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• Svstmt-if

Svstmt-if->then

Get the then field from a svstmt-if.

Signature

(svstmt-if->then x) → then

Arguments

x — Guard (svstmt-p x).

Returns

then — Type (svstmtlist-p then).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: svstmt-if->then$inline

(defun svstmt-if->then$inline (x)
  (declare (xargs :guard (svstmt-p x)))
  (declare (xargs :guard (equal (svstmt-kind x) :if)))
  (let ((__function__ 'svstmt-if->then))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (svstmt-kind x) :if) x)))
           (svstmtlist-fix (std::prod-car (std::prod-cdr (cdr x)))))
         :exec (std::prod-car (std::prod-cdr (cdr x))))))

Theorem: svstmtlist-p-of-svstmt-if->then

(defthm svstmtlist-p-of-svstmt-if->then
  (b* ((then (svstmt-if->then$inline x)))
    (svstmtlist-p then))
  :rule-classes :rewrite)

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

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

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

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

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

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