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Proof step 111 from proof int2bytes-rec-pos-any (previous step)

# int2bits(j % 2 ^ (i * 8)).rest % 8 = 0, # int2bits(j % 2 ^ (i * 8)) = i→n(i * 8) + 1, i→n(i) + 1 = # bits2bytes(true ' + firstn(i→n(i * 8) % 8, int2bits(j % 2 ^ (i * 8)).rest)) + # bits2bytes(restn(i→n(i * 8) % 8, int2bits(j % 2 ^ (i * 8)).rest)), 2 ^ (i * 8) ≤ j, 0 < i, j % 2 ^ (i * 8) < 0 ⊦ (i→n(i * 8) + 1) % 8 = 0, int2bits(j % 2 ^ (i * 8)).rest = [], bits2bytes(int2bits(j % 2 ^ (i * 8)).rest) = (bits2bytes(true ' + firstn(i→n(i * 8) % 8, int2bits(j % 2 ^ (i * 8)).rest)) + bits2bytes(restn(i→n(i * 8) % 8, int2bits(j % 2 ^ (i * 8)).rest)) ).rest

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 ≤ i ∧ 0 ≤ j → ¬ j % 2 ^ i < 0 subst: [i, j] → [i * 8, j] rotate: F spec: int-pot inst: name: mod2-pos

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ ¬ 2 ^ i < 0; Used terms: i * 8, j