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Theorem

Theorem->variables

Get the variables field from a theorem.

Signature
(theorem->variables x) → variables
Arguments: x — Guard (theoremp x).
Returns: variables — Type (typed-variable-listp variables).

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

Definitions and Theorems

Function: theorem->variables$inline

(defun theorem->variables$inline (x)
  (declare (xargs :guard (theoremp x)))
  (declare (xargs :guard t))
  (let ((__function__ 'theorem->variables))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (typed-variable-list-fix (cdr (std::da-nth 1 x))))
         :exec (cdr (std::da-nth 1 x)))))

Theorem: typed-variable-listp-of-theorem->variables

(defthm typed-variable-listp-of-theorem->variables
  (b* ((variables (theorem->variables$inline x)))
    (typed-variable-listp variables))
  :rule-classes :rewrite)

Theorem: theorem->variables$inline-of-theorem-fix-x

(defthm theorem->variables$inline-of-theorem-fix-x
  (equal (theorem->variables$inline (theorem-fix x))
         (theorem->variables$inline x)))

Theorem: theorem->variables$inline-theorem-equiv-congruence-on-x

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