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Proof step 45 from proof getsetShort-theorem (previous step)

0 < j / 256, 127 < j / 256, j < 32768, 0 ≤ j, 0 ≤ ub2i(i2b(j)), ub2i(i2b(j)) < 256 ⊦ 256 * b2i(i2b(j / 256)) + ub2i(i2b(j)) = j

User applied rule insert elim lemma

And obtained the following new goals

Proof step 46:
j = i * 256 + j0 ∧ 0 ≤ j0 ∧ j0 < 256 ∧ 0 ≤ i ∧ 0 < 256, 0 < i, 127 < i, j < 32768, 0 ≤ j, 0 ≤ ub2i(i2b(j)), ub2i(i2b(j)) < 256 ⊦ 256 * b2i(i2b(i)) + ub2i(i2b(j)) = j

Rule argument

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

Additional information

Used simplifier rules: lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%lels-04: ⊦ i ≤ j → (¬ ¬ j < i ↔ false); from specification int-abs%⊦ 0 < j ∧ 0 ≤ i → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j ∧ 0 ≤ i0); (elim) Used terms: j, 256, i, j0