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Proof step 1 from proof add-a (conclusion)

⊦ i + j + i0 = (i + j) + i0

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 2:
∀ i, j. i + j + i1 = (i + j) + i1 ⊦ i + j + i1 +1 = (i + j) + i1 +1
Proof step 5:
∀ i, j. i + j + i1 = (i + j) + i1 ⊦ i + j + i1 -1 = (i + j) + i1 -1

Rule argument

term: i0

Additional information

Used simplifier rules: add-zero: ⊦ i + 0 = i;%int generated by 0, +1, -1;;