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Proof step 7 from proof bib-neg-low (previous step)

i < ~128, i % 256 < ~128, i < 0, i % 256 < 0, i < ~128 ⊦ b2i(i2b(bits2int(lastn(8, int2bits(i))))) = i % 256 + 256

User applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
i = i0 * 256 + j ∧ j ≤ 0 ∧ abs(j) < 256 ∧ i0 ≤ 0 ∧ 0 < 256, i < ~128, j < ~128, i < 0, j < 0, i < ~128 ⊦ b2i(i2b(bits2int(lastn(8, int2bits(i))))) = j + 256

Rule argument

seq: ⊦ 0 < j ∧ i < 0 → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ j0 ≤ 0 ∧ abs(j0) < j ∧ i0 ≤ 0) subst: [i, j, i0, j0] → [i, 256, i0, j] rotate: T spec: int-div inst: name: div-elim-negpos

Additional information

Used simplifier rules: ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);%⊦ 0 < j ∧ i < 0 → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ j0 ≤ 0 ∧ abs(j0) < j ∧ i0 ≤ 0); (elim) Used terms: i, 256, i0, j