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• Vl-svstmt.lisp

Sv::svar->lhs-by-size

Given a variable and a size in bits, create an LHS that covers those bits.

Signature

(sv::svar->lhs-by-size acl2::x sv::size) → sv::lhs

Arguments

acl2::x — Guard (sv::svar-p acl2::x).

sv::size — Guard (natp sv::size).

Returns

sv::lhs — Type (sv::lhs-p sv::lhs).

Definitions and Theorems

Function: svar->lhs-by-size

(defun sv::svar->lhs-by-size (acl2::x sv::size)
 (declare (xargs :guard (and (sv::svar-p acl2::x)
                             (natp sv::size))))
 (let ((__function__ 'sv::svar->lhs-by-size))
  (declare (ignorable __function__))
  (if (mbe :logic (zp sv::size)
           :exec (eql sv::size 0))
      nil
    (list (sv::make-lhrange :w sv::size
                            :atom (sv::make-lhatom-var :name acl2::x
                                                       :rsh 0))))))

Theorem: lhs-p-of-svar->lhs-by-size

(defthm sv::lhs-p-of-svar->lhs-by-size
  (b* ((sv::lhs (sv::svar->lhs-by-size acl2::x sv::size)))
    (sv::lhs-p sv::lhs))
  :rule-classes :rewrite)

Theorem: vars-of-svar->lhs-by-size

(defthm sv::vars-of-svar->lhs-by-size
 (implies
  (not (equal sv::v (sv::svar-fix acl2::x)))
  (not
    (member
         sv::v
         (sv::lhs-vars (sv::svar->lhs-by-size acl2::x sv::size))))))

Theorem: svar->lhs-by-size-of-svar-fix-x

(defthm sv::svar->lhs-by-size-of-svar-fix-x
  (equal (sv::svar->lhs-by-size (sv::svar-fix acl2::x)
                                sv::size)
         (sv::svar->lhs-by-size acl2::x sv::size)))

Theorem: svar->lhs-by-size-svar-equiv-congruence-on-x

(defthm sv::svar->lhs-by-size-svar-equiv-congruence-on-x
  (implies (sv::svar-equiv acl2::x sv::x-equiv)
           (equal (sv::svar->lhs-by-size acl2::x sv::size)
                  (sv::svar->lhs-by-size sv::x-equiv sv::size)))
  :rule-classes :congruence)

Theorem: svar->lhs-by-size-of-nfix-size

(defthm sv::svar->lhs-by-size-of-nfix-size
  (equal (sv::svar->lhs-by-size acl2::x (nfix sv::size))
         (sv::svar->lhs-by-size acl2::x sv::size)))

Theorem: svar->lhs-by-size-nat-equiv-congruence-on-size

(defthm sv::svar->lhs-by-size-nat-equiv-congruence-on-size
  (implies (acl2::nat-equiv sv::size sv::size-equiv)
           (equal (sv::svar->lhs-by-size acl2::x sv::size)
                  (sv::svar->lhs-by-size acl2::x sv::size-equiv)))
  :rule-classes :congruence)