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Expr-extension

Expr-extension->expr

Get the expr field from a expr-extension.

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

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

Definitions and Theorems

Function: expr-extension->expr$inline

(defun expr-extension->expr$inline (x)
  (declare (xargs :guard (exprp x)))
  (declare (xargs :guard (equal (expr-kind x) :extension)))
  (mbe :logic
       (b* ((x (and (equal (expr-kind x) :extension)
                    x)))
         (expr-fix (cdr x)))
       :exec (cdr x)))

Theorem: exprp-of-expr-extension->expr

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

Theorem: expr-extension->expr$inline-of-expr-fix-x

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

Theorem: expr-extension->expr$inline-expr-equiv-congruence-on-x

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

Theorem: expr-extension->expr-when-wrong-kind

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