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Tyname

Tyname->specquals

Get the specquals field from a tyname.

Signature
(tyname->specquals x) → specquals
Arguments: x — Guard (tynamep x).
Returns: specquals — Type (spec/qual-listp specquals).

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

Definitions and Theorems

Function: tyname->specquals$inline

(defun tyname->specquals$inline (x)
  (declare (xargs :guard (tynamep x)))
  (declare (xargs :guard t))
  (mbe :logic
       (b* ((x (and t x)))
         (spec/qual-list-fix (car x)))
       :exec (car x)))

Theorem: spec/qual-listp-of-tyname->specquals

(defthm spec/qual-listp-of-tyname->specquals
  (b* ((specquals (tyname->specquals$inline x)))
    (spec/qual-listp specquals))
  :rule-classes :rewrite)

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

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

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

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