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Proof step 5 from proof zero-gr (previous step)

0 < i * j, 0 < i ⊦ 0 < j

User applied rule apply lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: noeth-zero-ls seq: abs(i) < i0, 0 < abs(i), 0 < j ⊦ 0 < abs(i) * j subst: [i, i0, j] → [i, i + 1, ~ j]

Additional information

Used simplifier rules: Mult-zero: ⊦ i * 0 = 0;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%minus-left: ⊦ ~ i * j = ~(i * j);%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;% ⊦ 0 < j → abs(j) = j; (s)% ⊦ 0 < ~ i ↔ i < 0; (s)% ⊦ i < j → ¬ j < i; (s)% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ i < j + 1 ↔ i ≤ j; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ i ≤ j ↔ ¬ j < i; (ss)% ⊦ ¬ i < i; (s)% ⊦ i ≤ j → (j ≤ i ↔ i = j); (s)%lf-03: ⊦ i < j ∧ i = i0 → i0 < j; (forward) from specification int-basic1 Used terms: i, i + 1, ~ j