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Branch

Branch->test

Get the test field from a branch.

Signature
(branch->test x) → test
Arguments: x — Guard (branchp x).
Returns: test — Type (expressionp test).

This is an ordinary field accessor created by fty::defprod.

Definitions and Theorems

Function: branch->test$inline

(defun branch->test$inline (x)
  (declare (xargs :guard (branchp x)))
  (declare (xargs :guard t))
  (let ((__function__ 'branch->test))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (expression-fix (cdr (std::da-nth 0 x))))
         :exec (cdr (std::da-nth 0 x)))))

Theorem: expressionp-of-branch->test

(defthm expressionp-of-branch->test
  (b* ((test (branch->test$inline x)))
    (expressionp test))
  :rule-classes :rewrite)

Theorem: branch->test$inline-of-branch-fix-x

(defthm branch->test$inline-of-branch-fix-x
  (equal (branch->test$inline (branch-fix x))
         (branch->test$inline x)))

Theorem: branch->test$inline-branch-equiv-congruence-on-x

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