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

@@ -436,7 +436,7 @@ theorem exists_eigenvalue (H : Set (Q (m + 1))) (hH : Card H ≥ 2 ^ m + 1) :
   rw [← finrank_eq_rank ℝ] at dim_le dim_add dimW ⊢
   rw [← finrank_eq_rank ℝ, ← finrank_eq_rank ℝ] at dim_add
   norm_cast at dim_le dim_add dimW ⊢
-  rw [pow_succ'] at dim_le
+  rw [pow_succ] at dim_le
   rw [Set.toFinset_card] at hH
   linarith
 #align sensitivity.exists_eigenvalue Sensitivity.exists_eigenvalue

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

@@ -143,7 +143,7 @@ theorem adj_iff_proj_adj {p q : Q (n + 1)} (h₀ : p 0 = q 0) : p.adjacent q ↔
   by
   constructor
   · rintro ⟨i, h_eq, h_uni⟩
-    have h_i : i ≠ 0 := fun h_i => absurd h₀ (by rwa [h_i] at h_eq )
+    have h_i : i ≠ 0 := fun h_i => absurd h₀ (by rwa [h_i] at h_eq)
     use i.pred h_i,
       show p (Fin.succ (Fin.pred i _)) ≠ q (Fin.succ (Fin.pred i _)) by rwa [Fin.succ_pred]
     intro y hy
@@ -225,7 +225,7 @@ theorem duality (p q : Q n) : ε p (e q) = if p = q then 1 else 0 :=
       try congr 1; rw [Q.succ_n_eq]; finish
       try
         erw [(ε _).map_zero]
-        have : p ≠ q := by intro h; rw [p.succ_n_eq q] at h ; finish
+        have : p ≠ q := by intro h; rw [p.succ_n_eq q] at h; finish
         simp [this]
 #align sensitivity.duality Sensitivity.duality
 
@@ -233,7 +233,7 @@ theorem duality (p q : Q n) : ε p (e q) = if p = q then 1 else 0 :=
 theorem epsilon_total {v : V n} (h : ∀ p : Q n, (ε p) v = 0) : v = 0 :=
   by
   induction' n with n ih
-  · dsimp [ε] at h ; exact h fun _ => tt
+  · dsimp [ε] at h; exact h fun _ => tt
   · cases' v with v₁ v₂
     ext <;> change _ = (0 : V n) <;> simp only <;> apply ih <;> intro p <;>
       [let q : Q (n + 1) := fun i => if h : i = 0 then tt else p (i.pred h);
@@ -241,8 +241,8 @@ theorem epsilon_total {v : V n} (h : ∀ p : Q n, (ε p) v = 0) : v = 0 :=
     all_goals
       specialize h q
       first
-      | rw [ε, show q 0 = tt from rfl, cond_tt] at h 
-      | rw [ε, show q 0 = ff from rfl, cond_ff] at h 
+      | rw [ε, show q 0 = tt from rfl, cond_tt] at h
+      | rw [ε, show q 0 = ff from rfl, cond_ff] at h
       rwa [show p = π q by ext; simp [q, Fin.succ_ne_zero, π]]
 #align sensitivity.epsilon_total Sensitivity.epsilon_total
 
@@ -273,7 +273,7 @@ instance : FiniteDimensional ℝ (V n) :=
 theorem finrank_v : finrank ℝ (V n) = 2 ^ n :=
   by
   have := @dim_v n
-  rw [← finrank_eq_rank] at this  <;> assumption_mod_cast
+  rw [← finrank_eq_rank] at this <;> assumption_mod_cast
 #align sensitivity.finrank_V Sensitivity.finrank_v
 
 /-! ### The linear map -/
@@ -357,7 +357,7 @@ theorem g_apply : ∀ v, g m v = (f m v + √ (m + 1) • v, v) := by delta g <;
 theorem g_injective : Injective (g m) := by
   rw [g]
   intro x₁ x₂ h
-  simp only [LinearMap.prod_apply, LinearMap.id_apply, Prod.mk.inj_iff, Pi.prod] at h 
+  simp only [LinearMap.prod_apply, LinearMap.id_apply, Prod.mk.inj_iff, Pi.prod] at h
   exact h.right
 #align sensitivity.g_injective Sensitivity.g_injective
 
