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Comm-if

Comm-if->then

Get the then field from a comm-if.

Signature
(comm-if->then x) → then
Arguments: x — Guard (commp x).
Returns: then — Type (comm-listp then).

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

Definitions and Theorems

Function: comm-if->then$inline

(defun comm-if->then$inline (x)
  (declare (xargs :guard (commp x)))
  (declare (xargs :guard (equal (comm-kind x) :if)))
  (let ((__function__ 'comm-if->then))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (comm-kind x) :if) x)))
           (comm-list-fix (std::da-nth 1 (cdr x))))
         :exec (std::da-nth 1 (cdr x)))))

Theorem: comm-listp-of-comm-if->then

(defthm comm-listp-of-comm-if->then
  (b* ((then (comm-if->then$inline x)))
    (comm-listp then))
  :rule-classes :rewrite)

Theorem: comm-if->then$inline-of-comm-fix-x

(defthm comm-if->then$inline-of-comm-fix-x
  (equal (comm-if->then$inline (comm-fix x))
         (comm-if->then$inline x)))

Theorem: comm-if->then$inline-comm-equiv-congruence-on-x

(defthm comm-if->then$inline-comm-equiv-congruence-on-x
  (implies (comm-equiv x x-equiv)
           (equal (comm-if->then$inline x)
                  (comm-if->then$inline x-equiv)))
  :rule-classes :congruence)

Theorem: comm-if->then-when-wrong-kind

(defthm comm-if->then-when-wrong-kind
  (implies (not (equal (comm-kind x) :if))
           (equal (comm-if->then x)
                  (comm-list-fix nil))))