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Proof step 3 from proof mod-nls-01 (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
⊦ 0 < j ∧ 0 ≤ i → (i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j)

Rule argument

spec: <toplevel> 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: <rotated> <all paths>

Additional information

Used simplifier rules: mod-pos-not-neg: ⊦ 0 < i1 ∧ 0 < i % i1 → ¬ i < 0;% ⊦ i < j → ¬ j < i; (s)% ⊦ i ≤ j ↔ ¬ j < i; (ss) Used terms: i, j, i1, j0