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Proof step 53 from proof rightshift-8-01 (previous step)

i % 256 = 0, i→n(j) < # int2bytes(i), i < 0, ∀ i, j0. i→n(j0) < i→n(j) → i→n(j0) < # int2bytes(i) → i >> 8 * abs(j0) = bytes2int(firstn(# int2bytes(i) - i→n(j0), int2bytes(i))) ⊦ j = 0, i / 256 >> 8 * (abs(j) - 1) = bytes2int(firstn(# int2bytes(i) - i→n(j), int2bytes(i)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 54:
⊦ i < ~256 ∧ i % 256 = 0 → int2bytes(i) = int2bytes(i / 256) + int2bytes(i % 256).last '
Proof step 55:
¬(i < ~256 ∧ i % 256 = 0), i % 256 = 0, i→n(j) < # int2bytes(i), i < 0, ∀ i, j0. i→n(j0) < i→n(j) → i→n(j0) < # int2bytes(i) → i >> 8 * abs(j0) = bytes2int(firstn(# int2bytes(i) - i→n(j0), int2bytes(i))) ⊦ j = 0, i / 256 >> 8 * (abs(j) - 1) = bytes2int(firstn(# int2bytes(i) - i→n(j), int2bytes(i)))
Proof step 78:
i < ~256 ∧ i % 256 = 0, i % 256 = 0, i→n(j) < #(int2bytes(i / 256) + int2bytes(i % 256).last '), i < 0, ∀ i, j0. i→n(j0) < i→n(j) → i→n(j0) < # int2bytes(i) → i >> 8 * abs(j0) = bytes2int(firstn(# int2bytes(i) - i→n(j0), int2bytes(i))) ⊦ j = 0, i / 256 >> 8 * (abs(j) - 1) = bytes2int(firstn(#(int2bytes(i / 256) + int2bytes(i % 256).last ') - i→n(j), int2bytes(i / 256) + int2bytes(i % 256).last '))

Rule argument

name: int2bytes-rec-neg-256 rotate: F subst: [i] → [i]

Additional information

Used terms: i