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