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Proof step 2 from proof ls-01 (previous step)

∀ j, i0. i1 + j < i1 + i0 ↔ j < i0 ⊦ i1 +1 + j < i1 +1 + i0 ↔ j < i0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ i +1 + j = (i + j)+1
Proof step 4:
∀ j, i0. i1 + j < i1 + i0 ↔ j < i0 ⊦ (i1 + j)+1 < i1 +1 + i0 ↔ j < i0

Rule argument

spec: inst: name: add-succ-02 seq: ⊦ i +1 + j = (i + j)+1 subst: [j, i] → [j, i1] flags: rewrite, current

Additional information

Used terms: j, i1