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Proof step 3 from proof abs-files-emp (previous step)

⊦ ∀ fid. (fid ∈ abs-files(∅) ↔ fid ∈ ∅) ∧ abs-files(∅)[fid] = (∅)[fid]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
fid ∈ abs-files(∅) ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ fid ∈ fs → fs[fid] = (∅)[fid]; (s)% ⊦ ¬ fid ∈ ∅; (s)