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

⊦ ⌜n1⌝ + ⌜n⌝ + ⌜m⌝ = ⌜n2⌝ + ⌜n0⌝ + ⌜n2⌝ ↔ n1 + n + m = n2 + n0 + n2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ ⌜m + n⌝ = ⌜m⌝ + ⌜n⌝
Proof step 3:
⊦ ⌜n1⌝ + ⌜n⌝ + ⌜m⌝ = ⌜n2⌝ + ⌜n0 + n2⌝ ↔ n1 + n + m = n2 + n0 + n2

Rule argument

spec: nat-inf inst: name: add-fin seq: ⊦ ⌜m + n⌝ = ⌜m⌝ + ⌜n⌝ subst: [n, m] → [n2, n0] flags: rewrite, current

Additional information

Used terms: n2, n0