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Proof step 178 from proof inv-mkdir (previous step)

(dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m6] = mkdir(m, md0, 0, m2, entries1), dirs0[m0] = mkdir(m3, md1, # links(m0, dirs0), m5, entries0), dirs0[m6] = mkdir(m4, md3, # links(m6, dirs0), m7, entries), dcache[dentrykey(m6, str0)] = mkdentry(str0, entries[str0]), afs-cons(dirs0, files), afs-cons ((dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m0, mkdir(m3 + 1, md2, # links(m0, dirs0), m5 + 1, entries0[str, ino0]) ], files), synced(dirs0, icache0, pcache), m0 ∈ dirs0, dentrykey(m6, str0) ∈ dcache, m6 ∈ dirs0, str0 ∈ entries, asynced1 → synced(files, icache0, pcache), ∀ key0. key0 ∈ dcache → key0.dentry? ∧ key0.name = dcache[key0].name ∧ key0.ino ∈ dirs0 ∧ (links(key0.ino, dirs0) ≠ ∅ ∨ key0.ino = ROOT_INO) ∧ (dcache[key0].ino ∈ dirs0 ∨ dcache[key0].ino ∈ files) ∧ dcache[key0].name ∈ dirs0[key0.ino].entries ∧ dcache[key0].ino = dirs0[key0.ino].entries[dcache[key0].name] ∧ dcache[key0].dentry?, entries[str0] ∈ dirs0 ∨ entries[str0] ∈ files, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ # links(m6, dirs0) = 0, entries[str0] = ino0, dentrykey(m6, str0) = dentrykey(m0, str), ino0 = 0, links(m6, dirs0) = ∅, m6 = ROOT_INO, m6 = m0, ino0 ∈ dirs0, ino0 ∈ files, str ∈ entries0

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: m6 = ino0

Additional information

Used simplifier rules: ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)%ino ∈ dirs, ino0 ≠ 0, ¬ ino0 ∈ dirs ⊦ ino ≠ ino0 → (dirs ++ ino0)[ino] = dirs[ino]; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)%afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n; (forward) from specification afs-base Used formulas: m6 = ino0