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Proof step 24 from proof int2bytes-rec-neg-02 (previous step)

j % 2 ^ (i * 8) < ~1, j + 2 ^ (i * 8) < 0, 0 < i, j % 2 ^ (i * 8) < 0, 2 ^ (i * 8) + j % 2 ^ (i * 8) < 0 ⊦ 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, j % 2 ^ (i * 8) = 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

Proof step 25:
⊦ 0 < j → ¬ j + i % j < 0

Rule argument

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

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; Used terms: j, 2 ^ (i * 8)