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Boolean-assert

Boolean-assert-lifting

Lifting of the circuit to a predicate.

Definitions and Theorems

Function: boolean-assert-pred

(defun boolean-assert-pred (x prime)
  (and (equal (pfield::mul (pfield::sub (mod 1 prime) x prime)
                           x prime)
              (mod 0 prime))))

Theorem: definition-satp-to-boolean-assert-pred

(defthm definition-satp-to-boolean-assert-pred
 (implies
  (and
   (equal
     (pfcs::lookup-definition '(:simple "boolean_assert")
                              pfcs::defs)
     '(:definition
           (name :simple "boolean_assert")
           (pfcs::para (:simple "x"))
           (pfcs::body
                (:equal (:mul (:sub (:const 1) (:var (:simple "x")))
                              (:var (:simple "x")))
                        (:const 0)))))
   (pfield::fep x prime)
   (primep prime))
  (equal (pfcs::definition-satp '(:simple "boolean_assert")
                                pfcs::defs (list x)
                                prime)
         (boolean-assert-pred x prime))))