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Proof step 98 from proof rightshift-8-01 (previous step)

i→n(j) < # int2bytes(i), 0 ≤ i, i ≤ 255, ∀ 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 >> 8 * (abs(j) - 1) = bytes2int(firstn(# int2bytes(i) - i→n(j), int2bytes(i))), j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 99:
127 < i, i ≤ 255 ⊦ int2bytes(i) = i2b(0) ' + i2b(i - 256) '
Proof step 100:
¬(127 < i ∧ i ≤ 255), i→n(j) < # int2bytes(i), 0 ≤ i, i ≤ 255, ∀ 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 >> 8 * (abs(j) - 1) = bytes2int(firstn(# int2bytes(i) - i→n(j), int2bytes(i))), j = 0
Proof step 103:
127 < i ∧ i ≤ 255, i→n(j) < #(i2b(0) ' + i2b(i - 256) '), 0 ≤ i, i ≤ 255, ∀ 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 >> 8 * (abs(j) - 1) = bytes2int(firstn(#(i2b(0) ' + i2b(i - 256) ') - i→n(j), i2b(0) ' + i2b(i - 256) ')), j = 0

Rule argument

name: int2bytes-le255 rotate: F subst: [i] → [i]

Additional information

Used terms: i