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chore(hott) the coercion doesn't seem to be the problem

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Jakob von Raumer 2016-03-30 13:59:55 +01:00 committed by Leonardo de Moura
parent 7a9e1c7f4f
commit 651df51cb7
1 changed files with 11 additions and 11 deletions
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22
hott/types/sum.hlean
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@ -231,31 +231,31 @@ namespace sum
esimp[unit_sum_equiv_cancel_map], apply sum.rec,
{ intro x, cases x with u Hu, esimp, apply sum.rec,
{ intro x, exfalso, cases x with u' Hu', apply empty_of_inl_eq_inr,
calc inl ⋆ = (to_fun H)⁻¹ (H (inl ⋆)) : (to_left_inv H (inl ⋆))⁻¹
... = (to_fun H)⁻¹ (inl u') : ap (to_fun H)⁻¹ Hu'
... = (to_fun H)⁻¹ (inl u) : {!is_prop.elim}
... = (to_fun H)⁻¹ (H (inr _)) : {Hu⁻¹}
calc inl ⋆ = H⁻¹ (H (inl ⋆)) : (to_left_inv H (inl ⋆))⁻¹
... = H⁻¹ (inl u') : ap H⁻¹ Hu'
... = H⁻¹ (inl u) : {!is_prop.elim}
... = H⁻¹ (H (inr _)) : {Hu⁻¹}
... = inr _ : to_left_inv H },
{ intro x, cases x with b' Hb', esimp, cases sum.mem_cases ((to_fun H)⁻¹ (inr b)) with x x,
{ intro x, cases x with b' Hb', esimp, cases sum.mem_cases (H⁻¹ (inr b)) with x x,
{ cases x with u' Hu', cases u', apply eq_of_inr_eq_inr,
calc inr b' = H (inl ⋆) : Hb'⁻¹
... = H ((to_fun H)⁻¹ (inr b)) : (ap (to_fun H) Hu')⁻¹
... = H (H⁻¹ (inr b)) : (ap H Hu')⁻¹
... = inr b : to_right_inv H (inr b)},
{ exfalso, cases x with a Ha, apply empty_of_inl_eq_inr,
cases u, apply concat, apply Hu⁻¹, apply concat, rotate 1, apply !(to_right_inv H),
apply ap (to_fun H),
apply ap H,
apply concat, rotate 1, apply Ha⁻¹, apply ap inr, esimp,
apply sum.rec, intro x, exfalso, apply empty_of_inl_eq_inr,
apply concat, exact x.2⁻¹, apply Ha,
intro x, cases x with a' Ha', esimp, apply eq_of_inr_eq_inr, apply Ha'⁻¹ ⬝ Ha } } },
{ intro x, cases x with b' Hb', esimp, apply eq_of_inr_eq_inr, refine Hb'⁻¹ ⬝ _,
cases sum.mem_cases ((to_fun H)⁻¹ (inr b)) with x x,
{ cases x with u Hu, esimp, cases sum.mem_cases ((to_fun H)⁻¹ (inl ⋆)) with x x,
cases sum.mem_cases (H⁻¹ (inr b)) with x x,
{ cases x with u Hu, esimp, cases sum.mem_cases (H⁻¹ (inl ⋆)) with x x,
{ cases x with u' Hu', exfalso, apply empty_of_inl_eq_inr,
calc inl ⋆ = H ((to_fun H)⁻¹ (inl ⋆)) : (to_right_inv H (inl ⋆))⁻¹
calc inl ⋆ = H (H⁻¹ (inl ⋆)) : (to_right_inv H (inl ⋆))⁻¹
... = H (inl u') : ap H Hu'
... = H (inl u) : by rewrite [is_prop.elim u' u]
... = H ((to_fun H)⁻¹ (inr b)) : ap H Hu⁻¹
... = H (H⁻¹ (inr b)) : ap H Hu⁻¹
... = inr b : to_right_inv H (inr b) },
{ cases x with a Ha, exfalso, apply empty_of_inl_eq_inr,
apply concat, rotate 1, exact Hb',