Finset.Sym
 import Mathlib.Data.Matrix.Basic
 
 #align_import combinatorics.simple_graph.inc_matrix from "leanprover-community/mathlib"@"bb168510ef455e9280a152e7f31673cabd3d7496"
@@ -180,7 +181,7 @@ theorem incMatrix_mul_transpose_apply_of_adj (h : G.Adj a b) :
     simp_rw [Matrix.mul_apply, Matrix.transpose_apply, incMatrix_apply_mul_incMatrix_apply,
       Set.indicator_apply, Pi.one_apply, sum_boole]
     convert @Nat.cast_one R _
-    convert card_singleton ⟦(a, b)⟧
+    convert card_singleton s(a, b)
     rw [← coe_eq_singleton, coe_filter_univ]
     exact G.incidenceSet_inter_incidenceSet_of_adj h
 #align simple_graph.inc_matrix_mul_transpose_apply_of_adj SimpleGraph.incMatrix_mul_transpose_apply_of_adj

bb168510

feat: (if P then 1 else 0) • a (#8347)

Two simple lemmas, smul_ite_zero, and ite_smul_zero. Also delete Finset.sum_univ_ite since it is now provable by simp thanks to these.

Rename and turn around the following to match the direction that simp goes in:

ite_mul_zero_left → ite_zero_mul
ite_mul_zero_right → mul_ite_zero
ite_and_mul_zero → ite_zero_mul_ite_zero

fba9b451

Diff

@@ -77,7 +77,7 @@ variable [MulZeroOneClass R] {a b : α} {e : Sym2 α}
 
 theorem incMatrix_apply_mul_incMatrix_apply : G.incMatrix R a e * G.incMatrix R b e =
     (G.incidenceSet a ∩ G.incidenceSet b).indicator 1 e := by
-  classical simp only [incMatrix, Set.indicator_apply, ← ite_and_mul_zero, Pi.one_apply, mul_one,
+  classical simp only [incMatrix, Set.indicator_apply, ite_zero_mul_ite_zero, Pi.one_apply, mul_one,
     Set.mem_inter_iff]
 #align simple_graph.inc_matrix_apply_mul_inc_matrix_apply SimpleGraph.incMatrix_apply_mul_incMatrix_apply
 
@@ -150,7 +150,7 @@ theorem sum_incMatrix_apply_of_not_mem_edgeSet (h : e ∉ G.edgeSet) :
 theorem incMatrix_transpose_mul_diag [DecidableRel G.Adj] :
     ((G.incMatrix R)ᵀ * G.incMatrix R) e e = if e ∈ G.edgeSet then 2 else 0 := by
   classical
-    simp only [Matrix.mul_apply, incMatrix_apply', transpose_apply, ← ite_and_mul_zero, one_mul,
+    simp only [Matrix.mul_apply, incMatrix_apply', transpose_apply, ite_zero_mul_ite_zero, one_mul,
       sum_boole, and_self_iff]
     split_ifs with h
     · revert h

bb168510

chore: clear some porting notes on rfl (#8063)

We remove some porting notes for rfls that by now work again.

Co-authored-by: Moritz Firsching <firsching@google.com>

c2d0272f

Diff

@@ -67,8 +67,8 @@ theorem incMatrix_apply [Zero R] [One R] {a : α} {e : Sym2 α} :
 /-- Entries of the incidence matrix can be computed given additional decidable instances. -/
 theorem incMatrix_apply' [Zero R] [One R] [DecidableEq α] [DecidableRel G.Adj] {a : α}
     {e : Sym2 α} : G.incMatrix R a e = if e ∈ G.incidenceSet a then 1 else 0 := by
-  unfold incMatrix Set.indicator -- Porting note: was `convert rfl`
-  simp only [Pi.one_apply]
+  unfold incMatrix Set.indicator
+  convert rfl
 #align simple_graph.inc_matrix_apply' SimpleGraph.incMatrix_apply'
 
 section MulZeroOneClass

bb168510

chore: remove nonterminal simp (#7580)

Removes nonterminal simps on lines looking like simp [...]

6fc8e6ec

Diff

@@ -157,7 +157,8 @@ theorem incMatrix_transpose_mul_diag [DecidableRel G.Adj] :
       refine' e.ind _
       intro v w h
       rw [← Nat.cast_two, ← card_doubleton (G.ne_of_adj h)]
-      simp [mk'_mem_incidenceSet_iff, G.mem_edgeSet.mp h]
+      simp only [mk'_mem_incidenceSet_iff, G.mem_edgeSet.mp h, true_and, mem_univ, forall_true_left,
+        forall_eq_or_imp, forall_eq, and_self, mem_singleton, ne_eq]
       congr 2
       ext u
       simp

bb168510

refactor(Data/Matrix): Eliminate ⬝ notation in favor of HMul (#6487)

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).

