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Proof step 3 from proof ls-pos (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
0 < i, ∀ i, j0. 0 < i → (i * j1 < i * j0 ↔ j1 < j0) ⊦ i * j1 + i < i * j0 ↔ j1 + 1 < j0

Rule argument

Additional information

Used simplifier rules: dist-rsplit: ⊦ i * (j + j0) = i * j + i * j0;%one: ⊦ 1 * i = i;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%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