Elim a double negation hypothesis in Coq Proof Assistant? -


could explain me why have prove ~a after elim ha.?

before "elim ha"

1 subgoals  : prop  ha : ~ ~ ______________________________________(1/1)

after

1 subgoals  : prop  ha : ~ ~ ______________________________________(1/1)  ~

is right means ~~a true, ~a true -> true?

in knowledge, know rule ~e ~a true, true -> falsehood true

in coq, ~ p notation p -> false. if i'm not mistaken, using elim on hypothesis of shape ~ p same directly using false_rect (you can print false_rect more info) p input.

doing so, coq "i know p holds, using p -> false, can derive proof of false" closes goal contradiction. that's why each time elim ~ p, coq asks provide proof of p. in case, p ~ a.


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