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Proof step 15 from proof lebs-lookup-subseteq (previous step)

@(m, m0, m1) ∈ ri[ks] ⊦ # ri[ks] = 0, ri[ks] = ∅, m ∈ ns, @(m, m0, m1) ∈ ri, ri[ks].lebs ⊆ ri.lebs

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: index-base name: lookup-keys seq: ⊦ adr ∈ ri[ks] ↔ (∃ key. key ∈ ks ∧ key ∈ ri ∧ adr = ri[key]) subst: [ks, ri, adr] → [ks, ri, @(m, m0, m1)] flags: <all paths>

Additional information

Used simplifier rules: in-data-explicit: ⊦ key ∈ ri ∧ ri[key] = adr → adr ∈ ri; Used terms: ks, ri, @(m, m0, m1)