@@ -429,15 +429,15 @@ theorem exists_eigenvalue (H : Set (Q (m + 1))) (hH : Card H ≥ 2 ^ m + 1) :
       convert (dual_bases_e_ε _).Basis.LinearIndependent.comp _ Subtype.val_injective
       rw [(dual_bases_e_ε _).coe_basis]
     have hdW := rank_span li
-    rw [Set.range_restrict] at hdW 
+    rw [Set.range_restrict] at hdW
     convert hdW
     rw [← (dual_bases_e_ε _).coe_basis, Cardinal.mk_image_eq (dual_bases_e_ε _).Basis.Injective,
       Cardinal.mk_fintype]
   rw [← finrank_eq_rank ℝ] at dim_le dim_add dimW ⊢
-  rw [← finrank_eq_rank ℝ, ← finrank_eq_rank ℝ] at dim_add 
+  rw [← finrank_eq_rank ℝ, ← finrank_eq_rank ℝ] at dim_add
   norm_cast at dim_le dim_add dimW ⊢
-  rw [pow_succ'] at dim_le 
-  rw [Set.toFinset_card] at hH 
+  rw [pow_succ'] at dim_le
+  rw [Set.toFinset_card] at hH
   linarith
 #align sensitivity.exists_eigenvalue Sensitivity.exists_eigenvalue
 
@@ -449,7 +449,7 @@ theorem huang_degree_theorem (H : Set (Q (m + 1))) (hH : Card H ≥ 2 ^ m + 1) :
   have coeffs_support : ((dual_bases_e_ε (m + 1)).coeffs y).support ⊆ H.to_finset :=
     by
     intro p p_in
-    rw [Finsupp.mem_support_iff] at p_in 
+    rw [Finsupp.mem_support_iff] at p_in
     rw [Set.mem_toFinset]
     exact (dual_bases_e_ε _).mem_of_mem_span y_mem_H p p_in
   obtain ⟨q, H_max⟩ : ∃ q : Q (m + 1), ∀ q' : Q (m + 1), |(ε q' : _) y| ≤ |ε q y|

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

@@ -487,7 +487,7 @@ theorem huang_degree_theorem (H : Set (Q (m + 1))) (hH : Card H ≥ 2 ^ m + 1) :
       by
       refine' (mul_le_mul_right H_q_pos).2 _
       norm_cast
-      apply Finset.card_le_of_subset
+      apply Finset.card_le_card
       rw [Set.toFinset_inter]
       convert Finset.inter_subset_inter_right coeffs_support
 #align sensitivity.huang_degree_theorem Sensitivity.huang_degree_theorem

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

@@ -4,12 +4,12 @@ Patrick Massot. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Reid Barton, Johan Commelin, Jesse Han, Chris Hughes, Robert Y. Lewis, Patrick Massot
 -/
-import Mathbin.Tactic.FinCases
-import Mathbin.Tactic.ApplyFun
-import Mathbin.LinearAlgebra.FiniteDimensional
-import Mathbin.LinearAlgebra.Dual
-import Mathbin.Analysis.NormedSpace.Basic
-import Mathbin.Data.Real.Sqrt
+import Tactic.FinCases
+import Tactic.ApplyFun
+import LinearAlgebra.FiniteDimensional
+import LinearAlgebra.Dual
+import Analysis.NormedSpace.Basic
+import Data.Real.Sqrt
 
 #align_import sensitivity from "leanprover-community/mathlib"@"08b081ea92d80e3a41f899eea36ef6d56e0f1db0"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/48a058d7e39a80ed56858505719a0b2197900999

@@ -420,7 +420,7 @@ theorem exists_eigenvalue (H : Set (Q (m + 1))) (hH : Card H ≥ 2 ^ m + 1) :
   have dim_add : dim (W ⊔ img) + dim (W ⊓ img) = dim W + 2 ^ m :=
     by
     convert ← Submodule.rank_sup_add_rank_inf_eq W img
-    rw [← rank_eq_of_injective (g m) g_injective]
+    rw [← rank_range_of_injective (g m) g_injective]
     apply dim_V
   have dimW : dim W = card H :=
     by

