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Proof step 19 from proof div2-nls (previous step)

i + j = i0 * 2 + j0, j0 < 2, j < i0, i ≤ j, 0 ≤ j0, 0 ≤ i0, 0 ≤ i + j, i < i0 ⊦ j0 = 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%zero-ge: ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j); from specification int-mult%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-zero-rev: ⊦ 0 + i = i; from specification int-basic2%lstwo: ⊦ i ≠ 1 ∧ 0 ≤ i → (i < 2 ↔ i = 0); from specification int-abs