chore: bump toolchain to v4.15.0
#281 adapt code to v4.15.0 and fix long heartbeats, e.g., toDualRep_apply_eq_contrOneTwoLeft. --------- Co-authored-by: jstoobysmith <72603918+jstoobysmith@users.noreply.github.com>
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KUO-TSAN HSU (Gordon)
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49 changed files with 484 additions and 472 deletions
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@ -149,11 +149,13 @@ lemma contrMap_prod_tprod_aux
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CoeSort.coe (S.FD.obj { as := (OverColor.mk c).hom i }))
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(q' : (i : (𝟭 Type).obj (OverColor.mk c1).left) →
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CoeSort.coe (S.FD.obj { as := (OverColor.mk c1).hom i })) :
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(lift.discreteSumEquiv S.FD l)
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(lift.discreteSumEquiv' S.FD l)
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(HepLean.PiTensorProduct.elimPureTensor
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(fun k => p (q.i.succAbove (q.j.succAbove k))) q' l) =
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(S.FD.map (eqToHom (by simp [h]))).hom
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((lift.discreteSumEquiv S.FD l')
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(S.FD.map (eqToHom (by
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simp only [mk_hom, h, mk_left, Discrete.mk.injEq]
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rfl))).hom
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((lift.discreteSumEquiv' S.FD l')
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(HepLean.PiTensorProduct.elimPureTensor p q' l')) := by
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subst h'
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match l with
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@ -167,6 +169,18 @@ lemma contrMap_prod_tprod_aux
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Function.comp_apply, Sum.map_inr, Discrete.functor_map_id, Action.id_hom]
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rfl
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lemma contrMap_prod_tprod_aux_2 (p : (i : (𝟭 Type).obj (OverColor.mk c).left) →
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CoeSort.coe (S.FD.obj { as := (OverColor.mk c).hom i }))
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(a : Fin n.succ.succ) (b : Fin (n + 1 + 1) ⊕ Fin n1)
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(h : b = Sum.inl a) : p a = (S.FD.map (Discrete.eqToHom (by rw [h]; simp))).hom
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((lift.discreteSumEquiv' S.FD b)
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(HepLean.PiTensorProduct.elimPureTensor p q' b)) := by
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subst h
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simp only [Nat.succ_eq_add_one, mk_hom, instMonoidalCategoryStruct_tensorObj_hom,
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Sum.elim_inl, eqToHom_refl, Discrete.functor_map_id, Action.id_hom, Functor.id_obj,
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ModuleCat.id_apply]
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rfl
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lemma contrMap_prod_tprod (p : (i : (𝟭 Type).obj (OverColor.mk c).left) →
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CoeSort.coe (S.FD.obj { as := (OverColor.mk c).hom i }))
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(q' : (i : (𝟭 Type).obj (OverColor.mk c1).left) →
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@ -202,15 +216,6 @@ lemma contrMap_prod_tprod (p : (i : (𝟭 Type).obj (OverColor.mk c).left) →
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((PiTensorProduct.tprod S.k) _))
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conv_rhs => rw [contrMap, TensorSpecies.contrMap_tprod]
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simp only [TensorProduct.smul_tmul, TensorProduct.tmul_smul, map_smul]
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have hL (a : Fin n.succ.succ) {b : Fin (n + 1 + 1) ⊕ Fin n1}
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(h : b = Sum.inl a) : p a = (S.FD.map (Discrete.eqToHom (by rw [h]; simp))).hom
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((lift.discreteSumEquiv S.FD b)
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(HepLean.PiTensorProduct.elimPureTensor p q' b)) := by
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subst h
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simp only [Nat.succ_eq_add_one, mk_hom, instMonoidalCategoryStruct_tensorObj_hom,
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Sum.elim_inl, eqToHom_refl, Discrete.functor_map_id, Action.id_hom, Functor.id_obj,
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ModuleCat.id_apply]
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rfl
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congr 1
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· apply congrArg
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simp only [Monoidal.tensorUnit_obj, Action.instMonoidalCategory_tensorUnit_V,
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@ -233,7 +238,7 @@ lemma contrMap_prod_tprod (p : (i : (𝟭 Type).obj (OverColor.mk c).left) →
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· erw [ModuleCat.id_apply, ModuleCat.id_apply, ModuleCat.id_apply, ModuleCat.id_apply]
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simp only [AddHom.toFun_eq_coe, LinearMap.coe_toAddHom, equivToIso_homToEquiv,
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LinearEquiv.coe_coe]
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apply hL
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apply contrMap_prod_tprod_aux_2
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exact Eq.symm ((fun f => (Equiv.apply_eq_iff_eq_symm_apply f).mp) finSumFinEquiv rfl)
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· simp only [Discrete.functor_obj_eq_as, Function.comp_apply, AddHom.toFun_eq_coe,
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LinearMap.coe_toAddHom, equivToIso_homToEquiv]
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@ -245,7 +250,7 @@ lemma contrMap_prod_tprod (p : (i : (𝟭 Type).obj (OverColor.mk c).left) →
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(h1' : b = Sum.inl a) (h2' : c a = S.τ (c d)) :
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(S.FD.map (Discrete.eqToHom h2')).hom (p a) =
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(S.FD.map (eqToHom (by subst h1'; simpa using h2'))).hom
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((lift.discreteSumEquiv S.FD b)
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((lift.discreteSumEquiv' S.FD b)