38c07226

Diff

@@ -123,7 +123,7 @@ theorem sum_incMatrix_apply [DecidableEq α] [DecidableRel G.Adj] :
 #align simple_graph.sum_inc_matrix_apply SimpleGraph.sum_incMatrix_apply
 
 theorem incMatrix_mul_transpose_diag [DecidableEq α] [DecidableRel G.Adj] :
-    (G.incMatrix R ⬝ (G.incMatrix R)ᵀ) a a = G.degree a := by
+    (G.incMatrix R * (G.incMatrix R)ᵀ) a a = G.degree a := by
   rw [← sum_incMatrix_apply]
   simp only [mul_apply, incMatrix_apply', transpose_apply, mul_ite, mul_one, mul_zero]
   simp_all only [ite_true, sum_boole]
@@ -148,7 +148,7 @@ theorem sum_incMatrix_apply_of_not_mem_edgeSet (h : e ∉ G.edgeSet) :
 #align simple_graph.sum_inc_matrix_apply_of_not_mem_edge_set SimpleGraph.sum_incMatrix_apply_of_not_mem_edgeSet
 
 theorem incMatrix_transpose_mul_diag [DecidableRel G.Adj] :
-    ((G.incMatrix R)ᵀ ⬝ G.incMatrix R) e e = if e ∈ G.edgeSet then 2 else 0 := by
+    ((G.incMatrix R)ᵀ * G.incMatrix R) e e = if e ∈ G.edgeSet then 2 else 0 := by
   classical
     simp only [Matrix.mul_apply, incMatrix_apply', transpose_apply, ← ite_and_mul_zero, one_mul,
       sum_boole, and_self_iff]
@@ -174,7 +174,7 @@ section Semiring
 variable [Fintype (Sym2 α)] [Semiring R] {a b : α} {e : Sym2 α}
 
 theorem incMatrix_mul_transpose_apply_of_adj (h : G.Adj a b) :
-    (G.incMatrix R ⬝ (G.incMatrix R)ᵀ) a b = (1 : R) := by
+    (G.incMatrix R * (G.incMatrix R)ᵀ) a b = (1 : R) := by
   classical
     simp_rw [Matrix.mul_apply, Matrix.transpose_apply, incMatrix_apply_mul_incMatrix_apply,
       Set.indicator_apply, Pi.one_apply, sum_boole]
@@ -185,7 +185,7 @@ theorem incMatrix_mul_transpose_apply_of_adj (h : G.Adj a b) :
 #align simple_graph.inc_matrix_mul_transpose_apply_of_adj SimpleGraph.incMatrix_mul_transpose_apply_of_adj
 
 theorem incMatrix_mul_transpose [Fintype α] [DecidableEq α] [DecidableRel G.Adj] :
-    G.incMatrix R ⬝ (G.incMatrix R)ᵀ = fun a b =>
+    G.incMatrix R * (G.incMatrix R)ᵀ = fun a b =>
       if a = b then (G.degree a : R) else if G.Adj a b then 1 else 0 := by
   ext a b
   split_ifs with h h'

bb168510

chore: banish Type _ and Sort _ (#6499)

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

32de3f67

Diff

@@ -49,7 +49,7 @@ open BigOperators Matrix
 
 namespace SimpleGraph
 
-variable (R : Type _) {α : Type _} (G : SimpleGraph α)
+variable (R : Type*) {α : Type*} (G : SimpleGraph α)
 
 /-- `G.incMatrix R` is the `α × Sym2 α` matrix whose `(a, e)`-entry is `1` if `e` is incident to
 `a` and `0` otherwise. -/

bb168510

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

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Gabriel Moise. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Gabriel Moise, Yaël Dillies, Kyle Miller
-
-! This file was ported from Lean 3 source module combinatorics.simple_graph.inc_matrix
-! leanprover-community/mathlib commit bb168510ef455e9280a152e7f31673cabd3d7496
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Combinatorics.SimpleGraph.Basic
 import Mathlib.Data.Matrix.Basic
 
+#align_import combinatorics.simple_graph.inc_matrix from "leanprover-community/mathlib"@"bb168510ef455e9280a152e7f31673cabd3d7496"
+
 /-!
 # Incidence matrix of a simple graph

bb168510

fix: ∑' precedence (#5615)

Also remove most superfluous parentheses around big operators (∑, ∏ and variants).
roughly the used regex: ([^a-zA-Zα-ωΑ-Ω'𝓝ℳ₀𝕂ₛ)]) $([∑∏][^()∑∏]*,[^()∑∏:]*)$ ([⊂⊆=<≤]) replaced by $1 $2 $3

