INDUCT : ((thm # thm) -> thm)

SYNOPSIS

Performs a proof by mathematical induction on the natural numbers.

DESCRIBE

The derived inference rule INDUCT implements the rule of mathematical induction:

      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].

FAILURE

INDUCT th1 th2 fails if the theorems th1 and th2 do not have the forms A1 |- P[0] and A2 |- !n. P[n] ==> P[SUC n] respectively.

SEEALSO  INDUCT_TAC