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Proof step 9 from proof referenced-adrs-lookup-keys-nodups (previous step)

ri-cons(ri, fs), adr ∈ ri, fs[adr].key ∈ fs[referenced-adrs(ax0, ri)].keys ⊦ dups(ax0), dups(fs[referenced-adrs(ax0, ri)].keys), adr ∈ ax0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ key ∈ kx ↔ (∃ kx0, kx1. kx = kx0 + (key + kx1))
Proof step 11:
ri-cons(ri, fs), adr ∈ ri, ∃ kx0, kx1. fs[referenced-adrs(ax0, ri)].keys = kx0 + (fs[adr].key + kx1) ⊦ dups(fs[referenced-adrs(ax0, ri)].keys), dups(ax0), adr ∈ ax0

Rule argument

spec: list, inst: key-list-set name: in-def seq: ⊦ key ∈ kx ↔ (∃ kx0, kx1. kx = kx0 + (key + kx1)) subst: [kx, key] → [fs[referenced-adrs(ax0, ri)].keys, fs[adr].key] flags: <all paths>

Additional information

Used terms: fs[referenced-adrs(ax0, ri)].keys, fs[adr].key