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Proof step 9 from proof inv-recover (previous step)

dirs = dirs0 \ orphans(dirs0, files), files0 = files \ orphans(dirs0, files), asynced, afs-cons(dirs0, files) ⊦ ⟪afs_recovery#(asynced0; dirs, files0; asynced1, err)⟫ (err = ESUCCESS → asynced1 ∧ afs-cons(dirs, files0))

A spec-lemma