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Amb?-expr/tyname-expr

Amb?-expr/tyname-expr->expr

Get the expr field from a amb?-expr/tyname-expr.

Signature
(amb?-expr/tyname-expr->expr x) → expr
Arguments: x — Guard (amb?-expr/tyname-p x).
Returns: expr — Type (exprp expr).

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

Definitions and Theorems

Function: amb?-expr/tyname-expr->expr$inline

(defun amb?-expr/tyname-expr->expr$inline (x)
  (declare (xargs :guard (amb?-expr/tyname-p x)))
  (declare (xargs :guard (equal (amb?-expr/tyname-kind x)
                                :expr)))
  (mbe :logic
       (b* ((x (and (equal (amb?-expr/tyname-kind x) :expr)
                    x)))
         (expr-fix (cdr x)))
       :exec (cdr x)))

Theorem: exprp-of-amb?-expr/tyname-expr->expr

(defthm exprp-of-amb?-expr/tyname-expr->expr
  (b* ((expr (amb?-expr/tyname-expr->expr$inline x)))
    (exprp expr))
  :rule-classes :rewrite)

Theorem: amb?-expr/tyname-expr->expr$inline-of-amb?-expr/tyname-fix-x

(defthm amb?-expr/tyname-expr->expr$inline-of-amb?-expr/tyname-fix-x
  (equal
       (amb?-expr/tyname-expr->expr$inline (amb?-expr/tyname-fix x))
       (amb?-expr/tyname-expr->expr$inline x)))

Theorem: amb?-expr/tyname-expr->expr$inline-amb?-expr/tyname-equiv-congruence-on-x

(defthm
 amb?-expr/tyname-expr->expr$inline-amb?-expr/tyname-equiv-congruence-on-x
 (implies (amb?-expr/tyname-equiv x x-equiv)
          (equal (amb?-expr/tyname-expr->expr$inline x)
                 (amb?-expr/tyname-expr->expr$inline x-equiv)))
 :rule-classes :congruence)

Theorem: amb?-expr/tyname-expr->expr-when-wrong-kind

(defthm amb?-expr/tyname-expr->expr-when-wrong-kind
  (implies (not (equal (amb?-expr/tyname-kind x) :expr))
           (equal (amb?-expr/tyname-expr->expr x)
                  (expr-fix nil))))