AP_THM

Thm.AP_THM : thm -> term -> thm

Proves equality of equal functions applied to a term.

When applied to a theorem A |- f = g and a term x, the inference rule AP_THM returns the theorem A |- f x = g x.

      A |- f = g
   ----------------  AP_THM (A |- f = g) x
    A |- f x = g x

Failure

Fails unless the conclusion of the theorem is an equation, both sides of which are functions whose domain type is the same as that of the supplied term.

See also

Tactic.AP_THM_TAC, Thm.AP_TERM, Drule.ETA_CONV, Drule.EXT, Conv.FUN_EQ_CONV, Thm.MK_COMB