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Proof step 7 from proof ls-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (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%zero-ge-add: ⊦ 0 ≤ j1 ∧ j1 < j → (0 ≤ i0 * j + j1 ↔ 0 ≤ i0); from specification int-mult