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Proof step 1 from proof to-adrs-append (conclusion)

⊦ (lax0 + lax1).to-adr(n) = lax0.to-adr(n) + lax1.to-adr(n)

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 2:
∀ lax1, n. (lax + lax1).to-adr(n) = lax.to-adr(n) + lax1.to-adr(n) ⊦ ((ladr + lax) + lax1).to-adr(n) = (ladr + lax).to-adr(n) + lax1.to-adr(n)

Rule argument

term: lax0

Additional information

Used simplifier rules: adrs-empty: ⊦ ([]).to-adr(n) = [];%to-adrs-eq: ⊦ lax0.to-adr(n) = lax1.to-adr(n) ↔ lax0 = lax1;%laddress-list freely generated by [], +;;% ⊦ [] + lax = lax; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]% ⊦ [] + ax = ax; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]