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Proof step 3 from proof inos-dom (previous step)

dom ri0 = dom ri1 ⊦ ri0.inos = ri1.inos

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ ks = ks0 ↔ (∀ key. key ∈ ks ↔ key ∈ ks0)
Proof step 5:
∀ key. key ∈ dom ri0 ↔ key ∈ dom ri1 ⊦ ri0.inos = ri1.inos

Rule argument

spec: set-basic, inst: node-index name: Extension seq: ⊦ ks = ks0 ↔ (∀ key. key ∈ ks ↔ key ∈ ks0) subst: [ks0, ks] → [dom ri1, dom ri0] flags: <all paths>

Additional information

Used terms: dom ri1, dom ri0