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Proof step 6 from proof lebs-write (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
⊦ (∃ adr. adr.lnum = n ∧ adr ∈ ri[key, @(m, m0, m1)]) ↔ n = m ∨ (∃ adr. adr.lnum = n ∧ adr ∈ ri), key ∈ ri

Rule argument

Additional information

Used simplifier rules: lebs-index: ⊦ n ∈ ri.lebs ↔ (∃ adr. adr.lnum = n ∧ adr ∈ ri);% ⊦ n ∈ ns ++ n0 ↔ n = n0 ∨ n ∈ ns; (s)