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• Path-scope

Path-scope->subpath

Get the subpath field from a path-scope.

Signature

(path-scope->subpath x) → subpath

Arguments

x — Guard (path-p x).

Returns

subpath — Type (path-p subpath).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: path-scope->subpath$inline

(defun path-scope->subpath$inline (x)
  (declare (xargs :guard (path-p x)))
  (declare (xargs :guard (equal (path-kind x) :scope)))
  (let ((__function__ 'path-scope->subpath))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (path-kind x) :scope) x)))
           (path-fix (cdr x)))
         :exec (cdr x))))

Theorem: path-p-of-path-scope->subpath

(defthm path-p-of-path-scope->subpath
  (b* ((subpath (path-scope->subpath$inline x)))
    (path-p subpath))
  :rule-classes :rewrite)

Theorem: path-scope->subpath$inline-of-path-fix-x

(defthm path-scope->subpath$inline-of-path-fix-x
  (equal (path-scope->subpath$inline (path-fix x))
         (path-scope->subpath$inline x)))

Theorem: path-scope->subpath$inline-path-equiv-congruence-on-x

(defthm path-scope->subpath$inline-path-equiv-congruence-on-x
  (implies (path-equiv x x-equiv)
           (equal (path-scope->subpath$inline x)
                  (path-scope->subpath$inline x-equiv)))
  :rule-classes :congruence)

Theorem: path-scope->subpath-when-wrong-kind

(defthm path-scope->subpath-when-wrong-kind
  (implies (not (equal (path-kind x) :scope))
           (equal (path-scope->subpath x)
                  (path-fix nil))))