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Proof step 10 from proof ls-pos (previous step)

j1 = i0 +1, 0 < i, ∀ i, j0. 0 < i → (i * j1 < i * j0 ↔ j1 < j0) ⊦ i * i0 < i * j0 ↔ i0 < j0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
0 < i, ∀ i1, j. 0 < i1 → (i0 * i1 + i1 < i1 * j ↔ i0 + 1 < j) ⊦ i * i0 < i * j0 ↔ i0 < j0

Rule argument

Additional information

Used simplifier rules: dist-lsplit: ⊦ (i + i0) * j = i * j + i0 * j;%one: ⊦ 1 * i = i;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%forward-le-05: ⊦ 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%succ-01: ⊦ i +1 = i + 1; from specification int-basic2