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• Observability-fix

M-assum-n-output-observability

Signature

(m-assum-n-output-observability m n aignet aignet2 config state) 
  → 
(mv new-aignet2 new-state)

Arguments

m — Guard (natp m).

n — Guard (natp n).

config — Guard (m-assum-n-output-observability-config-p config).

Definitions and Theorems

Function: m-assum-n-output-observability

(defun m-assum-n-output-observability
       (m n aignet aignet2 config state)
 (declare (xargs :stobjs (aignet aignet2 state)))
 (declare
  (xargs
     :guard (and (natp m)
                 (natp n)
                 (m-assum-n-output-observability-config-p config))))
 (declare (ignorable n))
 (declare (xargs :guard (<= (+ m n) (num-outs aignet))))
 (let ((__function__ 'm-assum-n-output-observability))
   (declare (ignorable __function__))
   (b*
     (((local-stobjs copy strash)
       (mv copy strash aignet2 state))
      ((mv copy aignet2)
       (init-copy-comb aignet copy aignet2))
      (m (mbe :logic (min (nfix m) (num-outs aignet))
              :exec m))
      (hyps (output-lit-range 0 m aignet))
      (concls (output-lit-range m (- (num-outs aignet) m)
                                aignet))
      ((mv ?hyp new-hyps
           new-concls copy strash aignet2 state)
       (observability-fix-hyps/concls
            hyps concls aignet copy
            (m-assum-n-output-observability-config->gatesimp config)
            strash aignet2 state))
      (aignet2 (aignet-add-outs new-hyps aignet2))
      (aignet2 (aignet-add-outs new-concls aignet2)))
     (mv copy strash aignet2 state))))

Theorem: normalize-inputs-of-m-assum-n-output-observability

(defthm normalize-inputs-of-m-assum-n-output-observability
 (b* nil
  (implies
   (syntaxp (not (equal aignet2 ''nil)))
   (equal
    (m-assum-n-output-observability m n aignet aignet2 config state)
    (let ((aignet2 nil))
      (m-assum-n-output-observability
           m n aignet aignet2 config state))))))

Theorem: num-ins-of-m-assum-n-output-observability

(defthm num-ins-of-m-assum-n-output-observability
  (b* (((mv ?new-aignet2 ?new-state)
        (m-assum-n-output-observability
             m n aignet aignet2 config state)))
    (equal (stype-count :pi new-aignet2)
           (stype-count :pi aignet))))

Theorem: num-regs-of-m-assum-n-output-observability

(defthm num-regs-of-m-assum-n-output-observability
  (b* (((mv ?new-aignet2 ?new-state)
        (m-assum-n-output-observability
             m n aignet aignet2 config state)))
    (equal (stype-count :reg new-aignet2)
           (stype-count :reg aignet))))

Theorem: num-outs-of-m-assum-n-output-observability

(defthm num-outs-of-m-assum-n-output-observability
  (b* (((mv ?new-aignet2 ?new-state)
        (m-assum-n-output-observability
             m n aignet aignet2 config state)))
    (equal (stype-count :po new-aignet2)
           (stype-count :po aignet))))

Theorem: m-assum-n-output-observability-eval-assumptions

(defthm m-assum-n-output-observability-eval-assumptions
  (b* (((mv ?new-aignet2 ?new-state)
        (m-assum-n-output-observability
             m n aignet aignet2 config state)))
    (implies (< (nfix i) (nfix m))
             (equal (output-eval i invals regvals new-aignet2)
                    (output-eval i invals regvals aignet)))))

Theorem: m-assum-n-output-observability-eval-conclusion

(defthm m-assum-n-output-observability-eval-conclusion
 (b* (((mv ?new-aignet2 ?new-state)
       (m-assum-n-output-observability
            m n aignet aignet2 config state)))
   (implies
        (and (< (nfix i) (+ (nfix m) (nfix n)))
             (equal (conjoin-output-range 0 m invals regvals aignet)
                    1))
        (equal (output-eval i invals regvals new-aignet2)
               (output-eval i invals regvals aignet)))))

Theorem: w-state-of-m-assum-n-output-observability

(defthm w-state-of-m-assum-n-output-observability
  (b* (((mv ?new-aignet2 ?new-state)
        (m-assum-n-output-observability
             m n aignet aignet2 config state)))
    (equal (w new-state) (w state))))

