File: truth-monotone.lisp

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; Copyright (C) 2016, Regents of the University of Texas
; Marijn Heule, Warren A. Hunt, Jr., and Matt Kaufmann
; License: A 3-clause BSD license.  See the LICENSE file distributed with ACL2.

; See soundness.lisp.  Here we prove a key lemma in support of that book.

(in-package "LRAT")

(include-book "lrat-checker")

(defthm member-equal-monotone
  (implies (and (subsetp-equal s1 s2)
                (member-equal a s1))
           (member-equal a s2)))

(defthm truth-monotone-clause
  (implies (and (subsetp-equal a1 a2)
                (equal (evaluate-clause clause a1) t))
           (equal (evaluate-clause clause a2) t)))

(defthm truth-monotone
  (implies (and (subsetp-equal a1 a2)
                (equal (formula-truep formula a1) t))
           (equal (formula-truep formula a2) t))
  :hints (("Goal"
           :expand ((formula-truep formula a2))
           :use ((:instance formula-truep-necc
                            (index (formula-truep-witness formula a2))
                            (assignment a1))))))