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• Module

Module->aliaspairs

Get the aliaspairs field from a module.

Signature

(module->aliaspairs x) → aliaspairs

Arguments

x — Guard (module-p x).

Returns

aliaspairs — Type (lhspairs-p aliaspairs).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: module->aliaspairs$inline

(defun module->aliaspairs$inline (x)
  (declare (xargs :guard (module-p x)))
  (declare (xargs :guard t))
  (let ((__function__ 'module->aliaspairs))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (lhspairs-fix (cdr (std::da-nth 5 x))))
         :exec (cdr (std::da-nth 5 x)))))

Theorem: lhspairs-p-of-module->aliaspairs

(defthm lhspairs-p-of-module->aliaspairs
  (b* ((aliaspairs (module->aliaspairs$inline x)))
    (lhspairs-p aliaspairs))
  :rule-classes :rewrite)

Theorem: module->aliaspairs$inline-of-module-fix-x

(defthm module->aliaspairs$inline-of-module-fix-x
  (equal (module->aliaspairs$inline (module-fix x))
         (module->aliaspairs$inline x)))

Theorem: module->aliaspairs$inline-module-equiv-congruence-on-x

(defthm module->aliaspairs$inline-module-equiv-congruence-on-x
  (implies (module-equiv x x-equiv)
           (equal (module->aliaspairs$inline x)
                  (module->aliaspairs$inline x-equiv)))
  :rule-classes :congruence)