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(HepLean.PiTensorProduct.elimPureTensor p q' b)) := by
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subst h1'
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rfl
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@ -280,6 +285,7 @@ lemma contrMap_prod :
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S.F.map (OverColor.equivToIso leftContrEquivSuccSucc).hom ≫ q.leftContr.contrMap
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≫ S.F.map (OverColor.mkIso (q.leftContr_map_eq)).hom := by
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ext1
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refine ModuleCat.hom_ext ?_
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exact HepLean.PiTensorProduct.induction_tmul (fun p q' => q.contrMap_prod_tprod p q')
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lemma contr_prod
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@ -296,7 +302,7 @@ lemma contr_prod
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simp only [Nat.succ_eq_add_one, Functor.id_obj, mk_hom, Action.instMonoidalCategory_tensorObj_V,
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Functor.const_obj_obj, Equiv.toFun_as_coe, Action.comp_hom, Equivalence.symm_inverse,
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Action.functorCategoryEquivalence_functor, Action.FunctorCategoryEquivalence.functor_obj_obj,
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ModuleCat.coe_comp, Function.comp_apply]
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ModuleCat.hom_comp, Function.comp_apply]
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apply congrArg
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apply congrArg
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rfl
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@ -448,7 +454,7 @@ lemma prod_contrMap_tprod (p : (i : (𝟭 Type).obj (OverColor.mk c1).left) →
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LinearEquiv.coe_coe]
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have hL (a : Fin n.succ.succ) {b : Fin n1 ⊕ Fin n.succ.succ}
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(h : b = Sum.inr a) : q' a = (S.FD.map (Discrete.eqToHom (by rw [h]; simp))).hom
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((lift.discreteSumEquiv S.FD b)
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((lift.discreteSumEquiv' S.FD b)
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(HepLean.PiTensorProduct.elimPureTensor p q' b)) := by
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subst h
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simp only [Nat.succ_eq_add_one, mk_hom, instMonoidalCategoryStruct_tensorObj_hom,
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@ -468,7 +474,7 @@ lemma prod_contrMap_tprod (p : (i : (𝟭 Type).obj (OverColor.mk c1).left) →
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(h1' : b = Sum.inr a) (h2' : c a = S.τ (c d)) :
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(S.FD.map (Discrete.eqToHom h2')).hom (q' a) =
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(S.FD.map (eqToHom (by subst h1'; simpa using h2'))).hom
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((lift.discreteSumEquiv S.FD b)
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((lift.discreteSumEquiv' S.FD b)
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(HepLean.PiTensorProduct.elimPureTensor p q' b)) := by
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subst h1'
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rfl
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@ -492,11 +498,13 @@ lemma prod_contrMap_tprod (p : (i : (𝟭 Type).obj (OverColor.mk c1).left) →
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(l' :Fin n1 ⊕ Fin n.succ.succ)
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(h : Sum.elim c1 c l' = Sum.elim c1 (c ∘ q.i.succAbove ∘ q.j.succAbove) l)
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(h' : l' = (Sum.map id (q.i.succAbove ∘ q.j.succAbove) l)) :
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(lift.discreteSumEquiv S.FD l)
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(lift.discreteSumEquiv' S.FD l)
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(HepLean.PiTensorProduct.elimPureTensor p
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(fun k => q' (q.i.succAbove (q.j.succAbove k))) l) =
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(S.FD.map (eqToHom (by simp [h]))).hom
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((lift.discreteSumEquiv S.FD l')
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(S.FD.map (eqToHom (by
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simp only [mk_hom, h, mk_left, Discrete.mk.injEq]
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rfl))).hom
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((lift.discreteSumEquiv' S.FD l')
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(HepLean.PiTensorProduct.elimPureTensor p q' l')) := by
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subst h'
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match l with
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@ -526,6 +534,7 @@ lemma prod_contrMap :
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S.F.map (OverColor.equivToIso finSumFinEquiv).hom ≫
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q.rightContr.contrMap ≫ S.F.map (OverColor.mkIso (q.rightContr_map_eq)).hom := by
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ext1
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refine ModuleCat.hom_ext ?_
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exact HepLean.PiTensorProduct.induction_tmul (fun p q' => q.prod_contrMap_tprod p q')
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lemma prod_contr (t1 : TensorTree S c1) (t : TensorTree S c) :
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@ -540,7 +549,7 @@ lemma prod_contr (t1 : TensorTree S c1) (t : TensorTree S c) :
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simp only [Nat.succ_eq_add_one, Functor.id_obj, mk_hom, Action.instMonoidalCategory_tensorObj_V,
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Functor.const_obj_obj, Equiv.toFun_as_coe, Action.comp_hom, Equivalence.symm_inverse,
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Action.functorCategoryEquivalence_functor, Action.FunctorCategoryEquivalence.functor_obj_obj,
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ModuleCat.coe_comp, Function.comp_apply]
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ModuleCat.hom_comp, Function.comp_apply]
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apply congrArg
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apply congrArg
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rfl
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