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Proof step 9 from proof crash-exists-h (previous step)

fid ∈ fs ⊦ ∃ fs0. (∀ fid0. fid0 ∈ fs0 ↔ fid0 = fid) ∧ (∀ fid. fid ∈ fs0 → fs0[fid] = fs[fid]), (∀ fid0. fid0 ∈ (∅)[fid, fs[fid]] ↔ fid0 = fid) ∧ (∀ fid0. fid0 ∈ (∅)[fid, fs[fid]] → (∅)[fid, fs[fid]][fid0] = fs[fid0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ fid ∈ fs[fid, f]; (s)% ⊦ ¬ fid ∈ ∅; (s)% ⊦ fid ≠ fid0 → (fid ∈ fs[fid0, f] ↔ fid ∈ fs); (s)