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Proof step 21 from proof int2bytes-rec-neg-02 (previous step)

i→n(i * 8) + 1 < # int2bits(j % 2 ^ (i * 8)), j + 2 ^ (i * 8) < 0, 0 < i, ~1 ≤ j % 2 ^ (i * 8), 0 < j % 2 ^ (i * 8) ⊦ bits2bytes(int2bits(j / 2 ^ (i * 8) - 1) + fillsgn(i→n(i * 8) + 1, int2bits(j % 2 ^ (i * 8))).rest) = bits2bytes(int2bits(j / 2 ^ (i * 8) - 1)) + fix(i→n(i) + 1, int2bytes(j % 2 ^ (i * 8))).rest, # 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 < 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 = 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 ≤ j0 → i < j0; (forward)% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i + j < j ↔ i < 0;% ⊦ ¬ 2 ^ i < 0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ # [] = 0;% ⊦ bits + [] = bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ bytes = bytes + bytes0 ↔ bytes0 = [];% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1; Used terms: 2 ^ (i * 8), j