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• Observability-fix

Observability-fix-hyp/concl

Signature

(observability-fix-hyp/concl hyp concl aignet 
                             copy gatesimp strash aignet2 state) 
 
  → 
(mv conj new-copy new-strash new-aignet2 new-state)

Arguments

hyp — Guard (litp hyp).

concl — Guard (litp concl).

gatesimp — Guard (gatesimp-p gatesimp).

Returns

conj — Type (litp conj).

Definitions and Theorems

Function: observability-fix-hyp/concl

(defun observability-fix-hyp/concl
       (hyp concl aignet
            copy gatesimp strash aignet2 state)
 (declare (xargs :stobjs (aignet copy strash aignet2 state)))
 (declare (xargs :guard (and (litp hyp)
                             (litp concl)
                             (gatesimp-p gatesimp))))
 (declare (xargs :guard (and (<= (num-fanins aignet)
                                 (lits-length copy))
                             (aignet-copies-in-bounds copy aignet2)
                             (fanin-litp hyp aignet)
                             (fanin-litp concl aignet)
                             (<= (num-ins aignet) (num-ins aignet2))
                             (<= (num-regs aignet)
                                 (num-regs aignet2)))))
 (let ((__function__ 'observability-fix-hyp/concl))
   (declare (ignorable __function__))
   (b* (((mv new-hyp ?hyp-copies
             new-concls copy strash aignet2 state)
         (observability-fix-hyps/concls
              (list hyp)
              (list concl)
              aignet
              copy gatesimp strash aignet2 state))
        ((mv conj strash aignet2)
         (aignet-hash-and new-hyp (car new-concls)
                          gatesimp strash aignet2)))
     (mv conj copy strash aignet2 state))))

Theorem: litp-of-observability-fix-hyp/concl.conj

(defthm litp-of-observability-fix-hyp/concl.conj
  (b* (((mv ?conj ?new-copy
            ?new-strash ?new-aignet2 ?new-state)
        (observability-fix-hyp/concl
             hyp concl aignet
             copy gatesimp strash aignet2 state)))
    (litp conj))
  :rule-classes :rewrite)

Theorem: aignet-extension-of-observability-fix-hyp/concl

(defthm aignet-extension-of-observability-fix-hyp/concl
  (b* (((mv ?conj ?new-copy
            ?new-strash ?new-aignet2 ?new-state)
        (observability-fix-hyp/concl
             hyp concl aignet
             copy gatesimp strash aignet2 state)))
    (aignet-extension-p new-aignet2 aignet2)))

Theorem: stype-counts-of-observability-fix-hyp/concl

(defthm stype-counts-of-observability-fix-hyp/concl
  (b* (((mv ?conj ?new-copy
            ?new-strash ?new-aignet2 ?new-state)
        (observability-fix-hyp/concl
             hyp concl aignet
             copy gatesimp strash aignet2 state)))
    (implies (and (not (equal (stype-fix stype) (and-stype)))
                  (not (equal (stype-fix stype) (xor-stype))))
             (equal (stype-count stype new-aignet2)
                    (stype-count stype aignet2)))))

Theorem: copy-length-of-observability-fix-hyp/concl

(defthm copy-length-of-observability-fix-hyp/concl
  (b* (((mv ?conj ?new-copy
            ?new-strash ?new-aignet2 ?new-state)
        (observability-fix-hyp/concl
             hyp concl aignet
             copy gatesimp strash aignet2 state)))
    (implies (and (<= (num-fanins aignet) (len copy))
                  (aignet-litp hyp aignet)
                  (aignet-litp concl aignet))
             (equal (len new-copy) (len copy)))))

Theorem: copies-in-bounds-of-observability-fix-hyp/concl

(defthm copies-in-bounds-of-observability-fix-hyp/concl
  (b* (((mv ?conj ?new-copy
            ?new-strash ?new-aignet2 ?new-state)
        (observability-fix-hyp/concl
             hyp concl aignet
             copy gatesimp strash aignet2 state)))
    (implies (and (aignet-copies-in-bounds copy aignet2)
                  (aignet-litp hyp aignet)
                  (aignet-litp concl aignet)
                  (<= (num-ins aignet) (num-ins aignet2))
                  (<= (num-regs aignet)
                      (num-regs aignet2)))
             (and (aignet-copies-in-bounds new-copy new-aignet2)
                  (aignet-litp conj new-aignet2)))))

Theorem: eval-of-observability-fix-hyp/concl

(defthm eval-of-observability-fix-hyp/concl
 (b* (((mv ?conj ?new-copy
           ?new-strash ?new-aignet2 ?new-state)
       (observability-fix-hyp/concl
            hyp concl aignet
            copy gatesimp strash aignet2 state)))
  (implies
   (and (aignet-copies-in-bounds copy aignet2)
        (aignet-litp hyp aignet)
        (aignet-litp concl aignet)
        (<= (num-ins aignet) (num-ins aignet2))
        (<= (num-regs aignet)
            (num-regs aignet2)))
   (equal
    (lit-eval conj invals regvals new-aignet2)
    (b-and
       (lit-eval
            hyp
            (input-copy-values 0 invals regvals aignet copy aignet2)
            (reg-copy-values 0 invals regvals aignet copy aignet2)
            aignet)
       (lit-eval
            concl
            (input-copy-values 0 invals regvals aignet copy aignet2)
            (reg-copy-values 0 invals regvals aignet copy aignet2)
            aignet))))))

