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Sponge

Sponge->index

Get the index field from a sponge.

Signature
(sponge->index x) → index
Arguments: x — Guard (spongep x).
Returns: index — Type (natp index).

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

Definitions and Theorems

Function: sponge->index$inline

(defun sponge->index$inline (x)
  (declare (xargs :guard (spongep x)))
  (declare (xargs :guard t))
  (let ((__function__ 'sponge->index))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (nfix (cdr (std::da-nth 2 x))))
         :exec (cdr (std::da-nth 2 x)))))

Theorem: natp-of-sponge->index

(defthm natp-of-sponge->index
  (b* ((index (sponge->index$inline x)))
    (natp index))
  :rule-classes :rewrite)

Theorem: sponge->index$inline-of-sponge-fix-x

(defthm sponge->index$inline-of-sponge-fix-x
  (equal (sponge->index$inline (sponge-fix x))
         (sponge->index$inline x)))

Theorem: sponge->index$inline-sponge-equiv-congruence-on-x

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