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Proof step 25 from proof abs-ls-same-01 (previous step)

j < 0, i < 0, i + i * j ≤ 0 ⊦ i = 0, j = ~1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ i * j + i = i * (j + 1)

Rule argument

spec: <toplevel> name: succ-rmerge seq: ⊦ i * j + i = i * (j + 1) subst: [j, i] → [j, i] flags: <all paths>

Additional information

Used simplifier rules: zero-le-01: ⊦ i < 0 → (i * j ≤ 0 ↔ 0 ≤ j);%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0; (s)% ⊦ i < 0 → (~1 ≤ i ↔ i = ~1); (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: j, i