Skip to content

Commit

Permalink
bump to nightly-2023-10-25-06
Browse files Browse the repository at this point in the history
  • Loading branch information
leanprover-community-bot committed Oct 25, 2023
1 parent 5b21425 commit 8f0bb51
Show file tree
Hide file tree
Showing 8 changed files with 112 additions and 112 deletions.
12 changes: 6 additions & 6 deletions Mathbin/Combinatorics/SetFamily/Shadow.lean
Expand Up @@ -318,9 +318,9 @@ theorem mem_upShadow_iff_exists_mem_card_add :
#align finset.mem_up_shadow_iff_exists_mem_card_add Finset.mem_upShadow_iff_exists_mem_card_add
-/

#print Finset.shadow_image_compl /-
#print Finset.upShadow_compls /-
@[simp]
theorem shadow_image_compl : ((∂ ) 𝒜).image compl = (∂⁺ ) (𝒜.image compl) :=
theorem upShadow_compls : ((∂ ) 𝒜).image compl = (∂⁺ ) (𝒜.image compl) :=
by
ext s
simp only [mem_image, exists_prop, mem_shadow_iff, mem_up_shadow_iff]
Expand All @@ -329,12 +329,12 @@ theorem shadow_image_compl : ((∂ ) 𝒜).image compl = (∂⁺ ) (𝒜.image c
exact ⟨sᶜ, ⟨s, hs, rfl⟩, a, not_mem_compl.2 ha, compl_erase.symm⟩
· rintro ⟨_, ⟨s, hs, rfl⟩, a, ha, rfl⟩
exact ⟨s.erase a, ⟨s, hs, a, not_mem_compl.1 ha, rfl⟩, compl_erase⟩
#align finset.shadow_image_compl Finset.shadow_image_compl
#align finset.shadow_image_compl Finset.upShadow_compls
-/

#print Finset.upShadow_image_compl /-
#print Finset.shadow_compls /-
@[simp]
theorem upShadow_image_compl : ((∂⁺ ) 𝒜).image compl = (∂ ) (𝒜.image compl) :=
theorem shadow_compls : ((∂⁺ ) 𝒜).image compl = (∂ ) (𝒜.image compl) :=
by
ext s
simp only [mem_image, exists_prop, mem_shadow_iff, mem_up_shadow_iff]
Expand All @@ -343,7 +343,7 @@ theorem upShadow_image_compl : ((∂⁺ ) 𝒜).image compl = (∂ ) (𝒜.image
exact ⟨sᶜ, ⟨s, hs, rfl⟩, a, mem_compl.2 ha, compl_insert.symm⟩
· rintro ⟨_, ⟨s, hs, rfl⟩, a, ha, rfl⟩
exact ⟨insert a s, ⟨s, hs, a, mem_compl.1 ha, rfl⟩, compl_insert⟩
#align finset.up_shadow_image_compl Finset.upShadow_image_compl
#align finset.up_shadow_image_compl Finset.shadow_compls
-/

end UpShadow
Expand Down
4 changes: 2 additions & 2 deletions Mathbin/Computability/RegularExpressions.lean
Expand Up @@ -279,7 +279,7 @@ theorem add_rmatch_iff (P Q : RegularExpression α) (x : List α) :
(P + Q).rmatch x ↔ P.rmatch x ∨ Q.rmatch x :=
by
induction' x with _ _ ih generalizing P Q
· simp only [rmatch, match_epsilon, Bool.or_coe_iff]
· simp only [rmatch, match_epsilon, Bool.coe_or_iff]
· repeat' rw [rmatch]
rw [deriv]
exact ih _ _
Expand All @@ -296,7 +296,7 @@ theorem mul_rmatch_iff (P Q : RegularExpression α) (x : List α) :
· intro h
refine' ⟨[], [], rfl, _⟩
rw [rmatch, rmatch]
rwa [Bool.and_coe_iff] at h
rwa [Bool.coe_and_iff] at h
· rintro ⟨t, u, h₁, h₂⟩
cases' List.append_eq_nil.1 h₁.symm with ht hu
subst ht
Expand Down
4 changes: 2 additions & 2 deletions Mathbin/Data/Bool/AllAny.lean
Expand Up @@ -39,7 +39,7 @@ theorem all_iff_forall {p : α → Bool} : all l p ↔ ∀ a ∈ l, p a :=
by
induction' l with a l ih
· exact iff_of_true rfl (forall_mem_nil _)
simp only [all_cons, Bool.and_coe_iff, ih, forall_mem_cons]
simp only [all_cons, Bool.coe_and_iff, ih, forall_mem_cons]
#align list.all_iff_forall List.all_iff_forall
-/

