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Proof step 20 from proof int2bytes-rec-pos-any (previous step)

i→n(i * 8) + 1 < # int2bits(j % 2 ^ (i * 8)), i→n(i * 8) < 8 * i→n(i), 0 < j, 2 ^ (i * 8) ≤ j, # int2bits(j % 2 ^ (i * 8)) ≤ 1 + 8 * i→n(i), 0 < i ⊦ bits2bytes(int2bits(j / 2 ^ (i * 8)) + fillsgn(1 + 8 * i→n(i), int2bits(j % 2 ^ (i * 8))).rest) = int2bytes(j / 2 ^ (i * 8)) + fix(i→n(i) + 1, int2bytes(j % 2 ^ (i * 8))).rest, i = 0, # fillsgn(i→n(i * 8) + 1, int2bits(j % 2 ^ (i * 8))).rest % 8 = 0 ∧ fillsgn(i→n(i * 8) + 1, int2bits(j % 2 ^ (i * 8))).rest ≠ []

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: 0 ≤ i, 0 ≤ j ⊦ i→n(i) * i→n(j) = i→n(i * j) subst: [j, i] → [8, i] rotate: T spec: intnat inst: name: i2np

Additional information

Used simplifier rules: ⊦ i < j → ¬ j < i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i * j = j * i;% ⊦ m * n = n * m;% ⊦ m + n = n + m;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ m ≤ n → (n < m ↔ false); Used terms: 8, i