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Proof step 1 from proof keys-append (conclusion)

⊦ keys(fs, ax0 + ax1) = keys(fs, ax0) + keys(fs, ax1)

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 2:
∀ fs, ax1. keys(fs, ax + ax1) = keys(fs, ax) + keys(fs, ax1) ⊦ keys(fs, (adr + ax) + ax1) = keys(fs, adr + ax) + keys(fs, ax1)

Rule argument

term: ax0

Additional information

Used simplifier rules: keys-base: ⊦ keys(fs, []) = [];%address-list freely generated by [], +;;% ⊦ [] + ax = ax; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ [] + kx = kx; (s)%a: ⊦ (kx + kx0) + kx1 = kx + kx0 + kx1; from specification list[key-list-set]