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• Observability-fix

Observability-fixed-inputs

Signature

(observability-fixed-inputs n invals inmasks hyp-lit 
                            aignet copy gatesimp strash aignet2) 
 
  → 
(mv new-copy new-strash new-aignet2)

Arguments

n — Guard (natp n).

hyp-lit — Guard (litp hyp-lit).

gatesimp — Guard (gatesimp-p gatesimp).

Definitions and Theorems

Function: observability-fixed-inputs

(defun observability-fixed-inputs
       (n invals inmasks hyp-lit
          aignet copy gatesimp strash aignet2)
 (declare
      (xargs :stobjs (invals inmasks aignet copy strash aignet2)))
 (declare (xargs :guard (and (natp n)
                             (litp hyp-lit)
                             (gatesimp-p gatesimp))))
 (declare (xargs :guard (and (<= (nfix n) (num-ins aignet))
                             (fanin-litp hyp-lit aignet2)
                             (aignet-copies-in-bounds copy aignet2)
                             (<= (num-ins aignet) (num-ins aignet2))
                             (<= (num-ins aignet)
                                 (bits-length invals))
                             (<= (num-ins aignet)
                                 (bits-length inmasks))
                             (<= (num-fanins aignet)
                                 (lits-length copy)))))
 (let ((__function__ 'observability-fixed-inputs))
   (declare (ignorable __function__))
   (b* (((when (mbe :logic (zp (- (num-ins aignet) (nfix n)))
                    :exec (eql (num-ins aignet) n)))
         (b* ((aignet2 (aignet-fix aignet2)))
           (mv copy strash aignet2)))
        (input-lit (get-lit (innum->id n aignet) copy))
        ((mv fixed-lit strash aignet2)
         (if (eql 1 (get-bit n inmasks))
             (aignet-hash-mux hyp-lit input-lit (get-bit n invals)
                              gatesimp strash aignet2)
           (mv input-lit strash aignet2)))
        (orig-id (innum->id n aignet))
        (copy (set-lit orig-id fixed-lit copy)))
     (observability-fixed-inputs
          (1+ (lnfix n))
          invals inmasks hyp-lit
          aignet copy gatesimp strash aignet2))))

Theorem: copies-in-bounds-of-observability-fixed-inputs

(defthm copies-in-bounds-of-observability-fixed-inputs
  (b* (((mv ?new-copy ?new-strash ?new-aignet2)
        (observability-fixed-inputs
             n invals inmasks hyp-lit
             aignet copy gatesimp strash aignet2)))
    (implies (and (aignet-copies-in-bounds copy aignet2)
                  (aignet-litp hyp-lit aignet2)
                  (<= (num-ins aignet) (num-ins aignet2)))
             (aignet-copies-in-bounds new-copy new-aignet2))))

Theorem: copy-length-of-observability-fixed-inputs

(defthm copy-length-of-observability-fixed-inputs
  (b* (((mv ?new-copy ?new-strash ?new-aignet2)
        (observability-fixed-inputs
             n invals inmasks hyp-lit
             aignet copy gatesimp strash aignet2)))
    (implies (<= (num-fanins aignet) (len copy))
             (equal (len new-copy) (len copy)))))

Theorem: aignet-extension-p-of-observability-fixed-inputs

(defthm aignet-extension-p-of-observability-fixed-inputs
  (b* (((mv ?new-copy ?new-strash ?new-aignet2)
        (observability-fixed-inputs
             n invals inmasks hyp-lit
             aignet copy gatesimp strash aignet2)))
    (aignet-extension-p new-aignet2 aignet2)))

Theorem: stypes-preserved-of-observability-fixed-inputs

(defthm stypes-preserved-of-observability-fixed-inputs
  (b* (((mv ?new-copy ?new-strash ?new-aignet2)
        (observability-fixed-inputs
             n invals inmasks hyp-lit
             aignet copy gatesimp strash aignet2)))
    (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: non-input-copy-of-observability-fixed-inputs

