Update the |FGL|::|DONT-REWRITE-UNDER-IF-TEST| field of a fgl-function-mode bit structure.
(!fgl-function-mode->dont-rewrite-under-if-test dont-rewrite-under-if-test x) → new-x
Function:
(defun !fgl-function-mode->dont-rewrite-under-if-test (dont-rewrite-under-if-test x) (declare (xargs :guard (and (booleanp dont-rewrite-under-if-test) (fgl-function-mode-p x)))) (mbe :logic (b* ((dont-rewrite-under-if-test (bool->bit dont-rewrite-under-if-test)) (x (fgl-function-mode-fix x))) (acl2::part-install dont-rewrite-under-if-test x :width 1 :low 4)) :exec (the (unsigned-byte 6) (logior (the (unsigned-byte 6) (logand (the (unsigned-byte 6) x) (the (signed-byte 6) -17))) (the (unsigned-byte 5) (ash (the (unsigned-byte 1) (bool->bit dont-rewrite-under-if-test)) 4))))))
Theorem:
(defthm fgl-function-mode-p-of-!fgl-function-mode->dont-rewrite-under-if-test (b* ((new-x (!fgl-function-mode->dont-rewrite-under-if-test dont-rewrite-under-if-test x))) (fgl-function-mode-p new-x)) :rule-classes :rewrite)
Theorem:
(defthm !fgl-function-mode->dont-rewrite-under-if-test-of-bool-fix-dont-rewrite-under-if-test (equal (!fgl-function-mode->dont-rewrite-under-if-test (bool-fix dont-rewrite-under-if-test) x) (!fgl-function-mode->dont-rewrite-under-if-test dont-rewrite-under-if-test x)))
Theorem:
(defthm !fgl-function-mode->dont-rewrite-under-if-test-iff-congruence-on-dont-rewrite-under-if-test (implies (iff dont-rewrite-under-if-test dont-rewrite-under-if-test-equiv) (equal (!fgl-function-mode->dont-rewrite-under-if-test dont-rewrite-under-if-test x) (!fgl-function-mode->dont-rewrite-under-if-test dont-rewrite-under-if-test-equiv x))) :rule-classes :congruence)
Theorem:
(defthm !fgl-function-mode->dont-rewrite-under-if-test-of-fgl-function-mode-fix-x (equal (!fgl-function-mode->dont-rewrite-under-if-test dont-rewrite-under-if-test (fgl-function-mode-fix x)) (!fgl-function-mode->dont-rewrite-under-if-test dont-rewrite-under-if-test x)))
Theorem:
(defthm !fgl-function-mode->dont-rewrite-under-if-test-fgl-function-mode-equiv-congruence-on-x (implies (fgl-function-mode-equiv x x-equiv) (equal (!fgl-function-mode->dont-rewrite-under-if-test dont-rewrite-under-if-test x) (!fgl-function-mode->dont-rewrite-under-if-test dont-rewrite-under-if-test x-equiv))) :rule-classes :congruence)
Theorem:
(defthm !fgl-function-mode->dont-rewrite-under-if-test-is-fgl-function-mode (equal (!fgl-function-mode->dont-rewrite-under-if-test dont-rewrite-under-if-test x) (change-fgl-function-mode x :dont-rewrite-under-if-test dont-rewrite-under-if-test)))
Theorem:
(defthm fgl-function-mode->dont-rewrite-under-if-test-of-!fgl-function-mode->dont-rewrite-under-if-test (b* ((?new-x (!fgl-function-mode->dont-rewrite-under-if-test dont-rewrite-under-if-test x))) (equal (fgl-function-mode->dont-rewrite-under-if-test new-x) (bool-fix dont-rewrite-under-if-test))))
Theorem:
(defthm !fgl-function-mode->dont-rewrite-under-if-test-equiv-under-mask (b* ((?new-x (!fgl-function-mode->dont-rewrite-under-if-test dont-rewrite-under-if-test x))) (fgl-function-mode-equiv-under-mask new-x x -17)))