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Proof step 4 from proof le-add-07 (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Proof step 5:
⊦ i + j0 ≤ i0 ∧ j0 ≥ 0 → i ≤ i0
Proof step 6:
0 < i0, 0 ≤ i, i0 + i2 + j ≤ i1, (i2 + j) + i0 ≤ i1 ∧ i0 ≥ 0 → i2 + j ≤ i1 ⊦ j + i2 ≤ i + i1

Rule argument

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

Additional information

Used terms: i2 + j, i0, i1