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Proof step 3 from proof ri-cons-range-ri (previous step)

∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]) ⊦ range ri ⊆ dom fs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ as ⊆ as0 ↔ (∀ adr. adr ∈ as → adr ∈ as0)
Proof step 5:
∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]) ⊦ ∀ adr. adr ∈ range ri → adr ∈ dom fs

Rule argument

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

Additional information

Used terms: dom fs, range ri