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Path-add-namespace

Signature

(path-add-namespace namespace x) → *

Arguments

namespace — Guard (name-p namespace).

x — Guard (path-p x).

Definitions and Theorems

Function: path-add-namespace$inline

(defun path-add-namespace$inline (namespace x)
       (declare (xargs :guard (and (name-p namespace) (path-p x))))
       (let ((__function__ 'path-add-namespace))
            (declare (ignorable __function__))
            (make-path-scope :namespace namespace
                             :subpath x)))

Theorem: path-add-namespace$inline-of-name-fix-namespace

(defthm path-add-namespace$inline-of-name-fix-namespace
        (equal (path-add-namespace$inline (name-fix namespace)
                                          x)
               (path-add-namespace$inline namespace x)))

Theorem: path-add-namespace$inline-name-equiv-congruence-on-namespace

(defthm
     path-add-namespace$inline-name-equiv-congruence-on-namespace
     (implies (name-equiv namespace namespace-equiv)
              (equal (path-add-namespace$inline namespace x)
                     (path-add-namespace$inline namespace-equiv x)))
     :rule-classes :congruence)

Theorem: path-add-namespace$inline-of-path-fix-x

(defthm path-add-namespace$inline-of-path-fix-x
        (equal (path-add-namespace$inline namespace (path-fix x))
               (path-add-namespace$inline namespace x)))

Theorem: path-add-namespace$inline-path-equiv-congruence-on-x

(defthm
     path-add-namespace$inline-path-equiv-congruence-on-x
     (implies (path-equiv x x-equiv)
              (equal (path-add-namespace$inline namespace x)
                     (path-add-namespace$inline namespace x-equiv)))
     :rule-classes :congruence)