Get the equiv field from a fgl-binder-rule-brewrite.
(fgl-binder-rule-brewrite->equiv x) → equiv
This is an ordinary field accessor created by defprod.
Function:
(defun fgl-binder-rule-brewrite->equiv$inline (x) (declare (xargs :guard (fgl-binder-rule-p x))) (declare (xargs :guard (equal (fgl-binder-rule-kind x) :brewrite))) (let ((__function__ 'fgl-binder-rule-brewrite->equiv)) (declare (ignorable __function__)) (mbe :logic (b* ((x (and (equal (fgl-binder-rule-kind x) :brewrite) x))) (pseudo-fnsym-fix (car (cdr (cdr (cdr x)))))) :exec (car (cdr (cdr (cdr x)))))))
Theorem:
(defthm pseudo-fnsym-p-of-fgl-binder-rule-brewrite->equiv (b* ((equiv (fgl-binder-rule-brewrite->equiv$inline x))) (pseudo-fnsym-p equiv)) :rule-classes :rewrite)
Theorem:
(defthm fgl-binder-rule-brewrite->equiv$inline-of-fgl-binder-rule-fix-x (equal (fgl-binder-rule-brewrite->equiv$inline (fgl-binder-rule-fix x)) (fgl-binder-rule-brewrite->equiv$inline x)))
Theorem:
(defthm fgl-binder-rule-brewrite->equiv$inline-fgl-binder-rule-equiv-congruence-on-x (implies (fgl-binder-rule-equiv x x-equiv) (equal (fgl-binder-rule-brewrite->equiv$inline x) (fgl-binder-rule-brewrite->equiv$inline x-equiv))) :rule-classes :congruence)
Theorem:
(defthm fgl-binder-rule-brewrite->equiv-when-wrong-kind (implies (not (equal (fgl-binder-rule-kind x) :brewrite)) (equal (fgl-binder-rule-brewrite->equiv x) (pseudo-fnsym-fix nil))))