• Top
  • Documentation
  • Books
  • Recursion-and-induction
  • Boolean-reasoning
    • Ipasir
    • Aignet
      • Base-api
      • Aignet-construction
      • Representation
      • Aignet-copy-init
      • Aignet-simplify-marked-with-tracking
      • Aignet-cnf
      • Aignet-simplify-with-tracking
      • Aignet-complete-copy
      • Aignet-eval
      • Semantics
      • Aignet-transforms
        • Aignet-comb-transforms
        • Aignet-m-assumption-n-output-transforms
          • M-assumption-n-output-comb-transform
            • M-assumption-n-output-comb-transform-fix
            • M-assumption-n-output-comb-transform-p
            • M-assumption-n-output-comb-transform-equiv
          • Apply-m-assumption-n-output-transform
        • Aignet-n-output-comb-transforms
      • Aignet-simplify-marked
      • Aignet-read-aiger
      • Aignet-write-aiger
      • Aignet-abc-interface
      • Utilities
    • 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

• M-assumption-n-output-comb-transform

M-assumption-n-output-comb-transform-fix

(m-assumption-n-output-comb-transform-fix x) is a ACL2::fty fixing function.

Signature

(m-assumption-n-output-comb-transform-fix x) → fty::newx

Arguments

x — Guard (m-assumption-n-output-comb-transform-p x).

Returns

fty::newx — Type (m-assumption-n-output-comb-transform-p fty::newx).

Note that in the execution this is just an inline identity function.

Definitions and Theorems

Function: m-assumption-n-output-comb-transform-fix$inline

(defun
 m-assumption-n-output-comb-transform-fix$inline
 (x)
 (declare (xargs :guard (m-assumption-n-output-comb-transform-p x)))
 (let
  ((__function__ 'm-assumption-n-output-comb-transform-fix))
  (declare (ignorable __function__))
  (mbe
    :logic
    (case (tag x)
          ((:balance-config
                :fraig-config :rewrite-config
                :abc-comb-simp-config :obs-constprop-config
                :observability-config :constprop-config
                :snapshot-config :prune-config
                :unreachability-config :dom-supergates-sweep-config)
           (comb-transform-fix x))
          ((:n-outputs-unreachability-config)
           (n-outputs-unreachability-config-fix x))
          ((:n-outputs-dom-supergates-sweep-config)
           (n-outputs-dom-supergates-sweep-config-fix x))
          (otherwise (m-assum-n-output-observability-config-fix x)))
    :exec x)))

Theorem: m-assumption-n-output-comb-transform-p-of-m-assumption-n-output-comb-transform-fix

(defthm
 m-assumption-n-output-comb-transform-p-of-m-assumption-n-output-comb-transform-fix
 (b*
   ((fty::newx (m-assumption-n-output-comb-transform-fix$inline x)))
   (m-assumption-n-output-comb-transform-p fty::newx))
 :rule-classes :rewrite)

Theorem: m-assumption-n-output-comb-transform-fix-when-m-assumption-n-output-comb-transform-p

(defthm
 m-assumption-n-output-comb-transform-fix-when-m-assumption-n-output-comb-transform-p
 (implies (m-assumption-n-output-comb-transform-p x)
          (equal (m-assumption-n-output-comb-transform-fix x)
                 x)))

Function: m-assumption-n-output-comb-transform-equiv$inline

(defun
 m-assumption-n-output-comb-transform-equiv$inline
 (x acl2::y)
 (declare
  (xargs
     :guard (and (m-assumption-n-output-comb-transform-p x)
                 (m-assumption-n-output-comb-transform-p acl2::y))))
 (equal (m-assumption-n-output-comb-transform-fix x)
        (m-assumption-n-output-comb-transform-fix acl2::y)))

Theorem: m-assumption-n-output-comb-transform-equiv-is-an-equivalence

(defthm
 m-assumption-n-output-comb-transform-equiv-is-an-equivalence
 (and
     (booleanp (m-assumption-n-output-comb-transform-equiv x y))
     (m-assumption-n-output-comb-transform-equiv x x)
     (implies (m-assumption-n-output-comb-transform-equiv x y)
              (m-assumption-n-output-comb-transform-equiv y x))
     (implies (and (m-assumption-n-output-comb-transform-equiv x y)
                   (m-assumption-n-output-comb-transform-equiv y z))
              (m-assumption-n-output-comb-transform-equiv x z)))
 :rule-classes (:equivalence))

Theorem: m-assumption-n-output-comb-transform-equiv-implies-equal-m-assumption-n-output-comb-transform-fix-1

