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Proof step 19 from proof inv-create (previous step)

root.dir?, root[parent(path)].dir?, fids-cons(root, fs, ofh), py(user, parent(path), root, fs), parent(path) ∈ root ⊦ path ∈ root, ∃ fid. ¬ fid ∈ fs

Heuristic use patterns applied rule apply lemma

And obtained the following new goals

Proof step 20:
⊦ ∃ fid. ¬ fid ∈ dom fs
Proof step 21:
root[parent(path)].dir?, root.dir?, fids-cons(root, fs, ofh), py(user, parent(path), root, fs), parent(path) ∈ root, ∃ fid. ¬ fid ∈ dom fs ⊦ path ∈ root, ∃ fid. ¬ fid ∈ fs

Rule argument

spec: posix-base name: inf-fids seq: ⊦ ∃ fid. ¬ fid ∈ dom fs subst: [fs] → [fs]

Additional information

Used terms: fs