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

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

User applied rule case distinction

And closed the goal!

Rule argument

pos: right 1

Additional information

Used simplifier rules: zero-left: ⊦ 0 * i = 0;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%zero-ls-02: ⊦ 0 ≤ i → (i * j < 0 ↔ j < 0 ∧ i ≠ 0);%zero-left: ⊦ 0 * i = 0;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%zero-ls-02: ⊦ 0 ≤ i → (i * j < 0 ↔ j < 0 ∧ i ≠ 0);% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ i ≤ j → (j ≤ i ↔ i = j); (s)% ⊦ i ≤ j → ¬ j < i; (s)