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Proof step 8 from proof ls-01 (previous step)

i = i2 * j0 + j2, j1 < i0, i1 < i2, 0 < j0, 0 < i0, j1 < j0, 0 < i2, j2 < j0, 0 ≤ i, 0 ≤ j1, i ≤ i1 * i0 + j1, i0 ≤ j0, 0 ≤ i1, 0 ≤ j2 ⊦ i0 = 0, j0 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
j2 < j0, j1 < j0, 0 < i0, 0 < j0, i1 < i2, j1 < i0, 0 < i2, 0 ≤ i1, i0 ≤ j0, i2 * j0 + j2 ≤ i1 * i0 + j1, 0 ≤ j1, 0 ≤ j2, 0 ≤ i2 ⊦ i0 = 0, j0 = 0

Rule argument

Additional information

Used simplifier rules: forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%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%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult% ⊦ 0 ≤ j1 ∧ j1 < j → (0 ≤ i0 * j + j1 ↔ 0 ≤ i0); (s)