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Proof step 79 from proof rightshift-8-01 (previous step)

i % 256 = 0, i < 0, i < ~256, i→n(j) ≤ # int2bytes(i / 256), ∀ 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) - i→n(j)) + 1, int2bytes(i / 256) + i2b(0) '))

User applied rule apply induction

And obtained the following new goals

Proof step 80:
i % 256 = 0, i < 0, i < ~256, i→n(j) ≤ # int2bytes(i / 256), ∀ 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), j = 0, i / 256 >> 8 * (abs(j) - 1) = bytes2int(firstn((# int2bytes(i / 256) - i→n(j)) + 1, int2bytes(i / 256) + i2b(0) '))
Proof step 83:
i % 256 = 0, i < 0, i < ~256, i→n(j) ≤ # int2bytes(i / 256), ∀ 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) < # int2bytes(i / 256), j = 0, i / 256 >> 8 * (abs(j) - 1) = bytes2int(firstn((# int2bytes(i / 256) - i→n(j)) + 1, int2bytes(i / 256) + i2b(0) '))
Proof step 86:
i / 256 >> 8 * abs(abs(j) - 1) = bytes2int(firstn(# int2bytes(i / 256) - i→n(abs(j) - 1), int2bytes(i / 256))), i % 256 = 0, i < 0, i < ~256, i→n(j) ≤ # int2bytes(i / 256), ∀ 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) - i→n(j)) + 1, int2bytes(i / 256) + i2b(0) '))

Rule argument

subst: [i, j0] → [i / 256, abs(j) - 1]

Additional information

Used terms: i / 256, abs(j) - 1