SET_RULE

bossLib.SET_RULE : term -> thm

Automatically prove a set-theoretic theorem by reduction to FOL.

An application DECIDE M, where M is a set-theoretic term, attempts to automatically prove M by reducing basic set-theoretic operators (IN, SUBSET, PSUBSET, INTER, UNION, INSERT, DELETE, REST, DISJOINT, BIGINTER, BIGUNION, IMAGE, SING and GSPEC) in M to their definitions in first-order logic. With SET_RULE, many simple set-theoretic results can be directly proved without finding needed lemmas in pred_setTheory.

Example

> SET_RULE ``!s t c. DISJOINT s t ==> DISJOINT (s INTER c) (t INTER c)``;
metis: r[+0+5]+0+0+0+0+1#
val it = ⊢ ∀s t c. DISJOINT s t ⇒ DISJOINT (s ∩ c) (t ∩ c): thm

Failure

Fails if the underlying resolution machinery used by METIS_TAC cannot prove the goal, e.g. when there are other set operators in the term.

Comments

SET_RULE calls SET_TAC without extra lemmas.

See also

bossLib.SET_TAC, bossLib.ASM_SET_TAC, bossLib.METIS_TAC