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• Ipasir$a

Ipasir-set-limit$a

Logic form of ipasir-set-limit. See ipasir for usage.

Signature

(ipasir-set-limit$a solver limit) → new-solver

Arguments

solver — Guard (ipasir$a-p solver).

limit — Guard (acl2::maybe-natp limit).

Returns

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

Definitions and Theorems

Function: ipasir-set-limit$a

(defun
 ipasir-set-limit$a (solver limit)
 (declare (xargs :guard (and (ipasir$a-p solver)
                             (acl2::maybe-natp limit))))
 (declare (xargs :guard (not (eq (ipasir-get-status$a solver)
                                 :undef))))
 (let
    ((__function__ 'ipasir-set-limit$a))
    (declare (ignorable __function__))
    (b* (((ipasir$a solver)))
        (change-ipasir$a
             solver
             :history (cons (cons ':limit
                                  (cons (acl2::maybe-natp-fix limit)
                                        'nil))
                            solver.history)))))

Theorem: ipasir$a-p-of-ipasir-set-limit$a

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

Theorem: status-of-ipasir-set-limit$a

(defthm status-of-ipasir-set-limit$a
        (b* ((?new-solver (ipasir-set-limit$a solver limit)))
            (equal (ipasir$a->status new-solver)
                   (ipasir$a->status solver))))

Theorem: new-clause-of-ipasir-set-limit$a

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

Theorem: formula-of-ipasir-set-limit$a

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

Theorem: assumption-of-ipasir-set-limit$a

(defthm assumption-of-ipasir-set-limit$a
        (b* ((?new-solver (ipasir-set-limit$a solver limit)))
            (b* (((ipasir$a solver))
                 ((ipasir$a new-solver)))
                (equal new-solver.assumption
                       solver.assumption))))

Theorem: ipasir-set-limit$a-of-ipasir$a-fix-solver

(defthm ipasir-set-limit$a-of-ipasir$a-fix-solver
        (equal (ipasir-set-limit$a (ipasir$a-fix solver)
                                   limit)
               (ipasir-set-limit$a solver limit)))

Theorem: ipasir-set-limit$a-ipasir$a-equiv-congruence-on-solver

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

Theorem: ipasir-set-limit$a-of-maybe-natp-fix-limit

(defthm
     ipasir-set-limit$a-of-maybe-natp-fix-limit
     (equal (ipasir-set-limit$a solver (acl2::maybe-natp-fix limit))
            (ipasir-set-limit$a solver limit)))

Theorem: ipasir-set-limit$a-maybe-nat-equiv-congruence-on-limit

(defthm ipasir-set-limit$a-maybe-nat-equiv-congruence-on-limit
        (implies (acl2::maybe-nat-equiv limit limit-equiv)
                 (equal (ipasir-set-limit$a solver limit)
                        (ipasir-set-limit$a solver limit-equiv)))
        :rule-classes :congruence)