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Bounded-lit-fix

Signature

(bounded-lit-fix x bound) → new-x

Arguments

x — Guard (satlink::litp x).

bound — Guard (natp bound).

Returns

new-x — Type (satlink::litp new-x).

Definitions and Theorems

Function: bounded-lit-fix$inline

(defun bounded-lit-fix$inline (x bound)
  (declare (xargs :guard (and (satlink::litp x) (natp bound))))
  (declare (xargs :guard (<= (satlink::lit->var x) bound)))
  (let ((__function__ 'bounded-lit-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (if (<= (satlink::lit->var x) (nfix bound))
             (satlink::lit-fix x)
           (satlink::make-lit 0 (satlink::lit->neg x)))
         :exec x)))

Theorem: litp-of-bounded-lit-fix

(defthm litp-of-bounded-lit-fix
  (b* ((new-x (bounded-lit-fix$inline x bound)))
    (satlink::litp new-x))
  :rule-classes :type-prescription)

Theorem: bound-of-bounded-lit-fix

(defthm bound-of-bounded-lit-fix
  (b* ((?new-x (bounded-lit-fix$inline x bound)))
    (<= (satlink::lit->var new-x)
        (nfix bound)))
  :rule-classes :linear)

Theorem: bounded-lit-fix-when-bounded

(defthm bounded-lit-fix-when-bounded
  (b* ((?new-x (bounded-lit-fix$inline x bound)))
    (implies (<= (satlink::lit->var x) (nfix bound))
             (equal new-x (satlink::lit-fix x)))))

Theorem: bounded-lit-fix$inline-of-lit-fix-x

(defthm bounded-lit-fix$inline-of-lit-fix-x
  (equal (bounded-lit-fix$inline (satlink::lit-fix x)
                                 bound)
         (bounded-lit-fix$inline x bound)))

Theorem: bounded-lit-fix$inline-lit-equiv-congruence-on-x

(defthm bounded-lit-fix$inline-lit-equiv-congruence-on-x
  (implies (satlink::lit-equiv x x-equiv)
           (equal (bounded-lit-fix$inline x bound)
                  (bounded-lit-fix$inline x-equiv bound)))
  :rule-classes :congruence)

Theorem: bounded-lit-fix$inline-of-nfix-bound

(defthm bounded-lit-fix$inline-of-nfix-bound
  (equal (bounded-lit-fix$inline x (nfix bound))
         (bounded-lit-fix$inline x bound)))

Theorem: bounded-lit-fix$inline-nat-equiv-congruence-on-bound

(defthm bounded-lit-fix$inline-nat-equiv-congruence-on-bound
  (implies (acl2::nat-equiv bound bound-equiv)
           (equal (bounded-lit-fix$inline x bound)
                  (bounded-lit-fix$inline x bound-equiv)))
  :rule-classes :congruence)