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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.
1
vote
How true are theorems proved by Coq?
Taken from the question How bad is Coq proving both $T$ and $\lnot T$?
Back in 2011 on the coq-club mailing list there was a thread:
Is the Daniel Schepler's inconsistency real?. … Proving $T$ and $\lnot T$ doesn't lead to proof of $False$,
with a Coq error. …
11
votes
How true are theorems proved by Coq?
In an internet post Pollack discusses Coq coercions:
The problem is that Coq coercions are informally specified and behave
somewhat unpredictably. … It is in Coq. Let me be more clear: a bug in the kernel of Coq
Inconsistency bugs appear more common, Preliminary compilation of critical bugs in stable releases of Coq. …