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Proof step 2 from proof ls-pos (previous step)

0 < i ⊦ i * j < i * j0 ↔ j < j0

User applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ i, j0. 0 < i → (i * j1 < i * j0 ↔ j1 < j0), 0 < i ⊦ i * j1 +1 < i * j0 ↔ j1 +1 < j0
Proof step 8:
∀ i, j0. 0 < i → (i * j1 < i * j0 ↔ j1 < j0), 0 < i ⊦ i * j1 -1 < i * j0 ↔ j1 -1 < j0

Rule argument

indvar: j

Additional information

Used simplifier rules: Mult-zero: ⊦ i * 0 = 0;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j);%int generated by 0, +1, -1;;