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Proof step 103 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)]), synced(files0, icache0, pcache), str ∈ entries0, entries0[str] ∈ files0, m0 ∈ dirs0, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ∀ ino. (ino ∈ files0 → synced(ino, icache0, pcache)) → ino ∈ files0[entries0[str], mkfile(m3, md0, m2, content0)] → synced (ino, icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ], pcache)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 104:
# 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), synced(files0, icache0, pcache), m0 ∈ dirs0, entries0[str] ∈ files0, str ∈ entries0, ino ∈ files0, ino ∈ icache0 → ¬ icache0[ino].dirty, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ( ino ∈ icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ] → ¬ icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ] [ino ] .dirty) ∧ (datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty)

Rule argument

Additional information

Used simplifier rules: ⊦ synced(ino, icache, pcache) ↔ (ino ∈ icache → ¬ icache[ino].dirty) ∧ (∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty); (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)