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Expr-binary

Expr-binary->arg1

Get the arg1 field from a expr-binary.

Signature
(expr-binary->arg1 x) → arg1
Arguments: x — Guard (exprp x).
Returns: arg1 — Type (exprp arg1).

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

Definitions and Theorems

Function: expr-binary->arg1$inline

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

Theorem: exprp-of-expr-binary->arg1

(defthm exprp-of-expr-binary->arg1
  (b* ((arg1 (expr-binary->arg1$inline x)))
    (exprp arg1))
  :rule-classes :rewrite)

Theorem: expr-binary->arg1$inline-of-expr-fix-x

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

Theorem: expr-binary->arg1$inline-expr-equiv-congruence-on-x

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

Theorem: expr-binary->arg1-when-wrong-kind

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