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Coq is a formal proof management system, also called an interactive theorem prover. It is used to express mathematical assertions, mechanically check proofs of these assertions, find formal proofs, and extract certified programs.

52 votes
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Function extensionality: does it make a difference? why would one keep it out of the axioms?

statement that if two functions $f$ and $g$ on the same domain satisfy $f\left(x\right) = g\left(x\right)$ for all $x$ in the domain, then $f = g$) is not an axiom in the standard constructive logic of Coq … (I must say the eta-expansion in Coq feels rather weird, too -- it is triggered by the reflexivity tactic. I expected it to be a tactic on its own...) …
darij grinberg's user avatar