(defthm non-input-copy-of-observability-fixed-inputs
  (b* (((mv ?new-copy ?new-strash ?new-aignet2)
        (observability-fixed-inputs
             n invals inmasks hyp-lit
             aignet copy gatesimp strash aignet2)))
    (implies (not (equal (stype (car (lookup-id id aignet)))
                         :pi))
             (equal (nth-lit id new-copy)
                    (nth-lit id copy)))))

Theorem: input-copy-of-observability-fixed-inputs

(defthm input-copy-of-observability-fixed-inputs
 (b* (((mv ?new-copy ?new-strash ?new-aignet2)
       (observability-fixed-inputs
            n invals inmasks hyp-lit
            aignet copy gatesimp strash aignet2)))
  (implies
   (and (<= (nfix n) (nfix innum))
        (< (nfix innum) (num-ins aignet))
        (aignet-litp hyp-lit aignet2)
        (aignet-copies-in-bounds copy aignet2)
        (<= (num-ins aignet) (num-ins aignet2))
        (equal 1
               (lit-eval hyp-lit
                         some-invals some-regvals aignet2)))
   (equal
    (lit-eval (nth-lit (fanin-count (lookup-stype innum :pi aignet))
                       new-copy)
              some-invals some-regvals new-aignet2)
    (lit-eval (nth-lit (fanin-count (lookup-stype innum :pi aignet))
                       copy)
              some-invals some-regvals aignet2)))))

Theorem: input-copy-values-of-observability-fixed-inputs

(defthm input-copy-values-of-observability-fixed-inputs
 (b* (((mv ?new-copy ?new-strash ?new-aignet2)
       (observability-fixed-inputs
            n invals inmasks hyp-lit
            aignet copy gatesimp strash aignet2)))
  (implies
     (and (aignet-litp hyp-lit aignet2)
          (aignet-copies-in-bounds copy aignet2)
          (<= (num-ins aignet) (num-ins aignet2))
          (equal 1
                 (lit-eval hyp-lit
                           some-invals some-regvals aignet2)))
     (equal (input-copy-values n some-invals some-regvals
                               aignet new-copy new-aignet2)
            (input-copy-values n some-invals
                               some-regvals aignet copy aignet2)))))

Theorem: reg-copy-values-of-observability-fixed-inputs

(defthm reg-copy-values-of-observability-fixed-inputs
 (b* (((mv ?new-copy ?new-strash ?new-aignet2)
       (observability-fixed-inputs
            n invals inmasks hyp-lit
            aignet copy gatesimp strash aignet2)))
  (implies
       (and (aignet-copies-in-bounds copy aignet2)
            (aignet-litp hyp-lit aignet2)
            (<= (num-ins aignet) (num-ins aignet2)))
       (equal (reg-copy-values 0 some-invals some-regvals
                               aignet new-copy new-aignet2)
              (reg-copy-values 0 some-invals
                               some-regvals aignet copy aignet2)))))

Theorem: observability-fixed-inputs-of-nfix-n

(defthm observability-fixed-inputs-of-nfix-n
 (equal
  (observability-fixed-inputs (nfix n)
                              invals inmasks hyp-lit
                              aignet copy gatesimp strash aignet2)
  (observability-fixed-inputs n invals inmasks hyp-lit
                              aignet copy gatesimp strash aignet2)))

Theorem: observability-fixed-inputs-nat-equiv-congruence-on-n

(defthm observability-fixed-inputs-nat-equiv-congruence-on-n
 (implies
  (nat-equiv n n-equiv)
  (equal
    (observability-fixed-inputs n invals inmasks hyp-lit
                                aignet copy gatesimp strash aignet2)
    (observability-fixed-inputs
         n-equiv invals inmasks hyp-lit
         aignet copy gatesimp strash aignet2)))
 :rule-classes :congruence)

