EXT

Drule.EXT : thm -> thm

Derives equality of functions from extensional equivalence.

When applied to a theorem A |- !x. t1 x = t2 x, the inference rule EXT returns the theorem A |- t1 = t2.

    A |- !x. t1 x = t2 x
   ----------------------  EXT          [where x is not free in t1 or t2]
        A |- t1 = t2

Failure

Fails if the theorem does not have the form indicated above, or if the variable x is free in either of the functions t1 or t2.

Comments

This rule is expressed as an equivalence in the theorem boolTheory.FUN_EQ_THM.

See also

Thm.AP_THM, Drule.ETA_CONV, Conv.FUN_EQ_CONV