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Proof step 7 from proof ri-cons-drop (previous step)

as ∩ range ri = ∅, key-cons(key, fs[ri[key]]), ri[key] ∈ fs, key ∈ ri ⊦ key-cons(key, (fs \ as)[ri[key]])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ as = as0 ↔ (∀ adr. adr ∈ as ↔ adr ∈ as0)
Proof step 9:
key-cons(key, fs[ri[key]]), key ∈ ri, ri[key] ∈ fs, ∀ adr. adr ∈ as ∩ range ri ↔ adr ∈ ∅ ⊦ key-cons(key, (fs \ as)[ri[key]])

Rule argument

spec: set-basic, inst: node-store name: Extension seq: ⊦ as = as0 ↔ (∀ adr. adr ∈ as ↔ adr ∈ as0) subst: [as0, as] → [∅, as ∩ range ri] flags: <all paths>

Additional information

Used terms: ∅, as ∩ range ri