03fc68aa

Diff

@@ -121,7 +121,7 @@ section NonAssocSemiring
 variable [Fintype α] [NonAssocSemiring R] {a b : α} {e : Sym2 α}
 
 theorem sum_incMatrix_apply [DecidableEq α] [DecidableRel G.Adj] :
-    (∑ e, G.incMatrix R a e) = G.degree a := by
+    ∑ e, G.incMatrix R a e = G.degree a := by
   simp [incMatrix_apply', sum_boole, Set.filter_mem_univ_eq_toFinset]
 #align simple_graph.sum_inc_matrix_apply SimpleGraph.sum_incMatrix_apply
 
@@ -133,7 +133,7 @@ theorem incMatrix_mul_transpose_diag [DecidableEq α] [DecidableRel G.Adj] :
 #align simple_graph.inc_matrix_mul_transpose_diag SimpleGraph.incMatrix_mul_transpose_diag
 
 theorem sum_incMatrix_apply_of_mem_edgeSet :
-    e ∈ G.edgeSet → (∑ a, G.incMatrix R a e) = 2 := by
+    e ∈ G.edgeSet → ∑ a, G.incMatrix R a e = 2 := by
   classical
     refine' e.ind _
     intro a b h
@@ -146,7 +146,7 @@ theorem sum_incMatrix_apply_of_mem_edgeSet :
 #align simple_graph.sum_inc_matrix_apply_of_mem_edge_set SimpleGraph.sum_incMatrix_apply_of_mem_edgeSet
 
 theorem sum_incMatrix_apply_of_not_mem_edgeSet (h : e ∉ G.edgeSet) :
-    (∑ a, G.incMatrix R a e) = 0 :=
+    ∑ a, G.incMatrix R a e = 0 :=
   sum_eq_zero fun _ _ => G.incMatrix_of_not_mem_incidenceSet fun he => h he.1
 #align simple_graph.sum_inc_matrix_apply_of_not_mem_edge_set SimpleGraph.sum_incMatrix_apply_of_not_mem_edgeSet

bb168510

chore: remove superfluous parentheses in calls to ext (#5258)

Co-authored-by: Xavier Roblot <46200072+xroblot@users.noreply.github.com> Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr> Co-authored-by: Riccardo Brasca <riccardo.brasca@gmail.com> Co-authored-by: Yury G. Kudryashov <urkud@urkud.name> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Pol'tta / Miyahara Kō <pol_tta@outlook.jp> Co-authored-by: Jason Yuen <jason_yuen2007@hotmail.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com> Co-authored-by: Jireh Loreaux <loreaujy@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Heather Macbeth <25316162+hrmacbeth@users.noreply.github.com> Co-authored-by: Jujian Zhang <jujian.zhang1998@outlook.com> Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

3d6731dc

Diff

@@ -190,7 +190,7 @@ theorem incMatrix_mul_transpose_apply_of_adj (h : G.Adj a b) :
 theorem incMatrix_mul_transpose [Fintype α] [DecidableEq α] [DecidableRel G.Adj] :
     G.incMatrix R ⬝ (G.incMatrix R)ᵀ = fun a b =>
       if a = b then (G.degree a : R) else if G.Adj a b then 1 else 0 := by
-  ext (a b)
+  ext a b
   split_ifs with h h'
   · subst b
     rename Semiring R => sr

bb168510

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

@@ -78,11 +78,10 @@ section MulZeroOneClass
 
 variable [MulZeroOneClass R] {a b : α} {e : Sym2 α}
 
-theorem incMatrix_apply_mul_incMatrix_apply :
-    G.incMatrix R a e * G.incMatrix R b e = (G.incidenceSet a ∩ G.incidenceSet b).indicator 1 e :=
-  by
+theorem incMatrix_apply_mul_incMatrix_apply : G.incMatrix R a e * G.incMatrix R b e =
+    (G.incidenceSet a ∩ G.incidenceSet b).indicator 1 e := by
   classical simp only [incMatrix, Set.indicator_apply, ← ite_and_mul_zero, Pi.one_apply, mul_one,
-      Set.mem_inter_iff]
+    Set.mem_inter_iff]
 #align simple_graph.inc_matrix_apply_mul_inc_matrix_apply SimpleGraph.incMatrix_apply_mul_incMatrix_apply
 
 theorem incMatrix_apply_mul_incMatrix_apply_of_not_adj (hab : a ≠ b) (h : ¬G.Adj a b) :

bb168510

feat: port Combinatorics.SimpleGraph.IncMatrix (#3274)

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

9ce81ec6

`combinatorics.simple_graph.inc_matrix` ⟷ `Mathlib.Combinatorics.SimpleGraph.IncMatrix`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 388

combinatorics.simple_graph.inc_matrix ⟷ Mathlib.Combinatorics.SimpleGraph.IncMatrix

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 388

`combinatorics.simple_graph.inc_matrix` ⟷ `Mathlib.Combinatorics.SimpleGraph.IncMatrix`