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• Ipasir$a

Ipasir-failed$a

Logic form of ipasir-failed. See ipasir for usage.

Signature

(ipasir-failed$a solver lit) → *

Arguments

solver — Guard (ipasir$a-p solver).

lit — Guard (litp lit).

Definitions and Theorems

Function: ipasir-failed$a

(defun ipasir-failed$a (solver lit)
 (declare (xargs :guard (and (ipasir$a-p solver) (litp lit))))
 (declare
  (xargs :guard (and (eq (ipasir-get-status$a solver) :unsat)
                     (member lit
                             (ipasir-solved-assumption$a solver)))))
 (let ((__function__ 'ipasir-failed$a))
   (declare (ignorable __function__))
   (b* (((ipasir$a solver))
        (lit (lit-fix lit)))
     (if (member lit solver.solution) 1 0))))

Theorem: ipasir-failed$a-of-ipasir$a-fix-solver

(defthm ipasir-failed$a-of-ipasir$a-fix-solver
  (equal (ipasir-failed$a (ipasir$a-fix solver)
                          lit)
         (ipasir-failed$a solver lit)))

Theorem: ipasir-failed$a-ipasir$a-equiv-congruence-on-solver

(defthm ipasir-failed$a-ipasir$a-equiv-congruence-on-solver
  (implies (ipasir$a-equiv solver solver-equiv)
           (equal (ipasir-failed$a solver lit)
                  (ipasir-failed$a solver-equiv lit)))
  :rule-classes :congruence)

Theorem: ipasir-failed$a-of-lit-fix-lit

(defthm ipasir-failed$a-of-lit-fix-lit
  (equal (ipasir-failed$a solver (lit-fix lit))
         (ipasir-failed$a solver lit)))

Theorem: ipasir-failed$a-lit-equiv-congruence-on-lit

(defthm ipasir-failed$a-lit-equiv-congruence-on-lit
  (implies (lit-equiv lit lit-equiv)
           (equal (ipasir-failed$a solver lit)
                  (ipasir-failed$a solver lit-equiv)))
  :rule-classes :congruence)