• Top
  • Documentation
  • Books
  • Recursion-and-induction
  • Boolean-reasoning
    • Ipasir
      • Ipasir$a
        • Ipasir$a-p
        • Ipasir$a-fix
        • Ipasir-set-limit$a
        • Ipasir-add-lit$a
        • Ipasir-assume$a
        • Ipasir-init$a
        • Make-ipasir$a
        • Ipasir-finalize-clause$a
        • Ipasir-reinit$a
        • Ipasir$a-equiv
        • Ipasir-input$a
        • Ipasir-val$a
        • Ipasir-release$a
        • Ipasir$a->solved-assumption
        • Ipasir$a->new-clause
        • Ipasir$a->callback-count
        • Ipasir$a->assumption
        • Ipasir-failed$a
        • Change-ipasir$a
        • Ipasir$a->solution
        • Ipasir$a->formula
        • Ipasir$a->status
        • Ipasir$a->history
        • Ipasir-callback-count$a
        • Ipasir-solved-assumption$a
        • Ipasir-some-history$a
        • Ipasir-get-status$a
        • Ipasir-get-assumption$a
        • Ipasir-empty-new-clause$a
        • Create-ipasir$a
        • Ipasir-solve$a
      • Building-an-ipasir-solver-library
      • Ipasir-formula
      • Ipasir-bump-activity-vars$a
      • Ipasir-set$a
      • Ipasir-bump-activity-vars$c
      • Ipasir-get$a
      • Ipasir-set-limit$c
      • Ipasir-set$c
      • Ipasir-failed$c
      • Ipasir-assume$c
      • Ipasir-add-lit$c
      • Ipasir-val$c
      • With-local-ipasir
      • Ipasir-solve$c
      • Ipasir-reinit$c
      • Ipasir-init$c
      • Ipasir-finalize-clause$c
      • Ipasir-some-history$c
      • Ipasir-solved-assumption$c
      • Ipasir-release$c
      • Ipasir-input$c
      • Ipasir-get$c
      • Ipasir-get-status$c
      • Ipasir-get-curr-stats$c
      • Ipasir-get-assumption$c
      • Ipasir-empty-new-clause$c
      • Ipasir-callback-count$c
      • Ipasir-val
      • Ipasir-solve
      • Ipasir-set-limit
      • Ipasir-reinit
      • Ipasir-failed
      • Ipasir-callback-count
      • Ipasir-release
      • Ipasir-input
      • Ipasir-init
      • Ipasir-finalize-clause
      • Ipasir-assume
      • Ipasir-add-lit
    • Aignet
    • Aig
    • Satlink
    • Truth
    • Ubdds
    • Bdd
    • Faig
    • Bed
    • 4v
  • Projects
  • Debugging
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Testing-utilities
  • Math

• Ipasir$a

Ipasir$a-fix

Fixing function for ipasir$a structures.

Signature

(ipasir$a-fix x) → new-x

Arguments

x — Guard (ipasir$a-p x).

Returns

new-x — Type (ipasir$a-p new-x).

Definitions and Theorems

Function: ipasir$a-fix$inline

(defun
 ipasir$a-fix$inline (x)
 (declare (xargs :guard (ipasir$a-p x)))
 (let
  ((__function__ 'ipasir$a-fix))
  (declare (ignorable __function__))
  (mbe
     :logic
     (b* ((formula (lit-list-list-fix (cdr (std::da-nth 0 x))))
          (assumption (lit-list-fix (cdr (std::da-nth 1 x))))
          (new-clause (lit-list-fix (cdr (std::da-nth 2 x))))
          (status (ipasir-status-fix (cdr (std::da-nth 3 x))))
          (solution (lit-list-fix (cdr (std::da-nth 4 x))))
          (solved-assumption (lit-list-fix (cdr (std::da-nth 5 x))))
          (callback-count (nfix (cdr (std::da-nth 6 x))))
          (history (cdr (std::da-nth 7 x))))
         (list (cons 'formula formula)
               (cons 'assumption assumption)
               (cons 'new-clause new-clause)
               (cons 'status status)
               (cons 'solution solution)
               (cons 'solved-assumption
                     solved-assumption)
               (cons 'callback-count callback-count)
               (cons 'history history)))
     :exec x)))

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

(defthm ipasir$a-p-of-ipasir$a-fix
        (b* ((new-x (ipasir$a-fix$inline x)))
            (ipasir$a-p new-x))
        :rule-classes :rewrite)

Theorem: ipasir$a-fix-when-ipasir$a-p

(defthm ipasir$a-fix-when-ipasir$a-p
        (implies (ipasir$a-p x)
                 (equal (ipasir$a-fix x) x)))

Function: ipasir$a-equiv$inline

(defun ipasir$a-equiv$inline (acl2::x acl2::y)
       (declare (xargs :guard (and (ipasir$a-p acl2::x)
                                   (ipasir$a-p acl2::y))))
       (equal (ipasir$a-fix acl2::x)
              (ipasir$a-fix acl2::y)))

Theorem: ipasir$a-equiv-is-an-equivalence

(defthm ipasir$a-equiv-is-an-equivalence
        (and (booleanp (ipasir$a-equiv x y))
             (ipasir$a-equiv x x)
             (implies (ipasir$a-equiv x y)
                      (ipasir$a-equiv y x))
             (implies (and (ipasir$a-equiv x y)
                           (ipasir$a-equiv y z))
                      (ipasir$a-equiv x z)))
        :rule-classes (:equivalence))

Theorem: ipasir$a-equiv-implies-equal-ipasir$a-fix-1

(defthm ipasir$a-equiv-implies-equal-ipasir$a-fix-1
        (implies (ipasir$a-equiv acl2::x x-equiv)
                 (equal (ipasir$a-fix acl2::x)
                        (ipasir$a-fix x-equiv)))
        :rule-classes (:congruence))

Theorem: ipasir$a-fix-under-ipasir$a-equiv

(defthm ipasir$a-fix-under-ipasir$a-equiv
        (ipasir$a-equiv (ipasir$a-fix acl2::x)
                        acl2::x)
        :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-ipasir$a-fix-1-forward-to-ipasir$a-equiv

(defthm equal-of-ipasir$a-fix-1-forward-to-ipasir$a-equiv
        (implies (equal (ipasir$a-fix acl2::x) acl2::y)
                 (ipasir$a-equiv acl2::x acl2::y))
        :rule-classes :forward-chaining)

Theorem: equal-of-ipasir$a-fix-2-forward-to-ipasir$a-equiv

(defthm equal-of-ipasir$a-fix-2-forward-to-ipasir$a-equiv
        (implies (equal acl2::x (ipasir$a-fix acl2::y))
                 (ipasir$a-equiv acl2::x acl2::y))
        :rule-classes :forward-chaining)

Theorem: ipasir$a-equiv-of-ipasir$a-fix-1-forward

(defthm ipasir$a-equiv-of-ipasir$a-fix-1-forward
        (implies (ipasir$a-equiv (ipasir$a-fix acl2::x)
                                 acl2::y)
                 (ipasir$a-equiv acl2::x acl2::y))
        :rule-classes :forward-chaining)

Theorem: ipasir$a-equiv-of-ipasir$a-fix-2-forward

(defthm ipasir$a-equiv-of-ipasir$a-fix-2-forward
        (implies (ipasir$a-equiv acl2::x (ipasir$a-fix acl2::y))
                 (ipasir$a-equiv acl2::x acl2::y))
        :rule-classes :forward-chaining)