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Proof step 7 from proof le-add-07 (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: le-add-03 seq: ⊦ i ≤ i0 ∧ j0 ≥ 0 → i ≤ i0 + j0 subst: [i, i0, j0] → [i2 + j, i1, i]

Additional information

Used simplifier rules: le-def: ⊦ i ≤ j ↔ ¬ j < i;%ge-def: ⊦ i ≥ j ↔ ¬ i < j;%lels-03: ⊦ i < j → (j ≤ i ↔ false);%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: i2 + j, i1, i