Expand All @@ -66,7 +66,7 @@ theorem any_iff_exists {p : α → Bool} : any l p ↔ ∃ a ∈ l, p a :=
by
induction' l with a l ih
· exact iff_of_false Bool.not_false' (not_exists_mem_nil _)
simp only [any_cons, Bool.or_coe_iff, ih, exists_mem_cons_iff]
simp only [any_cons, Bool.coe_or_iff, ih, exists_mem_cons_iff]
#align list.any_iff_exists List.any_iff_exists
-/

Expand Down
6 changes: 3 additions & 3 deletions Mathbin/Data/Bool/Basic.lean
Expand Up @@ -198,9 +198,9 @@ theorem not_ne_id : not ≠ id := fun h => false_ne_true <| congr_fun h true
#align bool.bnot_ne_id Bool.not_ne_id
-/

#print Bool.coe_bool_iff /-
theorem coe_bool_iff : ∀ {a b : Bool}, (a ↔ b) ↔ a = b := by decide
#align bool.coe_bool_iff Bool.coe_bool_iff
#print Bool.coe_iff_coe /-
theorem coe_iff_coe : ∀ {a b : Bool}, (a ↔ b) ↔ a = b := by decide
#align bool.coe_bool_iff Bool.coe_iff_coe
-/

#print Bool.eq_true_of_ne_false /-
Expand Down
26 changes: 13 additions & 13 deletions Mathbin/RepresentationTheory/GroupCohomology/Basic.lean
Expand Up @@ -80,20 +80,20 @@ namespace groupCohomology

variable [Monoid G]

#print GroupCohomology.linearYonedaObjResolution /-
#print groupCohomology.linearYonedaObjResolution /-
/-- The complex `Hom(P, A)`, where `P` is the standard resolution of `k` as a trivial `k`-linear
`G`-representation. -/
abbrev linearYonedaObjResolution (A : Rep k G) : CochainComplex (ModuleCat.{u} k) ℕ :=
HomologicalComplex.unop
((((linearYoneda k (Rep k G)).obj A).rightOp.mapHomologicalComplex _).obj (resolution k G))
#align group_cohomology.linear_yoneda_obj_resolution GroupCohomology.linearYonedaObjResolution
#align group_cohomology.linear_yoneda_obj_resolution groupCohomology.linearYonedaObjResolution
-/

#print GroupCohomology.linearYonedaObjResolution_d_apply /-
#print groupCohomology.linearYonedaObjResolution_d_apply /-
theorem linearYonedaObjResolution_d_apply {A : Rep k G} (i j : ℕ) (x : (resolution k G).pt i ⟶ A) :
(linearYonedaObjResolution A).d i j x = (resolution k G).d j i ≫ x :=
rfl
#align group_cohomology.linear_yoneda_obj_resolution_d_apply GroupCohomology.linearYonedaObjResolution_d_apply
#align group_cohomology.linear_yoneda_obj_resolution_d_apply groupCohomology.linearYonedaObjResolution_d_apply
-/

end groupCohomology
Expand All @@ -102,7 +102,7 @@ namespace InhomogeneousCochains

open Rep groupCohomology

#print InhomogeneousCochains.d /-
#print inhomogeneousCochains.d /-
/-- The differential in the complex of inhomogeneous cochains used to
calculate group cohomology. -/
@[simps]
Expand All @@ -119,12 +119,12 @@ def d [Monoid G] (n : ℕ) (A : Rep k G) : ((Fin n → G) → A) →ₗ[k] (Fin
ext x
simp only [Pi.smul_apply, RingHom.id_apply, map_smul, smul_add, Finset.smul_sum, ← smul_assoc,
smul_eq_mul, mul_comm r]
#align inhomogeneous_cochains.d InhomogeneousCochains.d
#align inhomogeneous_cochains.d inhomogeneousCochains.d
-/

variable [Group G] (n) (A : Rep k G)

