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Proof step 212 from proof inv-rename-dir-negdentry (previous step)

(entries6[str] = m9 ⊃ (links(entries6[str], dirs0) -- mklink(entries6[str], str)) ++ mklink(entries6[str], str0);links(m9, dirs0)) = ∅, dirs0[m9] = mkdir(m4 + 1, md8, # links(m9, dirs0), m7 + 1, entries6), dirs0[entries6[str]] = mkdir(m3, md2, # links(entries6[str], dirs0), m5, entries), afs-cons(dirs0, files), afs-cons(dirs0[m9, mkdir(m4 + 1, md0, # links(m9, dirs0), m7 + 1, (entries6 -- str)[str0, entries6[str]])], files), synced(dirs0, icache0, pcache), entries6[str] ∈ dirs0, str ∈ entries6, m9 ∈ dirs0, asynced2 → synced(files, icache0, pcache), dentrykey(m9, str0) ∈ dcache0 → str0 = dcache0[dentrykey(m9, str0)].name ∧ (dcache0[dentrykey(m9, str0)].ino ∈ dirs0 ∨ dcache0[dentrykey(m9, str0)].ino ∈ files) ∧ dcache0[dentrykey(m9, str0)].name ∈ entries6 ∧ dcache0[dentrykey(m9, str0)].ino = entries6[dcache0[dentrykey(m9, str0)].name] ∧ dcache0[dentrykey(m9, str0)].dentry?, ∀ key0. key0 ∈ dcache0 → key0.dentry? ∧ key0.name = dcache0[key0].name ∧ key0.ino ∈ dirs0 ∧ (links(key0.ino, dirs0) ≠ ∅ ∨ key0.ino = ROOT_INO) ∧ (dcache0[key0].ino ∈ dirs0 ∨ dcache0[key0].ino ∈ files) ∧ dcache0[key0].name ∈ dirs0[key0.ino].entries ∧ dcache0[key0].ino = dirs0[key0.ino].entries[dcache0[key0].name] ∧ dcache0[key0].dentry? ⊦ # links(m9, dirs0) = 0, links(m9, dirs0) = ∅, m9 = ROOT_INO, str0 ∈ entries6

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: entries6[str] = m9

Additional information

Used simplifier rules: ⊦ afs-cons(dirs, files) → ( links(ino, dirs) = ∅ ↔ (ino ∈ dirs → dirs[ino].nlink = 0) ∧ (ino ∈ files → files[ino].nlink = 0)); (ws)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)% ⊦ ∅ ≠ ls ++ alink; (s) Used formulas: entries6[str] = m9