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Proof step 38 from proof rightshift-8-01 (previous step)

i < 0, i < ~256, i→n(j) ≤ # int2bytes(i / 256 - 1), ∀ 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))) ⊦ i→n(abs(j) - 1) < i→n(j), i % 256 = 0, j = 0, (i / 256 - 1) >> 8 * (abs(j) - 1) = bytes2int(firstn((# int2bytes(i / 256 - 1) - i→n(j)) + 1, int2bytes(i / 256 - 1) + i2b(i % 256) '))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 39:
i < 0, i < ~256, i→n(j) ≤ # int2bytes(i / 256 - 1), abs(j) ≤ abs(abs(j) - 1), ∀ 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))) ⊦ i % 256 = 0, j = 0, (i / 256 - 1) >> 8 * (abs(j) - 1) = bytes2int(firstn((# int2bytes(i / 256 - 1) - i→n(j)) + 1, int2bytes(i / 256 - 1) + i2b(i % 256) '))

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i→n(i) < i→n(j) ↔ abs(i) < abs(j);