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• Trans-state

Extend-trans-state-list

Lift extend-trans-state to lists.

Signature

(extend-trans-state-list tops tstate) → new-tstate

Arguments

tops — Guard (toplevel-listp tops).

tstate — Guard (trans-statep tstate).

Returns

new-tstate — Type (trans-statep new-tstate).

Definitions and Theorems

Function: extend-trans-state-list

(defun extend-trans-state-list (tops tstate)
 (declare (xargs :guard (and (toplevel-listp tops)
                             (trans-statep tstate))))
 (let ((__function__ 'extend-trans-state-list))
  (declare (ignorable __function__))
  (cond ((endp tops) (trans-state-fix tstate))
        (t (extend-trans-state-list (cdr tops)
                                    (extend-trans-state (car tops)
                                                        tstate))))))

Theorem: trans-statep-of-extend-trans-state-list

(defthm trans-statep-of-extend-trans-state-list
  (b* ((new-tstate (extend-trans-state-list tops tstate)))
    (trans-statep new-tstate))
  :rule-classes :rewrite)

Theorem: extend-trans-state-list-of-toplevel-list-fix-tops

(defthm extend-trans-state-list-of-toplevel-list-fix-tops
  (equal (extend-trans-state-list (toplevel-list-fix tops)
                                  tstate)
         (extend-trans-state-list tops tstate)))

Theorem: extend-trans-state-list-toplevel-list-equiv-congruence-on-tops

(defthm
     extend-trans-state-list-toplevel-list-equiv-congruence-on-tops
  (implies (toplevel-list-equiv tops tops-equiv)
           (equal (extend-trans-state-list tops tstate)
                  (extend-trans-state-list tops-equiv tstate)))
  :rule-classes :congruence)

Theorem: extend-trans-state-list-of-trans-state-fix-tstate

(defthm extend-trans-state-list-of-trans-state-fix-tstate
  (equal (extend-trans-state-list tops (trans-state-fix tstate))
         (extend-trans-state-list tops tstate)))

Theorem: extend-trans-state-list-trans-state-equiv-congruence-on-tstate

(defthm
     extend-trans-state-list-trans-state-equiv-congruence-on-tstate
  (implies (trans-state-equiv tstate tstate-equiv)
           (equal (extend-trans-state-list tops tstate)
                  (extend-trans-state-list tops tstate-equiv)))
  :rule-classes :congruence)