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

@@ -3,11 +3,6 @@ Copyright (c) 2019 Reid Barton, Johan Commelin, Jesse Han, Chris Hughes, Robert
 Patrick Massot. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Reid Barton, Johan Commelin, Jesse Han, Chris Hughes, Robert Y. Lewis, Patrick Massot
-
-! This file was ported from Lean 3 source module sensitivity
-! leanprover-community/mathlib commit 08b081ea92d80e3a41f899eea36ef6d56e0f1db0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Tactic.FinCases
 import Mathbin.Tactic.ApplyFun
@@ -16,6 +11,8 @@ import Mathbin.LinearAlgebra.Dual
 import Mathbin.Analysis.NormedSpace.Basic
 import Mathbin.Data.Real.Sqrt
 
+#align_import sensitivity from "leanprover-community/mathlib"@"08b081ea92d80e3a41f899eea36ef6d56e0f1db0"
+
 /-!
 # Huang's sensitivity theorem
 

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

@@ -5,7 +5,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Reid Barton, Johan Commelin, Jesse Han, Chris Hughes, Robert Y. Lewis, Patrick Massot
 
 ! This file was ported from Lean 3 source module sensitivity
-! leanprover-community/mathlib commit 328375597f2c0dd00522d9c2e5a33b6a6128feeb
+! leanprover-community/mathlib commit 08b081ea92d80e3a41f899eea36ef6d56e0f1db0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -19,6 +19,9 @@ import Mathbin.Data.Real.Sqrt
 /-!
 # Huang's sensitivity theorem
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 A formalization of Hao Huang's sensitivity theorem: in the hypercube of
 dimension n ≥ 1, if one colors more than half the vertices then at least one
 vertex has at least √n colored neighbors.

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

@@ -53,7 +53,6 @@ open scoped Classical
 
 open scoped BigOperators
 
--- mathport name: «expr√»
 notation "√" => Real.sqrt
 
 open Function Bool LinearMap Fintype FiniteDimensional Module.DualBases
@@ -380,26 +379,22 @@ In this section, in order to enforce that `n` is positive, we write it as
 /-! `dim X` will denote the dimension of a subspace `X` as a cardinal. -/
 
 
--- mathport name: «exprdim »
 notation "dim " X:70 => Module.rank ℝ ↥X
 
 /-! `fdim X` will denote the (finite) dimension of a subspace `X` as a natural number. -/
 
 
--- mathport name: exprfdim
 notation "fdim" => finrank ℝ
 
 /-! `Span S` will denote the ℝ-subspace spanned by `S`. -/
 
 
--- mathport name: exprSpan
 notation "Span" => Submodule.span ℝ
 
 /-! `Card X` will denote the cardinal of a subset of a finite type, as a
 natural number. -/
 
 
--- mathport name: «exprCard »
 notation "Card " X:70 => X.toFinset.card
 
 /-! In the following, `⊓` and `⊔` will denote intersection and sums of ℝ-subspaces,

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

@@ -495,7 +495,6 @@ theorem huang_degree_theorem (H : Set (Q (m + 1))) (hH : Card H ≥ 2 ^ m + 1) :
       apply Finset.card_le_of_subset
       rw [Set.toFinset_inter]
       convert Finset.inter_subset_inter_right coeffs_support
-    
 #align sensitivity.huang_degree_theorem Sensitivity.huang_degree_theorem
 
 end Sensitivity

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3209ddf94136d36e5e5c624b10b2a347cc9d090

The termination checker has been getting more capable, and many of the termination_by or decreasing_by clauses in Mathlib are no longer needed.

(Note that termination_by? will show the automatically derived termination expression, so no information is being lost by removing these.)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -183,11 +183,11 @@ variable (n : ℕ)
 /-! `V n` is a real vector space whose equality relation is computable. -/
 
 
-instance : DecidableEq (V n) := by induction n <;> · dsimp only [V]; skip; infer_instance
+instance : DecidableEq (V n) := by induction n <;> · dsimp only [V]; infer_instance
 
-instance : AddCommGroup (V n) := by induction n <;> · dsimp only [V]; skip; infer_instance
+instance : AddCommGroup (V n) := by induction n <;> · dsimp only [V]; infer_instance
 
-instance : Module ℝ (V n) := by induction n <;> · dsimp only [V]; skip; infer_instance
+instance : Module ℝ (V n) := by induction n <;> · dsimp only [V]; infer_instance
 
 end V
 

This covers many instances, but is not exhaustive.

