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Proof step 6 from proof inos-dom (previous step)

∀ key. key ∈ ri0 ↔ key ∈ ri1 ⊦ ri0.inos = ri1.inos

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ ns = ns0 ↔ (∀ n. n ∈ ns ↔ n ∈ ns0)
Proof step 8:
∀ key. key ∈ ri0 ↔ key ∈ ri1 ⊦ ∀ n. n ∈ ri0.inos ↔ n ∈ ri1.inos

Rule argument

spec: set-basic, inst: nat-set name: Extension seq: ⊦ ns = ns0 ↔ (∀ n. n ∈ ns ↔ n ∈ ns0) subst: [ns0, ns] → [ri1.inos, ri0.inos] flags: <all paths>

Additional information

Used terms: ri1.inos, ri0.inos