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Proof step 6 from proof new-ext (previous step)

(adr0 ∈ log0 → ¬ adr0 ∈ fs) → new(log0, fs), ∀ adr0. adr0 = adr ∨ adr0 ∈ log0 → ¬ adr0 ∈ fs ⊦ ¬ adr ∈ fs ∧ new(log0, fs)

User applied rule case distinction

And obtained the following new goals

Proof step 7:
adr0 ∈ fs, adr0 ∈ log0, ∀ adr0. adr0 = adr ∨ adr0 ∈ log0 → ¬ adr0 ∈ fs ⊦ ¬ adr ∈ fs ∧ new(log0, fs)

Rule argument

pos: left 1

Additional information

Used simplifier rules: new-in-fs: ⊦ new(log, fs) ∧ adr ∈ fs → ¬ adr ∈ log;