feat: backport changes from lean-pr-testing-4096 (#12772)

These changes will be required after leanprover/lean4#4096, but they all look like positive readability changes to me anyway (the things being filled in are sort of hard to work out with time travelling to later lines in the proofs!), so I think we can backport them all to `master`. Co-authored-by: Scott Morrison <[email protected]>
leanprover-community · May 9, 2024 · b72ddd8 · b72ddd8
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diff --git a/Mathlib/Algebra/Order/CauSeq/Completion.lean b/Mathlib/Algebra/Order/CauSeq/Completion.lean
@@ -236,7 +236,7 @@ theorem inv_mk {f} (hf) : (@mk α _ β _ abv _ f)⁻¹ = mk (inv f hf) :=
 #align cau_seq.completion.inv_mk CauSeq.Completion.inv_mk
 
 theorem cau_seq_zero_ne_one : ¬(0 : CauSeq _ abv) ≈ 1 := fun h =>
-  have : LimZero (1 - 0) := Setoid.symm h
+  have : LimZero (1 - 0 : CauSeq _ abv) := Setoid.symm h
   have : LimZero 1 := by simpa
   by apply one_ne_zero <| const_limZero.1 this
 #align cau_seq.completion.cau_seq_zero_ne_one CauSeq.Completion.cau_seq_zero_ne_one

diff --git a/Mathlib/Analysis/NormedSpace/OperatorNorm/Prod.lean b/Mathlib/Analysis/NormedSpace/OperatorNorm/Prod.lean
@@ -160,7 +160,7 @@ variable (𝕜 E F)
     ‖fst 𝕜 E F‖ = 1 := by
   refine le_antisymm (norm_fst_le ..) ?_
   let ⟨e, he⟩ := exists_ne (0 : E)
-  have : ‖e‖ ≤ _ * max ‖e‖ ‖0‖ := (fst 𝕜 E F).le_opNorm (e, 0)
+  have : ‖e‖ ≤ _ * max ‖e‖ ‖(0 : F)‖ := (fst 𝕜 E F).le_opNorm (e, 0)
   rw [norm_zero, max_eq_left (norm_nonneg e)] at this
   rwa [← mul_le_mul_iff_of_pos_right (norm_pos_iff.mpr he), one_mul]
 
@@ -170,7 +170,7 @@ variable (𝕜 E F)
     ‖snd 𝕜 E F‖ = 1 := by
   refine le_antisymm (norm_snd_le ..) ?_
   let ⟨f, hf⟩ := exists_ne (0 : F)
-  have : ‖f‖ ≤ _ * max ‖0‖ ‖f‖ := (snd 𝕜 E F).le_opNorm (0, f)
+  have : ‖f‖ ≤ _ * max ‖(0 : E)‖ ‖f‖ := (snd 𝕜 E F).le_opNorm (0, f)
   rw [norm_zero, max_eq_right (norm_nonneg f)] at this
   rwa [← mul_le_mul_iff_of_pos_right (norm_pos_iff.mpr hf), one_mul]
 

diff --git a/Mathlib/Analysis/SpecialFunctions/ImproperIntegrals.lean b/Mathlib/Analysis/SpecialFunctions/ImproperIntegrals.lean
@@ -96,7 +96,7 @@ theorem not_integrableOn_Ioi_rpow (s : ℝ) : ¬ IntegrableOn (fun x ↦ x ^ s)
   · have : IntegrableOn (fun x ↦ x ^ s) (Ioo (0 : ℝ) 1) := h.mono Ioo_subset_Ioi_self le_rfl
     rw [integrableOn_Ioo_rpow_iff zero_lt_one] at this
     exact hs.not_lt this
-  · have : IntegrableOn (fun x ↦ x ^ s) (Ioi 1) := h.mono (Ioi_subset_Ioi zero_le_one) le_rfl
+  · have : IntegrableOn (fun x ↦ x ^ s) (Ioi (1 : ℝ)) := h.mono (Ioi_subset_Ioi zero_le_one) le_rfl
     rw [integrableOn_Ioi_rpow_iff zero_lt_one] at this
     exact hs.not_lt this
 

diff --git a/Mathlib/Computability/AkraBazzi/AkraBazzi.lean b/Mathlib/Computability/AkraBazzi/AkraBazzi.lean
@@ -520,7 +520,7 @@ lemma tendsto_zero_sumCoeffsExp : Tendsto (fun (p : ℝ) => ∑ i, a i * (b i) ^
   linarith
 
 lemma tendsto_atTop_sumCoeffsExp : Tendsto (fun (p : ℝ) => ∑ i, a i * (b i) ^ p) atBot atTop := by
-  have h₁ : Tendsto (fun p => (a (max_bi b) : ℝ) * b (max_bi b) ^ p) atBot atTop :=
+  have h₁ : Tendsto (fun p : ℝ => (a (max_bi b) : ℝ) * b (max_bi b) ^ p) atBot atTop :=
     Tendsto.mul_atTop (R.a_pos (max_bi b)) (by simp)
       <| tendsto_rpow_atBot_of_base_lt_one _
       (by have := R.b_pos (max_bi b); linarith) (R.b_lt_one _)

diff --git a/Mathlib/GroupTheory/Coset.lean b/Mathlib/GroupTheory/Coset.lean
@@ -148,7 +148,7 @@ variable [Monoid α] (s : Submonoid α)
 
