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Proof step 5 from proof orphans-del-file (previous step)

# links(ino, dirs) = 0, files[ino] = mkfile(n, md, 0, content), afs-cons(dirs, files), ino ∈ files ⊦ ino ∈ dirs, ∀ ino0. ino0 ∈ orphans(dirs, files -- ino) ↔ ino0 ∈ orphans(dirs, files) -- ino

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
# links(ino, dirs) = 0, files[ino] = mkfile(n, md, 0, content), afs-cons(dirs, files), ino ∈ files ⊦ ino0 ∈ orphans(dirs, files -- ino) ↔ ino0 ≠ ino ∧ ino0 ∈ orphans(dirs, files), ino ∈ dirs

Rule argument

Additional information

Used simplifier rules: ⊦ ino ∈ ns -- ino0 ↔ ino ≠ ino0 ∧ ino ∈ ns; (s)