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• Bfr

Aignet-lit->bfr

Signature

(aignet-lit->bfr x &optional (bfrstate 'bfrstate)) → bfr

Arguments

x — Guard (satlink::litp x).

bfrstate — Guard (bfrstate-p bfrstate).

Returns

bfr — Type (implies (bfrstate-mode-is :aignet) (bfr-p bfr)).

Definitions and Theorems

Function: aignet-lit->bfr-fn

(defun aignet-lit->bfr-fn (x bfrstate)
  (declare (xargs :guard (and (satlink::litp x)
                              (bfrstate-p bfrstate))))
  (declare (xargs :guard (and (bfrstate-mode-is :aignet)
                              (<= (satlink::lit->var x)
                                  (bfrstate->bound bfrstate)))))
  (let ((__function__ 'aignet-lit->bfr))
    (declare (ignorable __function__))
    (b* ((x (bounded-lit-fix x (bfrstate->bound bfrstate))))
      (case x (0 nil) (1 t) (t x)))))

Theorem: return-type-of-aignet-lit->bfr

(defthm return-type-of-aignet-lit->bfr
  (b* ((bfr (aignet-lit->bfr-fn x bfrstate)))
    (implies (bfrstate-mode-is :aignet)
             (bfr-p bfr)))
  :rule-classes :rewrite)

Theorem: aignet-lit->bfr-of-consts

(defthm aignet-lit->bfr-of-consts
  (and (equal (aignet-lit->bfr 0) nil)
       (equal (aignet-lit->bfr 1) t)))

Theorem: aignet-lit->bfr-fn-of-lit-fix-x

(defthm aignet-lit->bfr-fn-of-lit-fix-x
  (equal (aignet-lit->bfr-fn (satlink::lit-fix x)
                             bfrstate)
         (aignet-lit->bfr-fn x bfrstate)))

Theorem: aignet-lit->bfr-fn-lit-equiv-congruence-on-x

(defthm aignet-lit->bfr-fn-lit-equiv-congruence-on-x
  (implies (satlink::lit-equiv x x-equiv)
           (equal (aignet-lit->bfr-fn x bfrstate)
                  (aignet-lit->bfr-fn x-equiv bfrstate)))
  :rule-classes :congruence)

Theorem: aignet-lit->bfr-fn-of-bfrstate-fix-bfrstate

(defthm aignet-lit->bfr-fn-of-bfrstate-fix-bfrstate
  (equal (aignet-lit->bfr-fn x (bfrstate-fix bfrstate))
         (aignet-lit->bfr-fn x bfrstate)))

Theorem: aignet-lit->bfr-fn-bfrstate-equiv-congruence-on-bfrstate

(defthm aignet-lit->bfr-fn-bfrstate-equiv-congruence-on-bfrstate
  (implies (bfrstate-equiv bfrstate bfrstate-equiv)
           (equal (aignet-lit->bfr-fn x bfrstate)
                  (aignet-lit->bfr-fn x bfrstate-equiv)))
  :rule-classes :congruence)