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make apd10_eq_of_homotopy a homotopy

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This commit is contained in:
Floris van Doorn 2018-09-05 15:24:07 +02:00
parent a69a4226c6
commit 86c375b0c4
2 changed files with 5 additions and 2 deletions
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2
hott/homotopy/connectedness.hlean
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@ -99,7 +99,7 @@ namespace is_conn
intro r,
refine equiv.trans _ (eq_con_inv_equiv_con_eq q p
(ap (λv a, v (f a)) (eq_of_homotopy r))),
rewrite [-(ap (λv a, v (f a)) (apd10_eq_of_homotopy r))],
rewrite [-(ap (λv a, v (f a)) (apd10_eq_of_homotopy_fn r))],
rewrite [-(apd10_ap_precompose_dependent f (eq_of_homotopy r))],
apply equiv.symm,
apply eq_equiv_fn_eq (@apd10 A (λa, P (f a)) (λa, g (f a)) (λa, h (f a)))

5
hott/init/funext.hlean
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@ -245,9 +245,12 @@ namespace eq
definition eq_of_homotopy [reducible] : f ~ g → f = g :=
(@apd10 A P f g)⁻¹
definition apd10_eq_of_homotopy (p : f ~ g) : apd10 (eq_of_homotopy p) = p :=
definition apd10_eq_of_homotopy_fn (p : f ~ g) : apd10 (eq_of_homotopy p) = p :=
right_inv apd10 p
definition apd10_eq_of_homotopy (p : f ~ g) : apd10 (eq_of_homotopy p) ~ p :=
apd10 (right_inv apd10 p)
definition eq_of_homotopy_apd10 (p : f = g) : eq_of_homotopy (apd10 p) = p :=
left_inv apd10 p