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Proof step 7 from proof lebs-write (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 8:
∃ adr. adr.lnum = n ∧ adr ∈ ri[key, @(m, m0, m1)] ⊦ n = m, key ∈ ri, ∃ adr. adr.lnum = n ∧ adr ∈ ri
Proof step 12:
n = m ∨ (∃ adr. adr.lnum = n ∧ adr ∈ ri) ⊦ key ∈ ri, ∃ adr. adr.lnum = n ∧ adr ∈ ri[key, @(m, m0, m1)]

Rule argument

pos: right 1

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