Theorem: observability-fixed-inputs-of-lit-fix-hyp-lit

(defthm observability-fixed-inputs-of-lit-fix-hyp-lit
 (equal
  (observability-fixed-inputs n invals inmasks (lit-fix hyp-lit)
                              aignet copy gatesimp strash aignet2)
  (observability-fixed-inputs n invals inmasks hyp-lit
                              aignet copy gatesimp strash aignet2)))

Theorem: observability-fixed-inputs-lit-equiv-congruence-on-hyp-lit

(defthm observability-fixed-inputs-lit-equiv-congruence-on-hyp-lit
 (implies
  (lit-equiv hyp-lit hyp-lit-equiv)
  (equal
    (observability-fixed-inputs n invals inmasks hyp-lit
                                aignet copy gatesimp strash aignet2)
    (observability-fixed-inputs
         n invals inmasks hyp-lit-equiv
         aignet copy gatesimp strash aignet2)))
 :rule-classes :congruence)

Theorem: observability-fixed-inputs-of-node-list-fix-aignet

(defthm observability-fixed-inputs-of-node-list-fix-aignet
 (equal
  (observability-fixed-inputs n invals
                              inmasks hyp-lit (node-list-fix aignet)
                              copy gatesimp strash aignet2)
  (observability-fixed-inputs n invals inmasks hyp-lit
                              aignet copy gatesimp strash aignet2)))

Theorem: observability-fixed-inputs-node-list-equiv-congruence-on-aignet

(defthm
    observability-fixed-inputs-node-list-equiv-congruence-on-aignet
 (implies
  (node-list-equiv aignet aignet-equiv)
  (equal
   (observability-fixed-inputs n invals inmasks hyp-lit
                               aignet copy gatesimp strash aignet2)
   (observability-fixed-inputs n invals inmasks hyp-lit aignet-equiv
                               copy gatesimp strash aignet2)))
 :rule-classes :congruence)

Theorem: observability-fixed-inputs-of-gatesimp-fix-gatesimp

(defthm observability-fixed-inputs-of-gatesimp-fix-gatesimp
 (equal
  (observability-fixed-inputs n invals inmasks hyp-lit
                              aignet copy (gatesimp-fix gatesimp)
                              strash aignet2)
  (observability-fixed-inputs n invals inmasks hyp-lit
                              aignet copy gatesimp strash aignet2)))

Theorem: observability-fixed-inputs-gatesimp-equiv-congruence-on-gatesimp

(defthm
   observability-fixed-inputs-gatesimp-equiv-congruence-on-gatesimp
 (implies
  (gatesimp-equiv gatesimp gatesimp-equiv)
  (equal
   (observability-fixed-inputs n invals inmasks hyp-lit
                               aignet copy gatesimp strash aignet2)
   (observability-fixed-inputs n invals inmasks hyp-lit aignet
                               copy gatesimp-equiv strash aignet2)))
 :rule-classes :congruence)

Theorem: observability-fixed-inputs-of-node-list-fix-aignet2

(defthm observability-fixed-inputs-of-node-list-fix-aignet2
 (equal
  (observability-fixed-inputs
       n invals inmasks hyp-lit aignet copy
       gatesimp strash (node-list-fix aignet2))
  (observability-fixed-inputs n invals inmasks hyp-lit
                              aignet copy gatesimp strash aignet2)))

Theorem: observability-fixed-inputs-node-list-equiv-congruence-on-aignet2

(defthm
   observability-fixed-inputs-node-list-equiv-congruence-on-aignet2
 (implies
  (node-list-equiv aignet2 aignet2-equiv)
  (equal
   (observability-fixed-inputs n invals inmasks hyp-lit
                               aignet copy gatesimp strash aignet2)
   (observability-fixed-inputs n invals inmasks hyp-lit aignet
                               copy gatesimp strash aignet2-equiv)))
 :rule-classes :congruence)