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Proof step 1 from proof noeth-ls-pos (conclusion)

⊦ ∀ i0. abs(i0) < i → 0 < abs(i0) → (abs(i0) * j < abs(i0) * j0 ↔ j < j0)

User applied rule structural induction

And closed the goal!

Rule argument

indvar: i

Additional information

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