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Operands

Operands->op1

Get the op1 field from a operands.

Signature
(operands->op1 x) → op1
Arguments: x — Guard (operands-p x).
Returns: op1 — Type (operand-type-p op1).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: operands->op1$inline

(defun operands->op1$inline (x)
  (declare (xargs :guard (operands-p x)))
  (declare (xargs :guard t))
  (let ((__function__ 'operands->op1))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (operand-type-fix (std::prod-car (std::prod-car x))))
         :exec (std::prod-car (std::prod-car x)))))

Theorem: operand-type-p-of-operands->op1

(defthm operand-type-p-of-operands->op1
  (b* ((op1 (operands->op1$inline x)))
    (operand-type-p op1))
  :rule-classes :rewrite)

Theorem: operands->op1$inline-of-operands-fix-x

(defthm operands->op1$inline-of-operands-fix-x
  (equal (operands->op1$inline (operands-fix x))
         (operands->op1$inline x)))

Theorem: operands->op1$inline-operands-equiv-congruence-on-x

(defthm operands->op1$inline-operands-equiv-congruence-on-x
  (implies (operands-equiv x x-equiv)
           (equal (operands->op1$inline x)
                  (operands->op1$inline x-equiv)))
  :rule-classes :congruence)