Proving function for hypotheses, lemmas and assumptions. prove_x fmt name x should prove x, and be such that after executing it, x is among the coq hypotheses under the name name. The hypothesis should be the encoding of the given clause, i.e for a clause a \/ not b \/ c, the proved hypothesis should be: ~ a -> ~ ~ b -> ~ c -> False , keeping the same order as the one in the atoms array of the clause.