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Proof step 472 from proof inv-rename-file-dentry (previous step)

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), pcache-cons(pcache, dirs0, files), synced(dirs0, icache0, pcache), entries[str0] ∈ files, str0 ∈ entries, m3 ∈ dirs0, asynced2 → synced(files, icache0, pcache), links(m3, dirs0) ≠ ∅ ∨ m3 = ROOT_INO ⊦ entries[str0] ∈ dirs0, ∀ key. key ∈ pcache → key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ valid-file-ino (key.ino, dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files[entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content)]) ∧ ( ¬ pcache[key].dirty → key.part ∈ files[entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content)][key.ino].content ∧ pcache[key].page = files[entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content)][key.ino].content[key.part])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 473:
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)]), pcache-cons(pcache, dirs0, files), synced(dirs0, icache0, pcache), key ∈ pcache, m3 ∈ dirs0, str0 ∈ entries, entries[str0] ∈ files, asynced2 → synced(files, icache0, pcache), links(m3, dirs0) ≠ ∅ ∨ m3 = ROOT_INO ⊦ entries[str0] ∈ dirs0, key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ key.ino ∈ files ∧ ( ¬ pcache[key].dirty → key.part ∈ (key.ino = entries[str0] ⊃ mkfile(m, md3, # links(entries[str0], dirs0), content);files[key.ino]).content ∧ pcache[key].page = (key.ino = entries[str0] ⊃ mkfile(m, md3, # links(entries[str0], dirs0), content);files[key.ino]).content[key.part])

Rule argument

Additional information

Used simplifier rules: ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)