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Proof step 7 from proof le-add-05 (previous step)

0 < i2, i + i0 + i1 + i2 ≤ i3, 0 ≤ i, i1 + i2 + i0 ≤ i3 ⊦ i1 + i2 + i0 ≤ i + i3

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] → [i1 + i2 + i0, i3, i]

Additional information

Used simplifier rules: le-def: ⊦ i ≤ j ↔ ¬ j < i;%ge-def: ⊦ i ≥ j ↔ ¬ i < j;%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: i1 + i2 + i0, i3, i