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Proof step 2 from proof pnls-posneg (previous step)

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

User applied rule cut formula

And closed the goal!

Rule argument

fma: i * j ≤ i0 * j

Additional information

Used simplifier rules: ls-forward: ⊦ i * j < i * j0 → i ≠ 0;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%ls-pos: ⊦ 0 < i → (i * j < i * j0 ↔ j < j0);%ls-forward: ⊦ i * j < i * j0 → i ≠ 0;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%ls-neg: ⊦ i < 0 → (i * j < i * j0 ↔ j0 < j);%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs Used formulas: i * j ≤ i0 * j