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Proof step 164 from proof inv-unlink (previous step)

# links(entries0[str], dirs0) = m2 + 1, dirs0[m0] = mkdir(m8 + 1, md2, # links(m0, dirs0), m7, entries0), files0[entries0[str]] = mkfile(m1, md1, m2 + 1, content0), afs-cons(dirs0, files0), afs-cons(dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]), dcache-cons(dcache, dirs0, files0), synced(dirs0, icache0, pcache), str ∈ entries0, entries0[str] ∈ files0, m0 ∈ dirs0, asynced1 → synced(files0, icache0, pcache), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ∀ key. key ∈ dcache -- dentrykey(m0, str) → key.dentry? ∧ key.name = (dcache -- dentrykey(m0, str))[key].name ∧ valid-dentry (key.ino, (dcache -- dentrykey(m0, str))[key], dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 165:
# links(entries0[str], dirs0) = m2 + 1, files0[entries0[str]] = mkfile(m1, md1, m2 + 1, content0), dirs0[m0] = mkdir(m8 + 1, md2, # links(m0, dirs0), m7, entries0), afs-cons(dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]), afs-cons(dirs0, files0), dcache-cons(dcache, dirs0, files0), synced(dirs0, icache0, pcache), m0 ∈ dirs0, entries0[str] ∈ files0, str ∈ entries0, key ∈ dcache, asynced1 → synced(files0, icache0, pcache), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ key = dentrykey(m0, str), key.dentry? ∧ key.name = dcache[key].name ∧ key.ino ∈ dirs0 ∧ ((entries0[str] = key.ino ⊃ links(key.ino, dirs0) -- mklink(m0, str);links(key.ino, dirs0)) ≠ ∅ ∨ key.ino = ROOT_INO) ∧ (dcache[key].ino ∈ dirs0 ∨ dcache[key].ino ∈ files0) ∧ dcache[key].name ∈ (key.ino = m0 ⊃ mkdir(m8, md3, # links(key.ino, dirs0), m7, entries0 -- str);dirs0[key.ino]).entries ∧ dcache[key].ino = (key.ino = m0 ⊃ mkdir(m8, md3, # links(key.ino, dirs0), m7, entries0 -- str);dirs0[key.ino]).entries[dcache[key].name] ∧ dcache[key].dentry?

Rule argument

Additional information

Used simplifier rules: ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)%⊦ ino ∈ dirs ∧ dirs[ino] = mkdir(m0, md0, n1, n2, entries) → links(ino0, dirs[ino, mkdir(m, md, n, n0, entries)]) = links(ino0, dirs); (s)%⊦ ino0 ∈ dirs → links(ino, dirs[ino0, mkdir(m, md, n0, n1, entries -- str)]) = (str ∈ entries ∧ entries[str] = ino ⊃ links(ino, dirs[ino0, mkdir(m, md, n0, n1, entries)]) -- mklink(ino0, str) ;links(ino, dirs[ino0, mkdir(m, md, n0, n1, entries)]) ); (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)%⊦ valid-parent-ino(ino, dirs, files) ↔ ino ∈ dirs ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO); (s)%⊦ valid-dentry(ino, dent, dirs, files) ↔ valid-parent-ino(ino, dirs, files) ∧ valid-ino(dent.ino, dirs, files) ∧ dent.name ∈ dirs[ino].entries ∧ dent.ino = dirs[ino].entries[dent.name] ∧ dent.dentry?; (s)% ⊦ key ≠ key0 → (dcache -- key0)[key] = dcache[key]; (s)% ⊦ key ∈ dcache -- key0 ↔ key ≠ key0 ∧ key ∈ dcache; (s)