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Amb-expr/tyname

Amb-expr/tyname->tyname

Get the tyname field from a amb-expr/tyname.

Signature
(amb-expr/tyname->tyname x) → tyname
Arguments: x — Guard (amb-expr/tyname-p x).
Returns: tyname — Type (tynamep tyname).

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

Definitions and Theorems

Function: amb-expr/tyname->tyname$inline

(defun amb-expr/tyname->tyname$inline (x)
  (declare (xargs :guard (amb-expr/tyname-p x)))
  (declare (xargs :guard t))
  (mbe :logic
       (b* ((x (and t x)))
         (tyname-fix (cdr x)))
       :exec (cdr x)))

Theorem: tynamep-of-amb-expr/tyname->tyname

(defthm tynamep-of-amb-expr/tyname->tyname
  (b* ((tyname (amb-expr/tyname->tyname$inline x)))
    (tynamep tyname))
  :rule-classes :rewrite)

Theorem: amb-expr/tyname->tyname$inline-of-amb-expr/tyname-fix-x

(defthm amb-expr/tyname->tyname$inline-of-amb-expr/tyname-fix-x
  (equal (amb-expr/tyname->tyname$inline (amb-expr/tyname-fix x))
         (amb-expr/tyname->tyname$inline x)))

Theorem: amb-expr/tyname->tyname$inline-amb-expr/tyname-equiv-congruence-on-x

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