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Proof step 5 from proof div2-nle-02 (previous step)

i + j = i0 * 2 + j0, 0 < i0, i < j, i < i0, 0 < j, j0 < 2, 0 < 2, 0 ≤ i, j ≤ i0, 0 ≤ j0, 0 ≤ i0, 0 ≤ i + j ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
i + j = i0 * 2 + j0, j0 < 2, 0 < j, i < j, i < i0, 0 < i0, j ≤ i0, 0 ≤ i, 0 ≤ i + j, 0 ≤ i0, 0 ≤ j0 ⊦

Rule argument

Additional information

Used simplifier rules: forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs