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Proof step 3 from proof mod-sub-02 (previous step)

0 < i0, 2 < (i0 + 1) * j, j + 1 < (i0 + 1) * j, 1 < i, 0 < i, 0 < j, 0 ≤ i0, j < i, i0 * j ≤ i, i < (i0 + 1) * j, 0 ≤ i ⊦ i0 = i / j, i = i % j + i0 * j

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: int-div inst: name: is-div seq: ⊦ 0 ≤ i0 ∧ 0 ≤ i ∧ 0 < j ∧ i0 * j ≤ i ∧ i < (i0 + 1) * j → i0 = i / j subst: [i0, i, j] → [i0, i, j] flags: current, []

Additional information

Used simplifier rules: zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs Used terms: i0, i, j