Independently of whether that syntax should be avoided (similar to #10534), I think all these changes are small improvements.

@@ -436,8 +436,8 @@ theorem huang_degree_theorem (H : Set (Q m.succ)) (hH : Card H ≥ 2 ^ m + 1) :
     rw [Finsupp.mem_support_iff] at p_in
     rw [Set.mem_toFinset]
     exact (dualBases_e_ε _).mem_of_mem_span y_mem_H p p_in
-  obtain ⟨q, H_max⟩ : ∃ q : Q m.succ, ∀ q' : Q m.succ, |(ε q' : _) y| ≤ |ε q y|
-  exact Finite.exists_max _
+  obtain ⟨q, H_max⟩ : ∃ q : Q m.succ, ∀ q' : Q m.succ, |(ε q' : _) y| ≤ |ε q y| :=
+    Finite.exists_max _
   have H_q_pos : 0 < |ε q y| := by
     contrapose! y_ne
     exact epsilon_total fun p => abs_nonpos_iff.mp (le_trans (H_max p) y_ne)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -239,7 +239,7 @@ theorem epsilon_total {v : V n} (h : ∀ p : Q n, (ε p) v = 0) : v = 0 := by
       first
       | rw [ε, show q 0 = true from rfl, Bool.cond_true] at h
       | rw [ε, show q 0 = false from rfl, Bool.cond_false] at h
-      rwa [show p = π q by ext; simp [Fin.succ_ne_zero, π]]
+      rwa [show p = π q by ext; simp [q, Fin.succ_ne_zero, π]]
 #align sensitivity.epsilon_total Sensitivity.epsilon_total
 
 open Module

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

This follows on from #6964.

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

@@ -443,8 +443,7 @@ theorem huang_degree_theorem (H : Set (Q m.succ)) (hH : Card H ≥ 2 ^ m + 1) :
     exact epsilon_total fun p => abs_nonpos_iff.mp (le_trans (H_max p) y_ne)
   refine' ⟨q, (dualBases_e_ε _).mem_of_mem_span y_mem_H q (abs_pos.mp H_q_pos), _⟩
   let s := √ (m + 1)
-  suffices : s * |ε q y| ≤ _ * |ε q y|
-  exact (mul_le_mul_right H_q_pos).mp ‹_›
+  suffices s * |ε q y| ≤ _ * |ε q y| from (mul_le_mul_right H_q_pos).mp ‹_›
   let coeffs := (dualBases_e_ε m.succ).coeffs
   calc
     s * |ε q y| = |ε q (s • y)| := by

Also use lowercase for DualBases axioms.

@@ -248,7 +248,7 @@ open Module
 and `ε` computes coefficients of decompositions of vectors on that basis. -/
 theorem dualBases_e_ε (n : ℕ) : DualBases (@e n) (@ε n) where
   eval := duality
-  Total := @epsilon_total _
+  total := @epsilon_total _
 #align sensitivity.dual_bases_e_ε Sensitivity.dualBases_e_ε
 
 /-! We will now derive the dimension of `V`, first as a cardinal in `dim_V` and,

Change a few lemma names that have historically bothered me.

• Finset.card_le_of_subset → Finset.card_le_card
• Multiset.card_le_of_le → Multiset.card_le_card
• Multiset.card_lt_of_lt → Multiset.card_lt_card
• Set.ncard_le_of_subset → Set.ncard_le_ncard
• Finset.image_filter → Finset.filter_image
• CompleteLattice.finset_sup_compact_of_compact → CompleteLattice.isCompactElement_finset_sup

@@ -470,7 +470,7 @@ theorem huang_degree_theorem (H : Set (Q m.succ)) (hH : Card H ≥ 2 ^ m + 1) :
     _ ≤ Finset.card (H ∩ q.adjacent).toFinset * |ε q y| := by
       refine' (mul_le_mul_right H_q_pos).2 _
       norm_cast
-      apply Finset.card_le_of_subset
+      apply Finset.card_le_card
       rw [Set.toFinset_inter]
       convert Finset.inter_subset_inter_right coeffs_support
 #align sensitivity.huang_degree_theorem Sensitivity.huang_degree_theorem

We still have the exact_mod_cast tactic, used in a few places, which somehow (?) works a little bit harder to prevent the expected type influencing the elaboration of the term. I would like to get to the bottom of this, and it will be easier once the only usages of exact_mod_cast are the ones that don't work using the term elaborator by itself.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -353,7 +353,7 @@ theorem g_injective : Injective (g m) := by
 
 theorem f_image_g (w : V m.succ) (hv : ∃ v, g m v = w) : f m.succ w = √ (m + 1) • w := by
   rcases hv with ⟨v, rfl⟩
-  have : √ (m + 1) * √ (m + 1) = m + 1 := Real.mul_self_sqrt (by exact_mod_cast zero_le _)
+  have : √ (m + 1) * √ (m + 1) = m + 1 := Real.mul_self_sqrt (mod_cast zero_le _)
   rw [f_succ_apply, g_apply]
   simp [this, f_squared, smul_add, add_smul, smul_smul, V]
   abel
@@ -400,7 +400,7 @@ theorem exists_eigenvalue (H : Set (Q m.succ)) (hH : Card H ≥ 2 ^ m + 1) :
   let W := Span (e '' H)
   let img := range (g m)
   suffices 0 < dim (W ⊓ img) by
-    exact_mod_cast exists_mem_ne_zero_of_rank_pos this
+    exact mod_cast exists_mem_ne_zero_of_rank_pos this
   have dim_le : dim (W ⊔ img) ≤ 2 ^ (m + 1 : Cardinal) := by
     convert ← rank_submodule_le (W ⊔ img)
     rw [← Nat.cast_succ]

PR contents

This is the supremum of

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

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

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

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

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

• leanprover/lean4#2778
• leanprover/lean4#2790
• leanprover/lean4#2783
• leanprover/lean4#2825
• leanprover/lean4#2722

leanprover/lean4#2778

We can get rid of all the

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

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

leanprover/lean4#2722

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

leanprover/lean4#2783

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

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

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

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

@@ -401,7 +401,7 @@ theorem exists_eigenvalue (H : Set (Q m.succ)) (hH : Card H ≥ 2 ^ m + 1) :
   let img := range (g m)
   suffices 0 < dim (W ⊓ img) by
     exact_mod_cast exists_mem_ne_zero_of_rank_pos this
-  have dim_le : dim (W ⊔ img) ≤ 2 ^ (m + 1) := by
+  have dim_le : dim (W ⊔ img) ≤ 2 ^ (m + 1 : Cardinal) := by
     convert ← rank_submodule_le (W ⊔ img)
     rw [← Nat.cast_succ]
     apply dim_V

This eliminates (fun a ↦ β) α in the type when applying a FunLike.

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -455,7 +455,6 @@ theorem huang_degree_theorem (H : Set (Q m.succ)) (hH : Card H ≥ 2 ^ m + 1) :
         |(coeffs y).sum fun (i : Q m.succ) (a : ℝ) =>
             a • (ε q ∘ f m.succ ∘ fun i : Q m.succ => e i) i| := by
       erw [(f m.succ).map_finsupp_total, (ε q).map_finsupp_total, Finsupp.total_apply]
-      rfl
     _ ≤ ∑ p in (coeffs y).support, |coeffs y p * (ε q <| f m.succ <| e p)| :=
       (norm_sum_le _ fun p => coeffs y p * _)
     _ = ∑ p in (coeffs y).support, |coeffs y p| * ite (p ∈ q.adjacent) 1 0 := by

This reverts commit f3695eb2.

@@ -216,6 +216,7 @@ theorem duality (p q : Q n) : ε p (e q) = if p = q then 1 else 0 := by
   · rw [show p = q from Subsingleton.elim (α := Q 0) p q]
     dsimp [ε, e]
     simp
+    rfl
   · dsimp [ε, e]
     cases hp : p 0 <;> cases hq : q 0
     all_goals

This reverts commit 26eb2b0a.

@@ -216,7 +216,6 @@ theorem duality (p q : Q n) : ε p (e q) = if p = q then 1 else 0 := by
   · rw [show p = q from Subsingleton.elim (α := Q 0) p q]
     dsimp [ε, e]
     simp
-    rfl
   · dsimp [ε, e]
     cases hp : p 0 <;> cases hq : q 0
     all_goals

This includes all the changes from #7606.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -216,6 +216,7 @@ theorem duality (p q : Q n) : ε p (e q) = if p = q then 1 else 0 := by
   · rw [show p = q from Subsingleton.elim (α := Q 0) p q]
     dsimp [ε, e]
     simp
+    rfl
   · dsimp [ε, e]
     cases hp : p 0 <;> cases hq : q 0
     all_goals

Purely cosmetic PR.

@@ -138,7 +138,7 @@ theorem adj_iff_proj_adj {p q : Q n.succ} (h₀ : p 0 = q 0) :
     q ∈ p.adjacent ↔ π q ∈ (π p).adjacent := by
   constructor
   · rintro ⟨i, h_eq, h_uni⟩
-    have h_i : i ≠ 0 := fun h_i => absurd h₀ (by rwa [h_i] at h_eq )
+    have h_i : i ≠ 0 := fun h_i => absurd h₀ (by rwa [h_i] at h_eq)
     use i.pred h_i,
       show p (Fin.succ (Fin.pred i _)) ≠ q (Fin.succ (Fin.pred i _)) by rwa [Fin.succ_pred]
     intro y hy

Purely cosmetic PR

@@ -327,7 +327,7 @@ theorem f_matrix : ∀ p q : Q n, |ε q (f n (e p))| = if p ∈ q.adjacent then
 #align sensitivity.f_matrix Sensitivity.f_matrix
 
 /-- The linear operator $g_m$ corresponding to Knuth's matrix $B_m$. -/
-noncomputable def g (m : ℕ) : V m →ₗ[ℝ] V m.succ:=
+noncomputable def g (m : ℕ) : V m →ₗ[ℝ] V m.succ :=
   LinearMap.prod (f m + √ (m + 1) • LinearMap.id) LinearMap.id
 #align sensitivity.g Sensitivity.g
 

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -399,7 +399,6 @@ theorem exists_eigenvalue (H : Set (Q m.succ)) (hH : Card H ≥ 2 ^ m + 1) :
   let W := Span (e '' H)
   let img := range (g m)
   suffices 0 < dim (W ⊓ img) by
-    simp only [exists_prop]
     exact_mod_cast exists_mem_ne_zero_of_rank_pos this
   have dim_le : dim (W ⊔ img) ≤ 2 ^ (m + 1) := by
     convert ← rank_submodule_le (W ⊔ img)

The new definition is conceptually more satisfactory.

By also changing the definition of the Zero and One instances, we get ((0 : ℕ) : Cardinal) = 0 and ((1 : ℕ) : Cardinal) = 1 definitionally (which wasn't true before), which is in practice more convenient than definitional equality with PEmpty or PUnit.

@@ -403,6 +403,7 @@ theorem exists_eigenvalue (H : Set (Q m.succ)) (hH : Card H ≥ 2 ^ m + 1) :
     exact_mod_cast exists_mem_ne_zero_of_rank_pos this
   have dim_le : dim (W ⊔ img) ≤ 2 ^ (m + 1) := by
     convert ← rank_submodule_le (W ⊔ img)
+    rw [← Nat.cast_succ]
     apply dim_V
   have dim_add : dim (W ⊔ img) + dim (W ⊓ img) = dim W + 2 ^ m := by
     convert ← Submodule.rank_sup_add_rank_inf_eq W img

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -406,7 +406,7 @@ theorem exists_eigenvalue (H : Set (Q m.succ)) (hH : Card H ≥ 2 ^ m + 1) :
     apply dim_V
   have dim_add : dim (W ⊔ img) + dim (W ⊓ img) = dim W + 2 ^ m := by
     convert ← Submodule.rank_sup_add_rank_inf_eq W img
-    rw [← rank_eq_of_injective (g m) g_injective]
+    rw [rank_range_of_injective (g m) g_injective]
     apply dim_V
   have dimW : dim W = card H := by
     have li : LinearIndependent ℝ (H.restrict e) := by

Various adaptations to changes when Fin API was moved to Std. One notable change is that many lemmas are now stated in terms of i ≠ 0 (for i : Fin n) rather then i.1 ≠ 0, and as a consequence many Fin.vne_of_ne applications have been added or removed, mostly removed.

