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Proof step 5 from proof sub-less (previous step)

0 < i, j < i, 0 < j, 0 < i1, 1 < i ⊦ j < i + i1

User applied rule insert lemma

And obtained the following new goals

Proof step 6:
⊦ j > 0 → i < i + j
Proof step 7:
1 < i, 0 < i1, 0 < j, j < i, 0 < i, i > 0 → i1 < i1 + i ⊦ j < i + i1

Rule argument

spec: <toplevel> name: int-add-same-pos seq: ⊦ j > 0 → i < i + j subst: [j, i] → [i, i1]

Additional information

Used terms: i, i1