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State64

State64->mem

Get the mem field from a state64.

Signature
(state64->mem x) → mem
Arguments: x — Guard (state64p x).
Returns: mem — Type (memory64p mem).

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

Definitions and Theorems

Function: state64->mem$inline

(defun state64->mem$inline (x)
  (declare (xargs :guard (state64p x)))
  (declare (xargs :guard t))
  (let ((__function__ 'state64->mem))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (memory64-fix (std::da-nth 2 (cdr x))))
         :exec (std::da-nth 2 (cdr x)))))

Theorem: memory64p-of-state64->mem

(defthm memory64p-of-state64->mem
  (b* ((mem (state64->mem$inline x)))
    (memory64p mem))
  :rule-classes :rewrite)

Theorem: state64->mem$inline-of-state64-fix-x

(defthm state64->mem$inline-of-state64-fix-x
  (equal (state64->mem$inline (state64-fix x))
         (state64->mem$inline x)))

Theorem: state64->mem$inline-state64-equiv-congruence-on-x

(defthm state64->mem$inline-state64-equiv-congruence-on-x
  (implies (state64-equiv x x-equiv)
           (equal (state64->mem$inline x)
                  (state64->mem$inline x-equiv)))
  :rule-classes :congruence)