INDUCT : ((thm # thm) -> thm)
A1 |- P[0] A2 |- !n. P[n] ==> P[SUC n] ----------------------------------------------- INDUCT A1 u A2 |- !n. P[n]When supplied with a theorem A1 |- P[0], which asserts the base case of a proof of the proposition P[n] by induction on n, and the theorem A2 |- !n. P[n] ==> P[SUC n], which asserts the step case in the induction on n, the inference rule INDUCT returns A1 u A2 |- !n. P[n].