		Search-engine friendly clone of the ACL2 documentation.

Instruction-equal

Instruction-equal->op

Get the op field from a instruction-equal.

Signature
(instruction-equal->op x) → op
Arguments: x — Guard (instructionp x).
Returns: op — Type (equal-opp op).

This is an ordinary field accessor created by fty::defprod.

Definitions and Theorems

Function: instruction-equal->op$inline

(defun instruction-equal->op$inline (x)
  (declare (xargs :guard (instructionp x)))
  (declare (xargs :guard (equal (instruction-kind x) :equal)))
  (let ((__function__ 'instruction-equal->op))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (instruction-kind x) :equal)
                      x)))
           (equal-op-fix (std::da-nth 0 (cdr x))))
         :exec (std::da-nth 0 (cdr x)))))

Theorem: equal-opp-of-instruction-equal->op

(defthm equal-opp-of-instruction-equal->op
  (b* ((op (instruction-equal->op$inline x)))
    (equal-opp op))
  :rule-classes :rewrite)

Theorem: instruction-equal->op$inline-of-instruction-fix-x

(defthm instruction-equal->op$inline-of-instruction-fix-x
  (equal (instruction-equal->op$inline (instruction-fix x))
         (instruction-equal->op$inline x)))

Theorem: instruction-equal->op$inline-instruction-equiv-congruence-on-x

(defthm
     instruction-equal->op$inline-instruction-equiv-congruence-on-x
  (implies (instruction-equiv x x-equiv)
           (equal (instruction-equal->op$inline x)
                  (instruction-equal->op$inline x-equiv)))
  :rule-classes :congruence)

Theorem: instruction-equal->op-when-wrong-kind

(defthm instruction-equal->op-when-wrong-kind
  (implies (not (equal (instruction-kind x) :equal))
           (equal (instruction-equal->op x)
                  (equal-op-fix nil))))