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Proof step 21 from proof rightshift-8-01 (previous step)

i→n(j) < # int2bytes(i), i < 0, ~256 ≤ i, ∀ 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 - 1) >> 8 * (abs(j) - 1) = bytes2int(firstn(# int2bytes(i) - i→n(j), int2bytes(i))), i % 256 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ ~256 < i ∧ i < ~128 → int2bytes(i) = i2b(~1) ' + i2b(i) '
Proof step 23:
¬(~256 < i ∧ i < ~128), i→n(j) < # int2bytes(i), i < 0, ~256 ≤ i, ∀ 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 - 1) >> 8 * (abs(j) - 1) = bytes2int(firstn(# int2bytes(i) - i→n(j), int2bytes(i))), i % 256 = 0
Proof step 26:
~256 < i ∧ i < ~128, i→n(j) < #(i2b(~1) ' + i2b(i) '), i < 0, ~256 ≤ i, ∀ 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 - 1) >> 8 * (abs(j) - 1) = bytes2int(firstn(#(i2b(~1) ' + i2b(i) ') - i→n(j), i2b(~1) ' + i2b(i) ')), i % 256 = 0

Rule argument

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

Additional information

Used terms: i