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Is it possible to prove an equality of functions given they are equal pointwise? - i.e. to build following function:

pointwiseEquals: (f: a -> b) -> (g: a -> b) -> ((x: a) -> (f x) = (g x)) -> f = g

However, I doubt that it takes place in constructive logic, so maybe at least the following take place?

pointwiseEquals': (f: a -> b) -> (g: a -> b) -> ((x: a) -> (f x) = (g x)) -> (f = g -> Void) -> Void
stop-cran
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    This is kind of orthogonal to constructivism, so both things are not provable. – Anton Trunov Jul 18 '18 at 09:34
  • This statement is called `funext` and can be postulated without apparent contradictions: `postulate funext : {f, g : a -> b} -> ((x : a) -> f x = g x) -> f = g` – stop-cran Sep 18 '18 at 14:09

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