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

@@ -103,8 +103,8 @@ theorem succ_n_eq (p q : Q n.succ) : p = q ↔ p 0 = q 0 ∧ π p = π q := by
     ext x
     by_cases hx : x = 0
     · rwa [hx]
-    · rw [← Fin.succ_pred x <| Fin.vne_of_ne hx]
-      convert congr_fun h (Fin.pred x <| Fin.vne_of_ne hx)
+    · rw [← Fin.succ_pred x hx]
+      convert congr_fun h (Fin.pred x hx)
 #align sensitivity.Q.succ_n_eq Sensitivity.Q.succ_n_eq
 
 /-- The adjacency relation defining the graph structure on `Q n`:
@@ -128,7 +128,7 @@ theorem adj_iff_proj_eq {p q : Q n.succ} (h₀ : p 0 ≠ q 0) : q ∈ p.adjacent
     use 0, h₀
     intro y hy
     contrapose! hy
-    rw [← Fin.succ_pred _ <| Fin.vne_of_ne hy]
+    rw [← Fin.succ_pred _ hy]
     apply congr_fun heq
 #align sensitivity.Q.adj_iff_proj_eq Sensitivity.Q.adj_iff_proj_eq
 
@@ -139,14 +139,14 @@ theorem adj_iff_proj_adj {p q : Q n.succ} (h₀ : p 0 = q 0) :
   constructor
   · rintro ⟨i, h_eq, h_uni⟩
     have h_i : i ≠ 0 := fun h_i => absurd h₀ (by rwa [h_i] at h_eq )
-    use i.pred <| Fin.vne_of_ne h_i,
+    use i.pred h_i,
       show p (Fin.succ (Fin.pred i _)) ≠ q (Fin.succ (Fin.pred i _)) by rwa [Fin.succ_pred]
     intro y hy
     simp [Eq.symm (h_uni _ hy)]
   · rintro ⟨i, h_eq, h_uni⟩
     use i.succ, h_eq
     intro y hy
-    rw [← Fin.pred_inj (ha := Fin.vne_of_ne (?ha : y ≠ 0)) (hb := Fin.vne_of_ne (?hb : i.succ ≠ 0)),
+    rw [← Fin.pred_inj (ha := (?ha : y ≠ 0)) (hb := (?hb : i.succ ≠ 0)),
       Fin.pred_succ]
     case ha =>
       contrapose! hy
@@ -231,8 +231,8 @@ theorem epsilon_total {v : V n} (h : ∀ p : Q n, (ε p) v = 0) : v = 0 := by
   · dsimp [ε] at h; exact h fun _ => true
   · cases' v with v₁ v₂
     ext <;> change _ = (0 : V n) <;> simp only <;> apply ih <;> intro p <;>
-      [let q : Q n.succ := fun i => if h : i = 0 then true else p (i.pred <| Fin.vne_of_ne h);
-      let q : Q n.succ := fun i => if h : i = 0 then false else p (i.pred <| Fin.vne_of_ne h)]
+      [let q : Q n.succ := fun i => if h : i = 0 then true else p (i.pred h);
+      let q : Q n.succ := fun i => if h : i = 0 then false else p (i.pred h)]
     all_goals
       specialize h q
       first

• depends on: #5966

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

@@ -3,11 +3,6 @@ Copyright (c) 2019 Reid Barton, Johan Commelin, Jesse Han, Chris Hughes, Robert
 Patrick Massot. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Reid Barton, Johan Commelin, Jesse Han, Chris Hughes, Robert Y. Lewis, Patrick Massot
-
-! This file was ported from Lean 3 source module sensitivity
-! leanprover-community/mathlib commit 328375597f2c0dd00522d9c2e5a33b6a6128feeb
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Tactic.FinCases
 import Mathlib.Tactic.ApplyFun
@@ -16,6 +11,8 @@ import Mathlib.LinearAlgebra.Dual
 import Mathlib.Analysis.NormedSpace.Basic
 import Mathlib.Data.Real.Sqrt
 
+#align_import sensitivity from "leanprover-community/mathlib"@"328375597f2c0dd00522d9c2e5a33b6a6128feeb"
+
 /-!
 # Huang's sensitivity theorem
 

• depends on: https://github.com/leanprover/std4/pull/163
• depends on: #5584
• depends on: #5715
• depends on: #5729
• depends on: https://github.com/leanprover/std4/pull/173

