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Proof step 382 from proof int2bytes-rec-pos-any (previous step)

(# int2bits(j % 2 ^ (i * 8)) + (i→n(i * 8) - # int2bits(j % 2 ^ (i * 8)))) % 8 = 0, 2 ^ (i * 8) ≤ j, 0 < i, # int2bits(j % 2 ^ (i * 8)) ≤ i→n(i * 8), j % 2 ^ (i * 8) < 0 ⊦ i→n(i * 8) + 1 = # int2bits(j % 2 ^ (i * 8)), mklist(true, i→n(i * 8) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)) = [], bits2bytes(mklist(true, i→n(i * 8) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))) = fix(i→n(i) + 1, bits2bytes(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 → ¬ 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;% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ ¬ 2 ^ i < 0; Used terms: i * 8, j