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Proof step 2 from proof dist-rsplit (previous step)

∀ i, j. i * (j + j1) = i * j + i * j1 ⊦ i * (j + j1 +1) = i * j + i * j1 +1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
∀ i, j. i * (j + j1) = i * j + i * j1 ⊦ i * (j + j1) = i * j + i * j1

Rule argument

Additional information

Used simplifier rules: succ-rsplit: ⊦ i * (j + 1) = i * j + i;% ⊦ i + j = i + i0 ↔ j = i0; (s)%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2% ⊦ i +1 = i + 1; (s)