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Expression-mul

Expression-mul->arg1

Get the arg1 field from a expression-mul.

Signature
(expression-mul->arg1 x) → arg1
Arguments: x — Guard (expressionp x).
Returns: arg1 — Type (expressionp arg1).

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

Definitions and Theorems

Function: expression-mul->arg1$inline

(defun expression-mul->arg1$inline (x)
  (declare (xargs :guard (expressionp x)))
  (declare (xargs :guard (equal (expression-kind x) :mul)))
  (let ((__function__ 'expression-mul->arg1))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (expression-kind x) :mul)
                      x)))
           (expression-fix (std::da-nth 0 (cdr x))))
         :exec (std::da-nth 0 (cdr x)))))

Theorem: expressionp-of-expression-mul->arg1

(defthm expressionp-of-expression-mul->arg1
  (b* ((arg1 (expression-mul->arg1$inline x)))
    (expressionp arg1))
  :rule-classes :rewrite)

Theorem: expression-mul->arg1$inline-of-expression-fix-x

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

Theorem: expression-mul->arg1$inline-expression-equiv-congruence-on-x

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

Theorem: expression-mul->arg1-when-wrong-kind

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