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Applications that allow to create formal proofs. They assist the user by finding partial and checking complete proofs. General questions about proof assistants can also be asked on the Proof Assistants Stack Exchange site.
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Proving transitivity in an intuitionistic type theory without the K rule
In Agda, if I disable axiom $\mathbb{K}$ I'm not able to prove
$$
\forall\{A : \textbf{Set}\}\{a\ b : A\}\{p\ q : a \equiv b\} \to p \equiv q,
$$
which I guess is normal since the system does not trun …