lean2/tests/lean/hott/unfold_test.hlean

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import algebra.e_closure
open eq
namespace relation
section
parameters {A : Type}
(R : A → A → Type)
local abbreviation T := e_closure R
variables ⦃a a' : A⦄ {s : R a a'} {r : T a a}
parameter {R}
theorem ap_ap_e_closure_elim_h₁ {B C D : Type} {f : A → B}
{g : B → C} (h : C → D)
(e : Π⦃a a' : A⦄, R a a' → f a = f a')
{e' : Π⦃a a' : A⦄, R a a' → g (f a) = g (f a')}
(p : Π⦃a a' : A⦄ (s : R a a'), ap g (e s) = e' s) (t : T a a')
: square (ap (ap h) (ap_e_closure_elim_h e p t))
(ap_e_closure_elim_h e (λa a' s, ap_compose h g (e s)) t)
(ap_compose h g (e_closure.elim e t))⁻¹
(ap_e_closure_elim_h e' (λa a' s, (ap (ap h) (p s))⁻¹) t) :=
begin
induction t,
apply sorry,
apply sorry,
{
rewrite [↑e_closure.elim, ↑ap_e_closure_elim_h, ap_con (ap h)],
refine (transpose !ap_compose_inv)⁻¹ᵛ ⬝h _,
rewrite [con_inv,inv_inv,-inv2_inv],
exact !ap_inv2 ⬝v square_inv2 v_0
},
apply sorry
end
end
end relation