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Proof step 14 from proof div-est-num (previous step)

j1 < j, i1 < j0, i ≤ i1 * j + j1, j0 ≤ i / j, 0 < j, 0 ≤ j1, 0 ≤ i1, i1 < i / j, 0 < j0, 0 < i / j ⊦

User applied rule insert elim lemma

And obtained the following new goals

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] → [i, j, i0, j2] flags: rewrite, current

Additional information

Used simplifier rules: div-zero-ngr: ⊦ i < 0 ∧ 0 < j → ¬ 0 < i / j;%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs Used terms: i, j, i0, j2