#print InhomogeneousCochains.d_eq /-
#print inhomogeneousCochains.d_eq /-
/-- The theorem that our isomorphism `Fun(Gⁿ, A) ≅ Hom(k[Gⁿ⁺¹], A)` (where the righthand side is
morphisms in `Rep k G`) commutes with the differentials in the complex of inhomogeneous cochains
and the homogeneous `linear_yoneda_obj_resolution`. -/
Expand Down Expand Up @@ -152,7 +152,7 @@ theorem d_eq :
exact
Finset.sum_congr rfl fun j hj => by
rw [diagonal_hom_equiv_symm_partial_prod_succ, Fin.val_succ]
#align inhomogeneous_cochains.d_eq InhomogeneousCochains.d_eq
#align inhomogeneous_cochains.d_eq inhomogeneousCochains.d_eq
-/

end InhomogeneousCochains
Expand All @@ -163,24 +163,24 @@ variable [Group G] (n) (A : Rep k G)

open InhomogeneousCochains

#print GroupCohomology.inhomogeneousCochains /-
#print groupCohomology.inhomogeneousCochains /-
/-- Given a `k`-linear `G`-representation `A`, this is the complex of inhomogeneous cochains
$$0 \to \mathrm{Fun}(G^0, A) \to \mathrm{Fun}(G^1, A) \to \mathrm{Fun}(G^2, A) \to \dots$$
which calculates the group cohomology of `A`. -/
noncomputable abbrev inhomogeneousCochains : CochainComplex (ModuleCat k) ℕ :=
CochainComplex.of (fun n => ModuleCat.of k ((Fin n → G) → A))
(fun n => InhomogeneousCochains.d n A) fun n =>
(fun n => inhomogeneousCochains.d n A) fun n =>
by
ext x y
have := LinearMap.ext_iff.1 ((linear_yoneda_obj_resolution A).d_comp_d n (n + 1) (n + 2))
simp only [ModuleCat.coe_comp, Function.comp_apply] at this
simp only [ModuleCat.coe_comp, Function.comp_apply, d_eq, LinearEquiv.toModuleIso_hom,
LinearEquiv.toModuleIso_inv, LinearEquiv.coe_coe, LinearEquiv.symm_apply_apply, this,
LinearMap.zero_apply, map_zero, Pi.zero_apply]
#align group_cohomology.inhomogeneous_cochains GroupCohomology.inhomogeneousCochains
#align group_cohomology.inhomogeneous_cochains groupCohomology.inhomogeneousCochains
-/

#print GroupCohomology.inhomogeneousCochainsIso /-
#print groupCohomology.inhomogeneousCochainsIso /-
/-- Given a `k`-linear `G`-representation `A`, the complex of inhomogeneous cochains is isomorphic
to `Hom(P, A)`, where `P` is the standard resolution of `k` as a trivial `G`-representation. -/
def inhomogeneousCochainsIso : inhomogeneousCochains A ≅ linearYonedaObjResolution A :=
Expand All @@ -190,7 +190,7 @@ def inhomogeneousCochainsIso : inhomogeneousCochains A ≅ linearYonedaObjResolu
subst h
simp only [CochainComplex.of_d, d_eq, category.assoc, iso.symm_hom, iso.hom_inv_id,
category.comp_id]
#align group_cohomology.inhomogeneous_cochains_iso GroupCohomology.inhomogeneousCochainsIso
#align group_cohomology.inhomogeneous_cochains_iso groupCohomology.inhomogeneousCochainsIso
-/

end groupCohomology
Expand Down

0 comments on commit 8f0bb51

Please sign in to comment.