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• Bfr

Fgl-object-bindings-bfrs-ok

Signature

(fgl-object-bindings-bfrs-ok x &optional (bfrstate 'bfrstate)) 
  → 
*

Arguments

x — Guard (fgl-object-bindings-p x).

bfrstate — Guard (bfrstate-p bfrstate).

Definitions and Theorems

Function: fgl-object-bindings-bfrs-ok-fn

(defun fgl-object-bindings-bfrs-ok-fn (x bfrstate)
  (declare (xargs :guard (and (fgl-object-bindings-p x)
                              (bfrstate-p bfrstate))))
  (let ((__function__ 'fgl-object-bindings-bfrs-ok))
    (declare (ignorable __function__))
    (if (atom x)
        t
      (and (or (not (mbt (and (consp (car x))
                              (pseudo-var-p (caar x)))))
               (fgl-object-bfrs-ok (cdar x)))
           (fgl-object-bindings-bfrs-ok (cdr x))))))

Theorem: fgl-object-bindings-bfrs-ok-fn-of-fgl-object-bindings-fix-x

(defthm fgl-object-bindings-bfrs-ok-fn-of-fgl-object-bindings-fix-x
  (equal (fgl-object-bindings-bfrs-ok-fn (fgl-object-bindings-fix x)
                                         bfrstate)
         (fgl-object-bindings-bfrs-ok-fn x bfrstate)))

Theorem: fgl-object-bindings-bfrs-ok-fn-fgl-object-bindings-equiv-congruence-on-x

(defthm
 fgl-object-bindings-bfrs-ok-fn-fgl-object-bindings-equiv-congruence-on-x
 (implies (fgl-object-bindings-equiv x x-equiv)
          (equal (fgl-object-bindings-bfrs-ok-fn x bfrstate)
                 (fgl-object-bindings-bfrs-ok-fn x-equiv bfrstate)))
 :rule-classes :congruence)

Theorem: fgl-object-bindings-bfrs-ok-fn-of-bfrstate-fix-bfrstate

(defthm fgl-object-bindings-bfrs-ok-fn-of-bfrstate-fix-bfrstate
  (equal (fgl-object-bindings-bfrs-ok-fn x (bfrstate-fix bfrstate))
         (fgl-object-bindings-bfrs-ok-fn x bfrstate)))

Theorem: fgl-object-bindings-bfrs-ok-fn-bfrstate-equiv-congruence-on-bfrstate

(defthm
 fgl-object-bindings-bfrs-ok-fn-bfrstate-equiv-congruence-on-bfrstate
 (implies (bfrstate-equiv bfrstate bfrstate-equiv)
          (equal (fgl-object-bindings-bfrs-ok-fn x bfrstate)
                 (fgl-object-bindings-bfrs-ok-fn x bfrstate-equiv)))
 :rule-classes :congruence)