AP_THM : thm -> term -> thm

SYNOPSIS

Proves equality of equal functions applied to a term.

DESCRIPTION

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 CONDITIONS

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.

EXAMPLE

  # REWRITE_RULE[GSYM FUN_EQ_THM] ADD1;;
  val it : thm = |- SUC = (\m. m + 1)

  # AP_THM it `11`;;
  val it : thm = |- SUC 11 = (\m. m + 1) 11

SEE ALSO

AP_TERM, ETA_CONV, MK_COMB.