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Tyname

Tyname->tyspec

Get the tyspec field from a tyname.

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

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

Definitions and Theorems

Function: tyname->tyspec$inline

(defun tyname->tyspec$inline (x)
  (declare (xargs :guard (tynamep x)))
  (declare (xargs :guard t))
  (let ((__function__ 'tyname->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-tyname->tyspec

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

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

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

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

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