Created
December 12, 2012 23:10
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A lemma which explains how transport and function extensionalty interact.
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Variable A : Type. | |
Variable P : A -> Type. | |
Variable Q : forall x, P x -> Type. | |
Lemma transport_funext (f g : forall x, P x) (n : forall x, Q x (f x)) (E : forall x, f x = g x) (x : A) : | |
(transport (fun h => forall x, Q x (h x)) (funext E) n) x = transport (Q x) (E x) (n x). |
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Note:
funext
takes a pointwise equality of functions and turns it into equality of functions. It is the opposite ofhapply
.