Theorem: list-of-outputs-of-m-assum-n-output-observability

(defthm list-of-outputs-of-m-assum-n-output-observability
  (b* (((mv ?new-aignet2 ?new-state)
        (m-assum-n-output-observability
             m n aignet aignet2 config state)))
    (equal (list new-aignet2 new-state)
           (m-assum-n-output-observability
                m n aignet aignet2 config state))))

Theorem: m-assum-n-output-observability-of-nfix-m

(defthm m-assum-n-output-observability-of-nfix-m
 (equal
  (m-assum-n-output-observability (nfix m)
                                  n aignet aignet2 config state)
  (m-assum-n-output-observability m n aignet aignet2 config state)))

Theorem: m-assum-n-output-observability-nat-equiv-congruence-on-m

(defthm m-assum-n-output-observability-nat-equiv-congruence-on-m
 (implies
  (nat-equiv m m-equiv)
  (equal
    (m-assum-n-output-observability m n aignet aignet2 config state)
    (m-assum-n-output-observability
         m-equiv n aignet aignet2 config state)))
 :rule-classes :congruence)

Theorem: m-assum-n-output-observability-of-nfix-n

(defthm m-assum-n-output-observability-of-nfix-n
 (equal
  (m-assum-n-output-observability m (nfix n)
                                  aignet aignet2 config state)
  (m-assum-n-output-observability m n aignet aignet2 config state)))

Theorem: m-assum-n-output-observability-nat-equiv-congruence-on-n

(defthm m-assum-n-output-observability-nat-equiv-congruence-on-n
 (implies
  (nat-equiv n n-equiv)
  (equal
    (m-assum-n-output-observability m n aignet aignet2 config state)
    (m-assum-n-output-observability
         m n-equiv aignet aignet2 config state)))
 :rule-classes :congruence)

Theorem: m-assum-n-output-observability-of-node-list-fix-aignet

(defthm m-assum-n-output-observability-of-node-list-fix-aignet
 (equal
  (m-assum-n-output-observability m n (node-list-fix aignet)
                                  aignet2 config state)
  (m-assum-n-output-observability m n aignet aignet2 config state)))

Theorem: m-assum-n-output-observability-node-list-equiv-congruence-on-aignet

(defthm
 m-assum-n-output-observability-node-list-equiv-congruence-on-aignet
 (implies
  (node-list-equiv aignet aignet-equiv)
  (equal
    (m-assum-n-output-observability m n aignet aignet2 config state)
    (m-assum-n-output-observability
         m n aignet-equiv aignet2 config state)))
 :rule-classes :congruence)

Theorem: m-assum-n-output-observability-of-node-list-fix-aignet2

(defthm m-assum-n-output-observability-of-node-list-fix-aignet2
 (equal
  (m-assum-n-output-observability m n aignet (node-list-fix aignet2)
                                  config state)
  (m-assum-n-output-observability m n aignet aignet2 config state)))

Theorem: m-assum-n-output-observability-node-list-equiv-congruence-on-aignet2

(defthm
 m-assum-n-output-observability-node-list-equiv-congruence-on-aignet2
 (implies
  (node-list-equiv aignet2 aignet2-equiv)
  (equal
    (m-assum-n-output-observability m n aignet aignet2 config state)
    (m-assum-n-output-observability
         m n aignet aignet2-equiv config state)))
 :rule-classes :congruence)

Theorem: m-assum-n-output-observability-of-m-assum-n-output-observability-config-fix-config

(defthm
 m-assum-n-output-observability-of-m-assum-n-output-observability-config-fix-config
 (equal
  (m-assum-n-output-observability
       m n aignet aignet2
       (m-assum-n-output-observability-config-fix config)
       state)
  (m-assum-n-output-observability m n aignet aignet2 config state)))

Theorem: m-assum-n-output-observability-m-assum-n-output-observability-config-equiv-congruence-on-config

(defthm
 m-assum-n-output-observability-m-assum-n-output-observability-config-equiv-congruence-on-config
 (implies
  (m-assum-n-output-observability-config-equiv config config-equiv)
  (equal
    (m-assum-n-output-observability m n aignet aignet2 config state)
    (m-assum-n-output-observability
         m n aignet aignet2 config-equiv state)))
 :rule-classes :congruence)