(defthm
 m-assumption-n-output-comb-transform-equiv-implies-equal-m-assumption-n-output-comb-transform-fix-1
 (implies
      (m-assumption-n-output-comb-transform-equiv x x-equiv)
      (equal (m-assumption-n-output-comb-transform-fix x)
             (m-assumption-n-output-comb-transform-fix x-equiv)))
 :rule-classes (:congruence))

Theorem: m-assumption-n-output-comb-transform-fix-under-m-assumption-n-output-comb-transform-equiv

(defthm
 m-assumption-n-output-comb-transform-fix-under-m-assumption-n-output-comb-transform-equiv
 (m-assumption-n-output-comb-transform-equiv
      (m-assumption-n-output-comb-transform-fix x)
      x)
 :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-m-assumption-n-output-comb-transform-fix-1-forward-to-m-assumption-n-output-comb-transform-equiv

(defthm
 equal-of-m-assumption-n-output-comb-transform-fix-1-forward-to-m-assumption-n-output-comb-transform-equiv
 (implies (equal (m-assumption-n-output-comb-transform-fix x)
                 acl2::y)
          (m-assumption-n-output-comb-transform-equiv x acl2::y))
 :rule-classes :forward-chaining)

Theorem: equal-of-m-assumption-n-output-comb-transform-fix-2-forward-to-m-assumption-n-output-comb-transform-equiv

(defthm
 equal-of-m-assumption-n-output-comb-transform-fix-2-forward-to-m-assumption-n-output-comb-transform-equiv
 (implies (equal x
                 (m-assumption-n-output-comb-transform-fix acl2::y))
          (m-assumption-n-output-comb-transform-equiv x acl2::y))
 :rule-classes :forward-chaining)

Theorem: m-assumption-n-output-comb-transform-equiv-of-m-assumption-n-output-comb-transform-fix-1-forward

(defthm
 m-assumption-n-output-comb-transform-equiv-of-m-assumption-n-output-comb-transform-fix-1-forward
 (implies (m-assumption-n-output-comb-transform-equiv
               (m-assumption-n-output-comb-transform-fix x)
               acl2::y)
          (m-assumption-n-output-comb-transform-equiv x acl2::y))
 :rule-classes :forward-chaining)

Theorem: m-assumption-n-output-comb-transform-equiv-of-m-assumption-n-output-comb-transform-fix-2-forward

(defthm
 m-assumption-n-output-comb-transform-equiv-of-m-assumption-n-output-comb-transform-fix-2-forward
 (implies (m-assumption-n-output-comb-transform-equiv
               x
               (m-assumption-n-output-comb-transform-fix acl2::y))
          (m-assumption-n-output-comb-transform-equiv x acl2::y))
 :rule-classes :forward-chaining)

Theorem: tag-of-m-assumption-n-output-comb-transform-fix-forward

(defthm
     tag-of-m-assumption-n-output-comb-transform-fix-forward
     (or (equal (tag (m-assumption-n-output-comb-transform-fix x))
                :balance-config)
         (equal (tag (m-assumption-n-output-comb-transform-fix x))
                :fraig-config)
         (equal (tag (m-assumption-n-output-comb-transform-fix x))
                :rewrite-config)
         (equal (tag (m-assumption-n-output-comb-transform-fix x))
                :abc-comb-simp-config)
         (equal (tag (m-assumption-n-output-comb-transform-fix x))
                :obs-constprop-config)
         (equal (tag (m-assumption-n-output-comb-transform-fix x))
                :observability-config)
         (equal (tag (m-assumption-n-output-comb-transform-fix x))
                :constprop-config)
         (equal (tag (m-assumption-n-output-comb-transform-fix x))
                :snapshot-config)
         (equal (tag (m-assumption-n-output-comb-transform-fix x))
                :prune-config)
         (equal (tag (m-assumption-n-output-comb-transform-fix x))
                :unreachability-config)
         (equal (tag (m-assumption-n-output-comb-transform-fix x))
                :dom-supergates-sweep-config)
         (equal (tag (m-assumption-n-output-comb-transform-fix x))
                :n-outputs-unreachability-config)
         (equal (tag (m-assumption-n-output-comb-transform-fix x))
                :n-outputs-dom-supergates-sweep-config)
         (equal (tag (m-assumption-n-output-comb-transform-fix x))
                :m-assum-n-output-observability-config))
     :rule-classes
     ((:forward-chaining
           :trigger-terms
           ((tag (m-assumption-n-output-comb-transform-fix x))))))