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• Alias-norm.lisp

Lhs-replace-range

Signature

(lhs-replace-range start w repl x) → newx

Arguments

start — Guard (natp start).

w — Guard (natp w).

repl — Guard (lhs-p repl).

x — Guard (lhs-p x).

Returns

newx — Type (lhs-p newx).

Definitions and Theorems

Function: lhs-replace-range

(defun lhs-replace-range (start w repl x)
  (declare (xargs :guard (and (natp start)
                              (natp w)
                              (lhs-p repl)
                              (lhs-p x))))
  (let ((__function__ 'lhs-replace-range))
    (declare (ignorable __function__))
    (lhs-concat start x
                (lhs-concat w repl
                            (lhs-rsh (+ (lnfix start) (lnfix w))
                                     x)))))

Theorem: lhs-p-of-lhs-replace-range

(defthm lhs-p-of-lhs-replace-range
  (b* ((newx (lhs-replace-range start w repl x)))
    (lhs-p newx))
  :rule-classes :rewrite)

Theorem: lhs-replace-range-of-nfix-start

(defthm lhs-replace-range-of-nfix-start
  (equal (lhs-replace-range (nfix start)
                            w repl x)
         (lhs-replace-range start w repl x)))

Theorem: lhs-replace-range-nat-equiv-congruence-on-start

(defthm lhs-replace-range-nat-equiv-congruence-on-start
  (implies (nat-equiv start start-equiv)
           (equal (lhs-replace-range start w repl x)
                  (lhs-replace-range start-equiv w repl x)))
  :rule-classes :congruence)

Theorem: lhs-replace-range-of-nfix-w

(defthm lhs-replace-range-of-nfix-w
  (equal (lhs-replace-range start (nfix w)
                            repl x)
         (lhs-replace-range start w repl x)))

Theorem: lhs-replace-range-nat-equiv-congruence-on-w

(defthm lhs-replace-range-nat-equiv-congruence-on-w
  (implies (nat-equiv w w-equiv)
           (equal (lhs-replace-range start w repl x)
                  (lhs-replace-range start w-equiv repl x)))
  :rule-classes :congruence)

Theorem: lhs-replace-range-of-lhs-fix-repl

(defthm lhs-replace-range-of-lhs-fix-repl
  (equal (lhs-replace-range start w (lhs-fix repl)
                            x)
         (lhs-replace-range start w repl x)))

Theorem: lhs-replace-range-lhs-equiv-congruence-on-repl

(defthm lhs-replace-range-lhs-equiv-congruence-on-repl
  (implies (lhs-equiv repl repl-equiv)
           (equal (lhs-replace-range start w repl x)
                  (lhs-replace-range start w repl-equiv x)))
  :rule-classes :congruence)

Theorem: lhs-replace-range-of-lhs-fix-x

(defthm lhs-replace-range-of-lhs-fix-x
  (equal (lhs-replace-range start w repl (lhs-fix x))
         (lhs-replace-range start w repl x)))

Theorem: lhs-replace-range-lhs-equiv-congruence-on-x

(defthm lhs-replace-range-lhs-equiv-congruence-on-x
  (implies (lhs-equiv x x-equiv)
           (equal (lhs-replace-range start w repl x)
                  (lhs-replace-range start w repl x-equiv)))
  :rule-classes :congruence)

Theorem: lhs-vars-normorderedp-of-lhs-replace-range

(defthm lhs-vars-normorderedp-of-lhs-replace-range
 (implies
      (and (lhs-vars-normorderedp n m x)
           (lhs-vars-normorderedp n (+ (nfix m) (nfix start))
                                  repl))
      (lhs-vars-normorderedp n
                             m (lhs-replace-range start w repl x))))