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Proof step 7 from proof pnle-pos (previous step)

j < j0, 0 < j0, 0 < i0, i0 * j0 ≤ i * j, i ≤ i0, 0 ≤ j, 0 ≤ i ⊦ i0 = 0, 0 < i ∧ 0 < j

User applied rule case distinction

And closed the goal!

Rule argument

pos: right 2

Additional information

Used simplifier rules: zero-left: ⊦ 0 * i = 0;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%zero-le: ⊦ 0 < i → (i * j ≤ 0 ↔ j ≤ 0);%zero-left: ⊦ 0 * i = 0;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%zero-le: ⊦ 0 < i → (i * j ≤ 0 ↔ j ≤ 0);% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ i ≤ j → (j ≤ i ↔ i = j); (s)% ⊦ i < j → (j ≤ i ↔ false); (as)% ⊦ i ≠ j → (i ≤ j ↔ i < j); (s)