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Proof step 8 from proof zero-04 (previous step)

j / i0 < i0, j / i0 < j0, j / i0 < (i1 * i0 + j0) + j, j / i0 < i1, j / i0 < 0, i1 + j / i0 < i0, i1 + j / i0 < i1 * i0 + j0, 0 ≤ j0, j0 < i0, 0 ≤ (i1 * i0 + j0) + j, i1 + j / i0 < 0, (i1 + j / i0) + 1 < i0, 0 ≤ i1, 0 < i0, i1 + j / i0 < j0, i1 + j / i0 < (i1 * i0 + j0) + j, j / i0 + 1 < i0 ⊦

User applied rule insert elim lemma

And obtained the following new goals

Rule argument

spec: int-div inst: name: div-elim-pos seq: ⊦ 0 < j ∧ 0 ≤ i → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j) subst: [i, j, i0, j0] → [j, i0, i, j1] flags: rewrite, current

Additional information

Used simplifier rules: modzero-03: ⊦ i < 0 ∧ j0 < j ∧ 0 < j → ¬ 0 ≤ i * j + j0; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: j, i0, i, j1