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Proof step 431 from proof inv-rename-file-dentry (previous step)

dirs0[m3] = mkdir(m1, md1, # links(m3, dirs0), m4, entries), files[entries[str0]] = mkfile(m0, md0, # links(entries[str0], dirs0), content), afs-cons(dirs0, files), afs-cons (dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files[entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content)]), synced(files, icache0, pcache), m3 ∈ dirs0, str0 ∈ entries, entries[str0] ∈ files, links(m3, dirs0) ≠ ∅ ∨ m3 = ROOT_INO ⊦ entries[str0] ∈ dirs0, ∀ ino. (ino ∈ files → synced(ino, icache0, pcache)) → ino ∈ files[entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content)] → synced (ino, icache0[m3, mkientry(false, mkinode(m3, md2, true, # links(m3, dirs0), m4, m1))] [entries[str0], mkientry(false, mkinode(entries[str0], md3, false, # links(entries[str0], dirs0), 0, m)) ], pcache)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 432:
files[entries[str0]] = mkfile(m0, md0, # links(entries[str0], dirs0), content), dirs0[m3] = mkdir(m1, md1, # links(m3, dirs0), m4, entries), afs-cons (dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files[entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content)]), afs-cons(dirs0, files), synced(files, icache0, pcache), entries[str0] ∈ files, str0 ∈ entries, m3 ∈ dirs0, ino ∈ files, ino ∈ icache0 → ¬ icache0[ino].dirty, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty, links(m3, dirs0) ≠ ∅ ∨ m3 = ROOT_INO ⊦ entries[str0] ∈ dirs0, ( ino ∈ icache0[m3, mkientry(false, mkinode(m3, md2, true, # links(m3, dirs0), m4, m1))] [entries[str0], mkientry(false, mkinode(entries[str0], md3, false, # links(entries[str0], dirs0), 0, m)) ] → ¬ icache0[m3, mkientry(false, mkinode(m3, md2, true, # links(m3, dirs0), m4, m1))] [entries[str0], mkientry(false, mkinode(entries[str0], md3, false, # links(entries[str0], dirs0), 0, m)) ] [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)