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Proof step 2 from proof mod-nls-01 (previous step)

0 < j, 0 < i0, j < i % j, j ≤ i0, i0 < i % j, 0 < i % j, 1 < i % j ⊦

User applied rule insert elim lemma

And obtained the following new goals

Proof step 3:
⊦ 0 < j ∧ 0 ≤ i → (i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j)

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] → [i, j, i1, j0] flags: rewrite, current

Additional information

Used simplifier rules: mod-pos-not-neg: ⊦ 0 < i1 ∧ 0 < i % i1 → ¬ i < 0;%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs Used terms: i, j, i1, j0