Co-authored-by: Komyyy <pol_tta@outlook.jp> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -106,8 +106,8 @@ theorem succ_n_eq (p q : Q n.succ) : p = q ↔ p 0 = q 0 ∧ π p = π q := by
     ext x
     by_cases hx : x = 0
     · rwa [hx]
-    · rw [← Fin.succ_pred x hx]
-      convert congr_fun h (Fin.pred x hx)
+    · rw [← Fin.succ_pred x <| Fin.vne_of_ne hx]
+      convert congr_fun h (Fin.pred x <| Fin.vne_of_ne hx)
 #align sensitivity.Q.succ_n_eq Sensitivity.Q.succ_n_eq
 
 /-- The adjacency relation defining the graph structure on `Q n`:
@@ -131,7 +131,7 @@ theorem adj_iff_proj_eq {p q : Q n.succ} (h₀ : p 0 ≠ q 0) : q ∈ p.adjacent
     use 0, h₀
     intro y hy
     contrapose! hy
-    rw [← Fin.succ_pred _ hy]
+    rw [← Fin.succ_pred _ <| Fin.vne_of_ne hy]
     apply congr_fun heq
 #align sensitivity.Q.adj_iff_proj_eq Sensitivity.Q.adj_iff_proj_eq
 
@@ -142,14 +142,15 @@ theorem adj_iff_proj_adj {p q : Q n.succ} (h₀ : p 0 = q 0) :
   constructor
   · rintro ⟨i, h_eq, h_uni⟩
     have h_i : i ≠ 0 := fun h_i => absurd h₀ (by rwa [h_i] at h_eq )
-    use i.pred h_i,
+    use i.pred <| Fin.vne_of_ne h_i,
       show p (Fin.succ (Fin.pred i _)) ≠ q (Fin.succ (Fin.pred i _)) by rwa [Fin.succ_pred]
     intro y hy
     simp [Eq.symm (h_uni _ hy)]
   · rintro ⟨i, h_eq, h_uni⟩
     use i.succ, h_eq
     intro y hy
-    rw [← Fin.pred_inj (ha := ?ha) (hb := ?hb), Fin.pred_succ]
+    rw [← Fin.pred_inj (ha := Fin.vne_of_ne (?ha : y ≠ 0)) (hb := Fin.vne_of_ne (?hb : i.succ ≠ 0)),
+      Fin.pred_succ]
     case ha =>
       contrapose! hy
       rw [hy, h₀]
@@ -233,8 +234,8 @@ theorem epsilon_total {v : V n} (h : ∀ p : Q n, (ε p) v = 0) : v = 0 := by
   · dsimp [ε] at h; exact h fun _ => true
   · cases' v with v₁ v₂
     ext <;> change _ = (0 : V n) <;> simp only <;> apply ih <;> intro p <;>
-      [let q : Q n.succ := fun i => if h : i = 0 then true else p (i.pred h);
-      let q : Q n.succ := fun i => if h : i = 0 then false else p (i.pred h)]
+      [let q : Q n.succ := fun i => if h : i = 0 then true else p (i.pred <| Fin.vne_of_ne h);
+      let q : Q n.succ := fun i => if h : i = 0 then false else p (i.pred <| Fin.vne_of_ne h)]
     all_goals
       specialize h q
       first

This is the second half of the changes originally in #5699, removing all occurrences of ; after a space and implementing a linter rule to enforce it.

In most cases this 2-character substring has a space after it, so the following command was run first:

find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;

The remaining cases were few enough in number that they were done manually.

@@ -230,7 +230,7 @@ theorem duality (p q : Q n) : ε p (e q) = if p = q then 1 else 0 := by
 /-- Any vector in `V n` annihilated by all `ε p`'s is zero. -/
 theorem epsilon_total {v : V n} (h : ∀ p : Q n, (ε p) v = 0) : v = 0 := by
   induction' n with n ih
-  · dsimp [ε] at h ; exact h fun _ => true
+  · dsimp [ε] at h; exact h fun _ => true
   · cases' v with v₁ v₂
     ext <;> change _ = (0 : V n) <;> simp only <;> apply ih <;> intro p <;>
       [let q : Q n.succ := fun i => if h : i = 0 then true else p (i.pred h);