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Fundef

Fundef->tyspec

Get the tyspec field from a fundef.

Signature
(fundef->tyspec x) → tyspec
Arguments: x — Guard (fundefp x).
Returns: tyspec — Type (tyspecseqp tyspec).

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

Definitions and Theorems

Function: fundef->tyspec$inline

(defun fundef->tyspec$inline (x)
  (declare (xargs :guard (fundefp x)))
  (declare (xargs :guard t))
  (let ((__function__ 'fundef->tyspec))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (tyspecseq-fix (cdr (std::da-nth 0 (cdr x)))))
         :exec (cdr (std::da-nth 0 (cdr x))))))

Theorem: tyspecseqp-of-fundef->tyspec

(defthm tyspecseqp-of-fundef->tyspec
  (b* ((tyspec (fundef->tyspec$inline x)))
    (tyspecseqp tyspec))
  :rule-classes :rewrite)

Theorem: fundef->tyspec$inline-of-fundef-fix-x

(defthm fundef->tyspec$inline-of-fundef-fix-x
  (equal (fundef->tyspec$inline (fundef-fix x))
         (fundef->tyspec$inline x)))

Theorem: fundef->tyspec$inline-fundef-equiv-congruence-on-x

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