iffRL

Drule.iffRL : thm -> thm

Returns the right-to-left direction of a “guarded” iff theorem

A call to iffRL th, where th has the form

   A |- !x1 .. xn. p1 /\ .. /\ pm ==> !y... q1 /\ .. ==> ... ==> (l <=> r)

returns the right-to-left implication

   A |- !x1 .. xn. p1 /\ .. /\ pm ==> !y... q1 /\ .. ==> ... ==> r ==> l

The universal variables and various antecedents are said to “guard” the if-and-only-if conclusion l <=> r in this situation. They may be nested abitrarily deep, or not present at all. They are restored after a call to EQ_IMP_RULE is made.

Failure

Fails if the theorem is not of the form specified above.

See also

Drule.EQ_IMP_RULE, Drule.iffLR, Drule.underAIs