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Proof step 13 from proof refine-mkdir (previous step)

root.dir?, dom of < ino, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), of-cons(of, dirs, files), psynced → asynced ⊦ pre-mkdir(ε, md, EEXISTS, user, root, abs-files(files), abs-of(of)) ∧ ⟨err0 := EEXISTS; if err0 = ESUCCESS then root := dnode(md, ∅); psynced := ?⟩ (abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ EEXISTS = err0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
root.dir?, dom of < ino, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), of-cons(of, dirs, files), psynced → asynced ⊦ ⟨err0 := EEXISTS; if err0 = ESUCCESS then root := dnode(md, ∅); psynced := ?⟩ (abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ EEXISTS = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ ε ∈ tree; (s)% ⊦ pre-mkdir(p, md, EEXISTS, user, root, fs, ofh) ↔ p ∈ root; (s)