 @[to_additive mem_own_leftAddCoset]
 theorem mem_own_leftCoset (a : α) : a ∈ a • (s : Set α) :=
-  suffices a * 1 ∈ a • ↑s by simpa
+  suffices a * 1 ∈ a • (s : Set α) by simpa
   mem_leftCoset a (one_mem s : 1 ∈ s)
 #align mem_own_left_coset mem_own_leftCoset
 #align mem_own_left_add_coset mem_own_leftAddCoset

diff --git a/Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean b/Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean
@@ -118,7 +118,7 @@ def invertibleEquivDetInvertible : Invertible A ≃ Invertible A.det where
 variable {A B}
 
 theorem mul_eq_one_comm : A * B = 1 ↔ B * A = 1 :=
-  suffices ∀ A B, A * B = 1 → B * A = 1 from ⟨this A B, this B A⟩
+  suffices ∀ A B : Matrix n n α, A * B = 1 → B * A = 1 from ⟨this A B, this B A⟩
   fun A B h => by
   letI : Invertible B.det := detInvertibleOfLeftInverse _ _ h
   letI : Invertible B := invertibleOfDetInvertible B

diff --git a/Mathlib/MeasureTheory/Measure/Haar/Unique.lean b/Mathlib/MeasureTheory/Measure/Haar/Unique.lean
@@ -492,7 +492,7 @@ lemma measure_preimage_isMulLeftInvariant_eq_smul_of_hasCompactSupport
     · simpa using (u_mem n).2.le
   have I1 := I μ' (by infer_instance)
   simp_rw [M] at I1
-  have J1 : ∫ (x : G), indicator {1} (fun _ ↦ 1) (f x) ∂μ'
+  have J1 : ∫ (x : G), indicator {1} (fun _ ↦ (1 : ℝ)) (f x) ∂μ'
       = ∫ (x : G), indicator {1} (fun _ ↦ 1) (f x) ∂(haarScalarFactor μ' μ • μ) :=
     tendsto_nhds_unique I1 (I (haarScalarFactor μ' μ • μ) (by infer_instance))
   have J2 : ENNReal.toReal (μ' (f ⁻¹' {1}))

diff --git a/Mathlib/NumberTheory/Zsqrtd/QuadraticReciprocity.lean b/Mathlib/NumberTheory/Zsqrtd/QuadraticReciprocity.lean
@@ -88,7 +88,7 @@ theorem prime_of_nat_prime_of_mod_four_eq_three (p : ℕ) [hp : Fact p.Prime] (h
   irreducible_iff_prime.1 <|
     by_contradiction fun hpi =>
       let ⟨a, b, hab⟩ := sq_add_sq_of_nat_prime_of_not_irreducible p hpi
-      have : ∀ a b : ZMod 4, a ^ 2 + b ^ 2 ≠ ↑p := by
+      have : ∀ a b : ZMod 4, a ^ 2 + b ^ 2 ≠ (p : ZMod 4) := by
         erw [← ZMod.natCast_mod p 4, hp3]; decide
       this a b (hab ▸ by simp)
 #align gaussian_int.prime_of_nat_prime_of_mod_four_eq_three GaussianInt.prime_of_nat_prime_of_mod_four_eq_three

diff --git a/Mathlib/Order/PrimeIdeal.lean b/Mathlib/Order/PrimeIdeal.lean
@@ -158,7 +158,7 @@ instance (priority := 100) IsMaximal.isPrime [IsMaximal I] : IsPrime I := by
   let J := I ⊔ principal x
   have hJuniv : (J : Set P) = Set.univ :=
     IsMaximal.maximal_proper (lt_sup_principal_of_not_mem ‹_›)
-  have hyJ : y ∈ ↑J := Set.eq_univ_iff_forall.mp hJuniv y
+  have hyJ : y ∈ (J : Set P) := Set.eq_univ_iff_forall.mp hJuniv y
   rw [coe_sup_eq] at hyJ
   rcases hyJ with ⟨a, ha, b, hb, hy⟩
   rw [hy]

diff --git a/Mathlib/RingTheory/Polynomial/Eisenstein/Basic.lean b/Mathlib/RingTheory/Polynomial/Eisenstein/Basic.lean
@@ -175,7 +175,7 @@ theorem dvd_pow_natDegree_of_eval₂_eq_zero {f : R →+* A} (hf : Function.Inje
           (Ideal.mem_span_singleton.mpr <| dvd_refl x)).pow_natDegree_le_of_root_of_monic_mem
       _ ((monic_scaleRoots_iff x).mpr hp) _ le_rfl
   rw [injective_iff_map_eq_zero'] at hf
-  have : eval₂ _ _ (p.scaleRoots x) = 0 := scaleRoots_eval₂_eq_zero f h
+  have : eval₂ f _ (p.scaleRoots x) = 0 := scaleRoots_eval₂_eq_zero f h
   rwa [hz, Polynomial.eval₂_at_apply, hf] at this
 #align polynomial.dvd_pow_nat_degree_of_eval₂_eq_zero Polynomial.dvd_pow_natDegree_of_eval₂_eq_zero
 

diff --git a/Mathlib/Topology/ContinuousFunction/Bounded.lean b/Mathlib/Topology/ContinuousFunction/Bounded.lean
@@ -581,7 +581,7 @@ theorem arzela_ascoli₂ (s : Set β) (hs : IsCompact s) (A : Set (α →ᵇ β)
     IsCompact A := by
   /- This version is deduced from the previous one by restricting to the compact type in the target,
   using compactness there and then lifting everything to the original space. -/
-  have M : LipschitzWith 1 (↑) := LipschitzWith.subtype_val s
+  have M : LipschitzWith 1 Subtype.val := LipschitzWith.subtype_val s
   let F : (α →ᵇ s) → α →ᵇ β := comp (↑) M
   refine' IsCompact.of_isClosed_subset ((_ : IsCompact (F ⁻¹' A)).image (continuous_comp M)) closed
       fun f hf => _