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Proof step 2 from proof zero-gr-add (previous step)

0 < j ⊦ 0 < i * j + j ↔ 0 ≤ i

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: succ-lsplit seq: ⊦ (i + 1) * j = i * j + j subst: [j, i] → [j, i] flags: rewrite, current

Additional information

Used simplifier rules: zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j);%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%numls-02: ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; from specification int-abs%mone-06: ⊦ ~1 < i ↔ 0 ≤ i; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs Used terms: j, i