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Exprs-gin

Exprs-gin->proofs

Get the proofs field from a exprs-gin.

Signature
(exprs-gin->proofs x) → proofs
Arguments: x — Guard (exprs-ginp x).
Returns: proofs — Type (booleanp proofs).

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

Definitions and Theorems

Function: exprs-gin->proofs$inline

(defun exprs-gin->proofs$inline (x)
  (declare (xargs :guard (exprs-ginp x)))
  (declare (xargs :guard t))
  (let ((__function__ 'exprs-gin->proofs))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (acl2::bool-fix (cdr (std::da-nth 8 x))))
         :exec (cdr (std::da-nth 8 x)))))

Theorem: booleanp-of-exprs-gin->proofs

(defthm booleanp-of-exprs-gin->proofs
  (b* ((proofs (exprs-gin->proofs$inline x)))
    (booleanp proofs))
  :rule-classes :rewrite)

Theorem: exprs-gin->proofs$inline-of-exprs-gin-fix-x

(defthm exprs-gin->proofs$inline-of-exprs-gin-fix-x
  (equal (exprs-gin->proofs$inline (exprs-gin-fix x))
         (exprs-gin->proofs$inline x)))

Theorem: exprs-gin->proofs$inline-exprs-gin-equiv-congruence-on-x

(defthm exprs-gin->proofs$inline-exprs-gin-equiv-congruence-on-x
  (implies (exprs-gin-equiv x x-equiv)
           (equal (exprs-gin->proofs$inline x)
                  (exprs-gin->proofs$inline x-equiv)))
  :rule-classes :congruence)