add sorry's to make library compile
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2 changed files with 16 additions and 18 deletions
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@ -82,7 +82,7 @@ namespace fwedge
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{ reflexivity },
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{ apply eq_pathover_id_right,
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refine ap_compose pwedge_of_fwedge _ _ ⬝ ap02 _ !elim_glue ⬝ !ap_con ⬝
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!elim_glue ◾ (!ap_inv ⬝ !elim_glue⁻²) ⬝ph _, exact hrfl } end end}},
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!elim_glue ◾ (!ap_inv ⬝ !elim_glue⁻²) ⬝ph _, exact hrfl } end end}},
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{ exact glue ff }
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end
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@ -180,48 +180,48 @@ namespace fwedge
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end
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-- left:
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definition prod_funct_comp {A B X Y : Type*} (f : X →* Y) : (A →* X) × (B →* X) → (A →* Y) × (B →* Y) :=
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definition prod_funct_comp {A B X Y : Type*} (f : X →* Y) : (A →* X) × (B →* X) → (A →* Y) × (B →* Y) :=
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prod_functor (pcompose f) (pcompose f)
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-- right:
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definition left_comp_pi_bool_funct {A B X Y : Type*} (f : X →* Y) : (Π u, (bool.rec A B u →* X)) → (Π u, (bool.rec A B u →* Y)) :=
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definition left_comp_pi_bool_funct {A B X Y : Type*} (f : X →* Y) : (Π u, (bool.rec A B u →* X)) → (Π u, (bool.rec A B u →* Y)) :=
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begin
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intro, intro, exact f ∘* (a u)
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end
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definition left_comp_pi_bool {A B X Y : Type*} (f : X →* Y) : Π u, ((bool.rec A B u →* X) → (bool.rec A B u →* Y)) :=
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definition left_comp_pi_bool {A B X Y : Type*} (f : X →* Y) : Π u, ((bool.rec A B u →* X) → (bool.rec A B u →* Y)) :=
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begin
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intro, intro, exact f∘* a
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end
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-- hsquare 1:
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definition prod_to_pi_bool_nat_square {A B X Y : Type*} (f : X →* Y) :
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definition prod_to_pi_bool_nat_square {A B X Y : Type*} (f : X →* Y) :
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hsquare (prod_pi_bool_comp_funct X) (prod_pi_bool_comp_funct Y) (prod_funct_comp f) (@left_comp_pi_bool_funct A B X Y f) :=
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begin
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begin
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intro x, fapply eq_of_homotopy, intro u, induction u, esimp, esimp
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end
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-- hsquare 2:
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definition fwedge_pmap_nat_square {A B X Y : Type*} (f : X →* Y) :
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definition fwedge_pmap_nat_square {A B X Y : Type*} (f : X →* Y) :
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hsquare (fwedge_pmap_equiv (bool.rec A B) X)⁻¹ᵉ (fwedge_pmap_equiv (bool.rec A B) Y)⁻¹ᵉ (left_comp_pi_bool_funct f) (pcompose f) :=
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begin
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intro h, esimp, fapply pmap_eq,
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begin
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intro h, esimp, fapply pmap_eq,
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exact fwedge_pmap_nat₂ (λ u, bool.rec A B u) f h,
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esimp,
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end
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-- hsquare 3:
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definition fwedge_to_pwedge_nat_square {A B X Y : Type*} (f : X →* Y) :
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hsquare (pequiv_ppcompose_right (pwedge_pequiv_fwedge A B)) (pequiv_ppcompose_right (pwedge_pequiv_fwedge A B)) (pcompose f) (pcompose f) :=
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begin
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definition fwedge_to_pwedge_nat_square {A B X Y : Type*} (f : X →* Y) :
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hsquare (pequiv_ppcompose_right (pwedge_pequiv_fwedge A B)) (pequiv_ppcompose_right (pwedge_pequiv_fwedge A B)) (pcompose f) (pcompose f) :=
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begin
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exact sorry
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end
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definition pwedge_pmap_nat₂ (A B X Y : Type*) (f : X →* Y) (h : A →* X) (k : B →* X) : Π (w : A ∨ B),
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definition pwedge_pmap_nat₂ (A B X Y : Type*) (f : X →* Y) (h : A →* X) (k : B →* X) : Π (w : A ∨ B),
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(f ∘* (pwedge_pmap h k)) w = pwedge_pmap (f ∘* h )(f ∘* k) w :=
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have H : _, from
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(@prod_to_pi_bool_nat_square A B X Y f) ⬝htyh (fwedge_pmap_nat_square f) ⬝htyh (fwedge_to_pwedge_nat_square f),
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proof H qed
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sorry
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-- SA to here 7/5
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@ -23,7 +23,7 @@ namespace wedge
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induction x,
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{ reflexivity },
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{ reflexivity },
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{ apply eq_pathover_id_right,
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{ apply eq_pathover_id_right,
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apply hdeg_square,
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exact ap_compose wedge_flip _ _ ⬝ ap02 _ !elim_glue ⬝ !ap_inv ⬝ !elim_glue⁻² ⬝ !inv_inv }
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end
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@ -48,7 +48,7 @@ namespace wedge
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exact (glue ⋆),
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exact inr (inr a),
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-- exact elim_glue _ _ _,
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exact sorry
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end
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@ -65,5 +65,3 @@ namespace wedge
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... ≃* plift.{u v} A ∨ plift.{u v} B : by exact pwedge_pequiv !pequiv_plift !pequiv_plift
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end wedge
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