Theorem: w-state-of-observability-fix-hyp/concl

(defthm w-state-of-observability-fix-hyp/concl
  (b* (((mv ?conj ?new-copy
            ?new-strash ?new-aignet2 ?new-state)
        (observability-fix-hyp/concl
             hyp concl aignet
             copy gatesimp strash aignet2 state)))
    (equal (w new-state) (w state))))

Theorem: observability-fix-hyp/concl-of-lit-fix-hyp

(defthm observability-fix-hyp/concl-of-lit-fix-hyp
 (equal
  (observability-fix-hyp/concl (lit-fix hyp)
                               concl aignet
                               copy gatesimp strash aignet2 state)
  (observability-fix-hyp/concl hyp concl aignet
                               copy gatesimp strash aignet2 state)))

Theorem: observability-fix-hyp/concl-lit-equiv-congruence-on-hyp

(defthm observability-fix-hyp/concl-lit-equiv-congruence-on-hyp
 (implies
  (lit-equiv hyp hyp-equiv)
  (equal
    (observability-fix-hyp/concl hyp concl aignet
                                 copy gatesimp strash aignet2 state)
    (observability-fix-hyp/concl
         hyp-equiv concl aignet
         copy gatesimp strash aignet2 state)))
 :rule-classes :congruence)

Theorem: observability-fix-hyp/concl-of-lit-fix-concl

(defthm observability-fix-hyp/concl-of-lit-fix-concl
 (equal
  (observability-fix-hyp/concl hyp (lit-fix concl)
                               aignet
                               copy gatesimp strash aignet2 state)
  (observability-fix-hyp/concl hyp concl aignet
                               copy gatesimp strash aignet2 state)))

Theorem: observability-fix-hyp/concl-lit-equiv-congruence-on-concl

(defthm observability-fix-hyp/concl-lit-equiv-congruence-on-concl
 (implies
  (lit-equiv concl concl-equiv)
  (equal
    (observability-fix-hyp/concl hyp concl aignet
                                 copy gatesimp strash aignet2 state)
    (observability-fix-hyp/concl
         hyp concl-equiv aignet
         copy gatesimp strash aignet2 state)))
 :rule-classes :congruence)

Theorem: observability-fix-hyp/concl-of-node-list-fix-aignet

(defthm observability-fix-hyp/concl-of-node-list-fix-aignet
 (equal
  (observability-fix-hyp/concl hyp concl (node-list-fix aignet)
                               copy gatesimp strash aignet2 state)
  (observability-fix-hyp/concl hyp concl aignet
                               copy gatesimp strash aignet2 state)))

Theorem: observability-fix-hyp/concl-node-list-equiv-congruence-on-aignet

(defthm
   observability-fix-hyp/concl-node-list-equiv-congruence-on-aignet
 (implies
  (node-list-equiv aignet aignet-equiv)
  (equal
    (observability-fix-hyp/concl hyp concl aignet
                                 copy gatesimp strash aignet2 state)
    (observability-fix-hyp/concl
         hyp concl aignet-equiv
         copy gatesimp strash aignet2 state)))
 :rule-classes :congruence)

Theorem: observability-fix-hyp/concl-of-gatesimp-fix-gatesimp

(defthm observability-fix-hyp/concl-of-gatesimp-fix-gatesimp
 (equal
  (observability-fix-hyp/concl hyp concl
                               aignet copy (gatesimp-fix gatesimp)
                               strash aignet2 state)
  (observability-fix-hyp/concl hyp concl aignet
                               copy gatesimp strash aignet2 state)))

Theorem: observability-fix-hyp/concl-gatesimp-equiv-congruence-on-gatesimp

(defthm
  observability-fix-hyp/concl-gatesimp-equiv-congruence-on-gatesimp
 (implies
  (gatesimp-equiv gatesimp gatesimp-equiv)
  (equal
    (observability-fix-hyp/concl hyp concl aignet
                                 copy gatesimp strash aignet2 state)
    (observability-fix-hyp/concl
         hyp concl aignet copy
         gatesimp-equiv strash aignet2 state)))
 :rule-classes :congruence)

Theorem: observability-fix-hyp/concl-of-node-list-fix-aignet2

(defthm observability-fix-hyp/concl-of-node-list-fix-aignet2
 (equal
  (observability-fix-hyp/concl
       hyp concl aignet copy
       gatesimp strash (node-list-fix aignet2)
       state)
  (observability-fix-hyp/concl hyp concl aignet
                               copy gatesimp strash aignet2 state)))

Theorem: observability-fix-hyp/concl-node-list-equiv-congruence-on-aignet2

(defthm
  observability-fix-hyp/concl-node-list-equiv-congruence-on-aignet2
 (implies
  (node-list-equiv aignet2 aignet2-equiv)
  (equal
    (observability-fix-hyp/concl hyp concl aignet
                                 copy gatesimp strash aignet2 state)
    (observability-fix-hyp/concl
         hyp concl aignet copy
         gatesimp strash aignet2-equiv state)))
 :rule-classes :congruence)