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Theorem

Theorem->formula

Get the formula field from a theorem.

Signature
(theorem->formula x) → formula
Arguments: x — Guard (theoremp x).
Returns: formula — Type (expressionp formula).

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

Definitions and Theorems

Function: theorem->formula$inline

(defun theorem->formula$inline (x)
  (declare (xargs :guard (theoremp x)))
  (declare (xargs :guard t))
  (let ((__function__ 'theorem->formula))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (expression-fix (cdr (std::da-nth 2 x))))
         :exec (cdr (std::da-nth 2 x)))))

Theorem: expressionp-of-theorem->formula

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

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

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

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

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