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Proof step 3 from proof in-read-in-dom (previous step)

adr ∈ ri[kx], kx.toSet ⊆ dom ri ⊦ adr ∈ ri

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 4:
adr ∈ ri[key + kx0], (key + kx0).toSet ⊆ dom ri, ∀ adr, ri. adr ∈ ri[kx0] ∧ kx0.toSet ⊆ dom ri → adr ∈ ri ⊦ adr ∈ ri

Rule argument

term: kx

Additional information

Used simplifier rules: index-lookup-base: ⊦ ri[[]] = [];%key-list freely generated by [], +;;% ⊦ [].toSet = ∅; (s)% ⊦ ∅ ⊆ ks; (s)% ⊦ ¬ adr ∈ []; (s)