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Proof step 3 from proof toSet-subseteq-domri-notin (previous step)

key ∈ kx, kx.toSet ⊆ dom ri ⊦ key ∈ ri

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 ∈ kx, ∀ key. key ∈ kx.toSet → key ∈ dom ri ⊦ key ∈ ri

Rule argument

spec: set-basic, inst: node-index name: Subset seq: ⊦ ks ⊆ ks0 ↔ (∀ key. key ∈ ks → key ∈ ks0) subst: [ks0, ks] → [dom ri, kx.toSet] flags: <all paths>

Additional information

Used terms: dom ri, kx.toSet