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• Fgl-function-mode

!fgl-function-mode->dont-rewrite-under-if-test

Update the |FGL|::|DONT-REWRITE-UNDER-IF-TEST| field of a fgl-function-mode bit structure.

Signature

(!fgl-function-mode->dont-rewrite-under-if-test 
     dont-rewrite-under-if-test x) 
 
  → 
new-x

Arguments

dont-rewrite-under-if-test — Guard (booleanp dont-rewrite-under-if-test).

x — Guard (fgl-function-mode-p x).

Returns

new-x — Type (fgl-function-mode-p new-x).

Definitions and Theorems

Function: !fgl-function-mode->dont-rewrite-under-if-test

(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: fgl-function-mode-p-of-!fgl-function-mode->dont-rewrite-under-if-test

(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: !fgl-function-mode->dont-rewrite-under-if-test-of-bool-fix-dont-rewrite-under-if-test

(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: !fgl-function-mode->dont-rewrite-under-if-test-iff-congruence-on-dont-rewrite-under-if-test

(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: !fgl-function-mode->dont-rewrite-under-if-test-of-fgl-function-mode-fix-x

(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: !fgl-function-mode->dont-rewrite-under-if-test-fgl-function-mode-equiv-congruence-on-x

(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: !fgl-function-mode->dont-rewrite-under-if-test-is-fgl-function-mode

(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: fgl-function-mode->dont-rewrite-under-if-test-of-!fgl-function-mode->dont-rewrite-under-if-test

(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: !fgl-function-mode->dont-rewrite-under-if-test-equiv-under-mask

(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)))