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Proof step 1 from proof add-succ-02 (conclusion)

⊦ i +1 + j = (i + j)+1

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 2:
∀ i. i +1 + j0 = (i + j0)+1 ⊦ i +1 + j0 +1 = (i + j0 +1)+1
Proof step 4:
∀ i. i +1 + j0 = (i + j0)+1 ⊦ i +1 + j0 -1 = (i + j0 -1)+1

Rule argument

term: j

Additional information

Used simplifier rules: add-zero: ⊦ i + 0 = i;%add-a: ⊦ i + j + i0 = (i + j) + i0;%int generated by 0, +1, -1;;%succ-in: ⊦ i +1 = j +1 ↔ i = j; from specification int-basic1