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Proof step 1 from proof ls-natinf-to-nat-1-3 (conclusion)

⊦ ⌜n1⌝ < ⌜n0⌝ + ⌜n⌝ + ⌜m⌝ ↔ n1 < n0 + n + m

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ ⌜m + n⌝ = ⌜m⌝ + ⌜n⌝
Proof step 3:
⊦ ⌜n1⌝ < ⌜n0⌝ + ⌜n + m⌝ ↔ n1 < n0 + n + m

Rule argument

spec: nat-inf inst: name: add-fin seq: ⊦ ⌜m + n⌝ = ⌜m⌝ + ⌜n⌝ subst: [n, m] → [m, n] flags: rewrite, current

Additional information

Used terms: m, n