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Proof step 12 from proof le-add-08 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: le-def: ⊦ i ≤ j ↔ ¬ j < i;%ge-def: ⊦ i ≥ j ↔ ¬ i < j; Used terms: i0, j, i1 + i2