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Proof step 24 from proof getsetShort-theorem (previous step)

i ≤ ~256, ub2i(i2b(i + 255)) < 256, ~33023 ≤ i, i < 0, 0 ≤ ub2i(i2b(i + 255)), i / 256 < ~128 ⊦ 256 * b2i(i2b(i / 256)) + ub2i(i2b(i + 255)) = i + 255

User applied rule insert elim lemma

And obtained the following new goals

Proof step 25:
i = i0 * 256 + j ∧ j ≤ 0 ∧ abs(j) < 256 ∧ i0 ≤ 0 ∧ 0 < 256, i ≤ ~256, ub2i(i2b(i + 255)) < 256, ~33023 ≤ i, i < 0, 0 ≤ ub2i(i2b(i + 255)), i0 < ~128 ⊦ 256 * b2i(i2b(i0)) + ub2i(i2b(i + 255)) = i + 255

Rule argument

spec: int-div inst: name: div-elim-negpos 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] flags: []

Additional information

Used simplifier rules: lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs%⊦ 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