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Proof step 1 from proof abs-ls-same (conclusion)

⊦ abs(i) * abs(j) < i ↔ 0 < i ∧ j = 0

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: zero-left: ⊦ 0 * i = 0;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%abs-not-neg: ⊦ ¬ abs(i) * abs(j) < 0;%ls-same: ⊦ 0 < i → (i * j < i ↔ j < 1);%abs-zero: ⊦ abs(i) ≤ 0 ↔ i = 0; from specification int-abs%lsone: ⊦ i < 1 ↔ i ≤ 0; from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%abs-16: ⊦ 0 < j → abs(j) = j; from specification int-abs