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use have instead of assert

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This commit is contained in:
Floris van Doorn 2016-03-03 11:05:44 -05:00
parent 1213001a6a
commit b7c4f3b6a7
2 changed files with 30 additions and 18 deletions
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8
group_theory/basic.hlean
View file

@ -105,12 +105,14 @@ namespace group
definition is_set_homomorphism [instance] (G₁ G₂ : Group) : is_set (G₁ →g G₂) :=
begin
assert H : G₁ →g G₂ ≃ Σ(f : G₁ → G₂), Π(g₁ g₂ : G₁), f (g₁ * g₂) = f g₁ * f g₂,
{ fapply equiv.MK,
have H : G₁ →g G₂ ≃ Σ(f : G₁ → G₂), Π(g₁ g₂ : G₁), f (g₁ * g₂) = f g₁ * f g₂,
begin
fapply equiv.MK,
{ intro φ, induction φ, constructor, assumption},
{ intro v, induction v, constructor, assumption},
{ intro v, induction v, reflexivity},
{ intro φ, induction φ, reflexivity}},
{ intro φ, induction φ, reflexivity}
end,
apply is_trunc_equiv_closed_rev, exact H
end

40
homotopy/chain_complex.hlean
View file

@ -206,10 +206,12 @@ namespace chain_complex
: is_exact_at_t (transfer_type_chain_complex2 X f c @g @e @p) m :=
begin
intro y q, esimp at *,
assert H2 : tcc_to_fn X (f m) ((equiv_of_eq (ap (λx, X x) (c m)))⁻¹ᵉ (e⁻¹ y)) = pt,
{ refine _ ⬝ ap e⁻¹ᵉ* q ⬝ (respect_pt (e⁻¹ᵉ*)), apply eq_inv_of_eq, clear q, revert y,
have H2 : tcc_to_fn X (f m) ((equiv_of_eq (ap (λx, X x) (c m)))⁻¹ᵉ (e⁻¹ y)) = pt,
begin
refine _ ⬝ ap e⁻¹ᵉ* q ⬝ (respect_pt (e⁻¹ᵉ*)), apply eq_inv_of_eq, clear q, revert y,
refine inv_homotopy_of_homotopy (pequiv.to_equiv e) _,
apply inv_homotopy_of_homotopy, apply p},
apply inv_homotopy_of_homotopy, apply p
end,
induction (H _ H2) with x r,
refine fiber.mk (e (cast (ap (λx, X x) (c (S m))) (cast (ap (λx, X (S x)) (c m)) x))) _,
refine (p _)⁻¹ ⬝ _,
@ -293,10 +295,12 @@ namespace chain_complex
{n : N} (H : is_exact_at X n) : is_exact_at (transfer_chain_complex X @g @e @p) n :=
begin
intro y q, esimp at *,
assert H2 : cc_to_fn X n (e⁻¹ᵉ* y) = pt,
{ refine (inv_commute (λn, equiv_of_pequiv e) _ _ @p _)⁻¹ᵖ ⬝ _,
have H2 : cc_to_fn X n (e⁻¹ᵉ* y) = pt,
begin
refine (inv_commute (λn, equiv_of_pequiv e) _ _ @p _)⁻¹ᵖ ⬝ _,
refine ap _ q ⬝ _,
exact respect_pt e⁻¹ᵉ*},
exact respect_pt e⁻¹ᵉ*
end,
induction (H _ H2) with x,
induction x with x r,
refine image.mk (e x) _,
@ -336,12 +340,14 @@ namespace chain_complex
chain_complex.mk Y @g
begin
refine equiv_rect f _ _, intro n,
assert H : Π (x : Y (f (S (S n)))), g (c n ▸ g (c (S n) ▸ x)) = pt,
{ apply equiv_rect (equiv_of_pequiv e), intro x,
have H : Π (x : Y (f (S (S n)))), g (c n ▸ g (c (S n) ▸ x)) = pt,
begin
apply equiv_rect (equiv_of_pequiv e), intro x,
refine ap (λx, g (c n ▸ x)) (@p (S n) x)⁻¹ᵖ ⬝ _,
refine (p _)⁻¹ ⬝ _,
refine ap e (cc_is_chain_complex X n _) ⬝ _,
apply respect_pt},
apply respect_pt
end,
refine pi.pi_functor _ _ H,
{ intro x, exact (c (S n))⁻¹ ▸ (c n)⁻¹ ▸ x}, -- with implicit arguments, this is:
-- transport (λx, Y x) (c (S n))⁻¹ (transport (λx, Y (S x)) (c n)⁻¹ x)
@ -355,10 +361,12 @@ namespace chain_complex
{n : N} (H : is_exact_at X n) : is_exact_at (transfer_chain_complex2' X f c @g @e @p) (f n) :=
begin
intro y q, esimp at *,
assert H2 : cc_to_fn X n (e⁻¹ᵉ* ((c n)⁻¹ ▸ y)) = pt,
{ refine (inv_commute (λn, equiv_of_pequiv e) _ _ @p _)⁻¹ᵖ ⬝ _,
have H2 : cc_to_fn X n (e⁻¹ᵉ* ((c n)⁻¹ ▸ y)) = pt,
begin
refine (inv_commute (λn, equiv_of_pequiv e) _ _ @p _)⁻¹ᵖ ⬝ _,
rewrite [tr_inv_tr, q],
exact respect_pt e⁻¹ᵉ*},
exact respect_pt e⁻¹ᵉ*
end,
induction (H _ H2) with x,
induction x with x r,
refine image.mk (c n ▸ c (S n) ▸ e x) _,
@ -448,10 +456,12 @@ namespace chain_complex
-- (H : is_exact_at_lg X n) : is_exact_at_lg (transfer_left_group_chain_complex X @g @e @p) n :=
-- begin
-- intro y q, esimp at *,
-- assert H2 : lgcc_to_fn X n (e⁻¹ᵉ* y) = pt,
-- { refine (inv_commute (λn, equiv_of_pequiv e) _ _ @p _)⁻¹ᵖ ⬝ _,
-- have H2 : lgcc_to_fn X n (e⁻¹ᵉ* y) = pt,
-- begin
-- refine (inv_commute (λn, equiv_of_pequiv e) _ _ @p _)⁻¹ᵖ ⬝ _,
-- refine ap _ q ⬝ _,
-- exact respect_pt e⁻¹ᵉ*},
-- exact respect_pt e⁻¹ᵉ*
-- end,
-- cases (H _ H2) with x r,
-- refine image.mk (e x) _,
-- refine (p x)⁻¹ ⬝ _,