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Fgl-syntactic-checker-binders

Check-true

FGL binder that checks whether X is syntactically known true.

Signature
(check-true ans x) → *

See fgl-syntactic-checker-binders and see binder for details.

Definitions and Theorems

Function: check-true

(defun check-true (ans x)
  (declare (xargs :guard t))
  (let ((__function__ 'check-true))
    (declare (ignorable __function__))
    (and x ans t)))

Theorem: check-true-implies-true

(defthm check-true-implies-true
  (implies (check-true ans x) x)
  :rule-classes :forward-chaining)

Theorem: iff-implies-equal-check-true-2

(defthm iff-implies-equal-check-true-2
  (implies (iff x x-equiv)
           (equal (check-true ans x)
                  (check-true ans x-equiv)))
  :rule-classes (:congruence))