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Expr-cond

Expr-cond->then

Get the then field from a expr-cond.

Signature
(expr-cond->then x) → then
Arguments: x — Guard (exprp x).
Returns: then — Type (expr-optionp then).

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

Definitions and Theorems

Function: expr-cond->then$inline

(defun expr-cond->then$inline (x)
  (declare (xargs :guard (exprp x)))
  (declare (xargs :guard (equal (expr-kind x) :cond)))
  (let ((__function__ 'expr-cond->then))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (expr-kind x) :cond) x)))
           (expr-option-fix (std::da-nth 1 (cdr x))))
         :exec (std::da-nth 1 (cdr x)))))

Theorem: expr-optionp-of-expr-cond->then

(defthm expr-optionp-of-expr-cond->then
  (b* ((then (expr-cond->then$inline x)))
    (expr-optionp then))
  :rule-classes :rewrite)

Theorem: expr-cond->then$inline-of-expr-fix-x

(defthm expr-cond->then$inline-of-expr-fix-x
  (equal (expr-cond->then$inline (expr-fix x))
         (expr-cond->then$inline x)))

Theorem: expr-cond->then$inline-expr-equiv-congruence-on-x

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

Theorem: expr-cond->then-when-wrong-kind

(defthm expr-cond->then-when-wrong-kind
  (implies (not (equal (expr-kind x) :cond))
           (equal (expr-cond->then x)
                  (expr-option-fix nil))))