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Proof step 5 from proof keys-firstn (previous step)

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

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 6:
∀ fs, ax1. firstn(# ax, keys(fs, ax) + keys(fs, ax1)) = keys(fs, ax) ⊦ firstn(#(adr + ax), keys(fs, adr + ax) + keys(fs, ax1)) = keys(fs, adr + ax)

Rule argument

term: ax0

Additional information

Used simplifier rules: keys-base: ⊦ keys(fs, []) = [];%address-list freely generated by [], +;;% ⊦ # [] = 0; (s)% ⊦ [] + kx = kx; (s)%a: ⊦ (kx + kx0) + kx1 = kx + kx0 + kx1; from specification list[key-list-set]% ⊦ firstn(0, kx) = []; (s)