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Proof step 149 from proof int2bytes-rec-neg-05 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 < j ∧ i < 0 → ¬ 0 < i % j subst: [j, i] → [2 ^ (i * 8), j] rotate: F spec: int-div inst: name: mod-grz

Additional information

Used simplifier rules: ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward)% ⊦ i + j < j ↔ i < 0;% ⊦ ¬ 2 ^ i < 0; Used terms: 2 ^ (i * 8), j