Get the proofs field from a expr-gin.
This is an ordinary field accessor created by fty::defprod.
Function:
(defun expr-gin->proofs$inline (x) (declare (xargs :guard (expr-ginp x))) (declare (xargs :guard t)) (let ((__function__ 'expr-gin->proofs)) (declare (ignorable __function__)) (mbe :logic (b* ((x (and t x))) (acl2::bool-fix (cdr (std::da-nth 8 x)))) :exec (cdr (std::da-nth 8 x)))))
Theorem:
(defthm booleanp-of-expr-gin->proofs (b* ((proofs (expr-gin->proofs$inline x))) (booleanp proofs)) :rule-classes :rewrite)
Theorem:
(defthm expr-gin->proofs$inline-of-expr-gin-fix-x (equal (expr-gin->proofs$inline (expr-gin-fix x)) (expr-gin->proofs$inline x)))
Theorem:
(defthm expr-gin->proofs$inline-expr-gin-equiv-congruence-on-x (implies (expr-gin-equiv x x-equiv) (equal (expr-gin->proofs$inline x) (expr-gin->proofs$inline x-equiv))) :rule-classes :congruence)