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Branch

Branch->action

Get the action field from a branch.

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

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

Definitions and Theorems

Function: branch->action$inline

(defun branch->action$inline (x)
  (declare (xargs :guard (branchp x)))
  (declare (xargs :guard t))
  (let ((__function__ 'branch->action))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (expression-fix (cdr (std::da-nth 1 x))))
         :exec (cdr (std::da-nth 1 x)))))

Theorem: expressionp-of-branch->action

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

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

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

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

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