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Proof step 2 from proof le-add-08 (previous step)

i0 + j < i1 + i2, 0 < i, 0 ≤ i0, i0 + i1 + i2 + i ≤ j ⊦

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
⊦ i + j0 ≤ i0 ∧ j0 ≥ 0 → i ≤ i0
Proof step 4:
0 < i, i0 + j < i1 + i2, i0 + i1 + i2 + i ≤ j, 0 ≤ i0, (i1 + i2 + i) + i0 ≤ j ∧ i0 ≥ 0 → i1 + i2 + i ≤ j ⊦

Rule argument

spec: <toplevel> name: le-add-02 seq: ⊦ i + j0 ≤ i0 ∧ j0 ≥ 0 → i ≤ i0 subst: [i, j0, i0] → [i1 + i2 + i, i0, j]

Additional information

Used terms: i1 + i2 + i, i0, j