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Proof step 3 from proof new-write (previous step)

new(ax, fs) ⊦ new(ax, fs[adr, nd]) ↔ ¬ adr ∈ ax

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 4:
new(adr0 + ax0, fs), ∀ fs, adr, nd. new(ax0, fs) → (new(ax0, fs[adr, nd]) ↔ ¬ adr ∈ ax0) ⊦ new(adr0 + ax0, fs[adr, nd]) ↔ ¬ adr ∈ adr0 + ax0

Rule argument

term: ax

Additional information

Used simplifier rules: new-base: ⊦ new([], fs);%address-list freely generated by [], +;;% ⊦ ¬ adr ∈ []; (s)