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• Lhs.lisp

Lhrange-combinable-dec

Signature

(lhrange-combinable-dec x.w x.atom y) → *

Arguments

x.w — Guard (posp x.w).

x.atom — Guard (lhatom-p x.atom).

y — Guard (lhatom-p y).

Definitions and Theorems

Function: lhrange-combinable-dec

(defun lhrange-combinable-dec (x.w x.atom y)
 (declare (xargs :guard (and (posp x.w)
                             (lhatom-p x.atom)
                             (lhatom-p y))))
 (let ((__function__ 'lhrange-combinable-dec))
  (declare (ignorable __function__))
  (mbe :logic
       (equal (lhatom-fix y)
              (lhrange-nextbit (lhrange x.w x.atom)))
       :exec
       (b* ((xkind (lhatom-kind x.atom))
            (ykind (lhatom-kind y)))
         (and (eq xkind ykind)
              (or (eq xkind :z)
                  (and (equal (lhatom-var->name x.atom)
                              (lhatom-var->name y))
                       (eql (lhatom-var->rsh y)
                            (+ (lhatom-var->rsh x.atom) x.w)))))))))

Theorem: lhrange-combinable-dec-of-pos-fix-x.w

(defthm lhrange-combinable-dec-of-pos-fix-x.w
  (equal (lhrange-combinable-dec (pos-fix x.w)
                                 x.atom y)
         (lhrange-combinable-dec x.w x.atom y)))

Theorem: lhrange-combinable-dec-pos-equiv-congruence-on-x.w

(defthm lhrange-combinable-dec-pos-equiv-congruence-on-x.w
  (implies (pos-equiv x.w x.w-equiv)
           (equal (lhrange-combinable-dec x.w x.atom y)
                  (lhrange-combinable-dec x.w-equiv x.atom y)))
  :rule-classes :congruence)

Theorem: lhrange-combinable-dec-of-lhatom-fix-x.atom

(defthm lhrange-combinable-dec-of-lhatom-fix-x.atom
  (equal (lhrange-combinable-dec x.w (lhatom-fix x.atom)
                                 y)
         (lhrange-combinable-dec x.w x.atom y)))

Theorem: lhrange-combinable-dec-lhatom-equiv-congruence-on-x.atom

(defthm lhrange-combinable-dec-lhatom-equiv-congruence-on-x.atom
  (implies (lhatom-equiv x.atom x.atom-equiv)
           (equal (lhrange-combinable-dec x.w x.atom y)
                  (lhrange-combinable-dec x.w x.atom-equiv y)))
  :rule-classes :congruence)

Theorem: lhrange-combinable-dec-of-lhatom-fix-y

(defthm lhrange-combinable-dec-of-lhatom-fix-y
  (equal (lhrange-combinable-dec x.w x.atom (lhatom-fix y))
         (lhrange-combinable-dec x.w x.atom y)))

Theorem: lhrange-combinable-dec-lhatom-equiv-congruence-on-y

(defthm lhrange-combinable-dec-lhatom-equiv-congruence-on-y
  (implies (lhatom-equiv y y-equiv)
           (equal (lhrange-combinable-dec x.w x.atom y)
                  (lhrange-combinable-dec x.w x.atom y-equiv)))
  :rule-classes :congruence)