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Expr-ident

Expr-ident->ident

Get the ident field from a expr-ident.

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

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

Definitions and Theorems

Function: expr-ident->ident$inline

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

Theorem: identp-of-expr-ident->ident

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

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

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

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

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

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

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