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Proof step 3 from proof lst-02 (previous step)

i < j + i0 ⊦ j0 < j, i < j0 + i0

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 4:
i < j + 0 ⊦ i < j0 + 0, j0 < j
Proof step 7:
i < j + i1 +1, ∀ i, j, j0. i < j + i1 → j0 < j ∨ i < j0 + i1 ⊦ i < j0 + i1 +1, j0 < j
Proof step 9:
i < j + i1 -1, ∀ i, j, j0. i < j + i1 → j0 < j ∨ i < j0 + i1 ⊦ i < j0 + i1 -1, j0 < j

Rule argument

term: i0

Additional information

Used simplifier rules: int generated by 0, +1, -1;;