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Proof step 4 from proof lebs-write (previous step)

⊦ ri[key, @(m, m0, m1)].lebs = ri.lebs ++ m, key ∈ ri

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ ns = ns0 ↔ (∀ n. n ∈ ns ↔ n ∈ ns0)
Proof step 6:
⊦ key ∈ ri, ∀ n. n ∈ ri[key, @(m, m0, m1)].lebs ↔ n ∈ ri.lebs ++ m

Rule argument

spec: set-basic, inst: nat-set name: Extension seq: ⊦ ns = ns0 ↔ (∀ n. n ∈ ns ↔ n ∈ ns0) subst: [ns0, ns] → [ri.lebs ++ m, ri[key, @(m, m0, m1)].lebs] flags: <all paths>

Additional information

Used terms: ri.lebs ++ m, ri[key, @(m, m0, m1)].lebs