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Instruction-equal

Instruction-equal->arg1

Get the arg1 field from a instruction-equal.

Signature
(instruction-equal->arg1 x) → arg1
Arguments: x — Guard (instructionp x).
Returns: arg1 — Type (operandp arg1).

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

Definitions and Theorems

Function: instruction-equal->arg1$inline

(defun instruction-equal->arg1$inline (x)
  (declare (xargs :guard (instructionp x)))
  (declare (xargs :guard (equal (instruction-kind x) :equal)))
  (let ((__function__ 'instruction-equal->arg1))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (instruction-kind x) :equal)
                      x)))
           (operand-fix (std::da-nth 1 (cdr x))))
         :exec (std::da-nth 1 (cdr x)))))

Theorem: operandp-of-instruction-equal->arg1

(defthm operandp-of-instruction-equal->arg1
  (b* ((arg1 (instruction-equal->arg1$inline x)))
    (operandp arg1))
  :rule-classes :rewrite)

Theorem: instruction-equal->arg1$inline-of-instruction-fix-x

(defthm instruction-equal->arg1$inline-of-instruction-fix-x
  (equal (instruction-equal->arg1$inline (instruction-fix x))
         (instruction-equal->arg1$inline x)))

Theorem: instruction-equal->arg1$inline-instruction-equiv-congruence-on-x

(defthm
   instruction-equal->arg1$inline-instruction-equiv-congruence-on-x
  (implies (instruction-equiv x x-equiv)
           (equal (instruction-equal->arg1$inline x)
                  (instruction-equal->arg1$inline x-equiv)))
  :rule-classes :congruence)

Theorem: instruction-equal->arg1-when-wrong-kind

(defthm instruction-equal->arg1-when-wrong-kind
  (implies (not (equal (instruction-kind x) :equal))
           (equal (instruction-equal->arg1 x)
                  (operand-fix nil))))