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• Ipasir$a

Ipasir-assume$a

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

Signature

(ipasir-assume$a solver lit) → new-solver

Arguments

solver — Guard (ipasir$a-p solver).

lit — Guard (litp lit).

Returns

new-solver — Type (ipasir$a-p new-solver).

Definitions and Theorems

Function: ipasir-assume$a

(defun ipasir-assume$a (solver lit)
 (declare (xargs :guard (and (ipasir$a-p solver) (litp lit))))
 (declare (xargs :guard (not (eq (ipasir-get-status$a solver)
                                 :undef))))
 (let ((__function__ 'ipasir-assume$a))
   (declare (ignorable __function__))
   (b* (((ipasir$a solver))
        (lit (lit-fix lit)))
     (change-ipasir$a solver
                      :assumption (cons lit solver.assumption)
                      :status :input
                      :history (cons (cons ':assume (cons lit 'nil))
                                     solver.history)))))

Theorem: ipasir$a-p-of-ipasir-assume$a

(defthm ipasir$a-p-of-ipasir-assume$a
  (b* ((new-solver (ipasir-assume$a solver lit)))
    (ipasir$a-p new-solver))
  :rule-classes :rewrite)

Theorem: status-of-ipasir-assume$a

(defthm status-of-ipasir-assume$a
  (b* ((?new-solver (ipasir-assume$a solver lit)))
    (equal (ipasir$a->status new-solver)
           :input)))

Theorem: new-clause-of-ipasir-assume$a

(defthm new-clause-of-ipasir-assume$a
  (b* ((?new-solver (ipasir-assume$a solver lit)))
    (equal (ipasir$a->new-clause new-solver)
           (ipasir$a->new-clause solver))))

Theorem: formula-of-ipasir-assume$a

(defthm formula-of-ipasir-assume$a
  (b* ((?new-solver (ipasir-assume$a solver lit)))
    (equal (ipasir$a->formula new-solver)
           (ipasir$a->formula solver))))

Theorem: assumption-of-ipasir-assume$a

(defthm assumption-of-ipasir-assume$a
  (b* ((?new-solver (ipasir-assume$a solver lit)))
    (b* (((ipasir$a solver))
         ((ipasir$a new-solver)))
      (equal new-solver.assumption
             (cons (lit-fix lit)
                   solver.assumption)))))

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

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

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

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

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

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

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

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