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Proof step 188 from proof inv-rename-file-negdentry (previous step)

# links (entries[str], dirs0 [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m, mkdir(m12, md5, m13, m14, entries3) ]) = # links(entries[str], dirs0), (m = m8 ⊃ mkdir(m1 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])) = mkdir(m12, md6, m13, m14, entries3), (m8 = m ⊃ mkdir(m1 + 1, md5, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md0, # links(m8, dirs0), m5, entries -- str)) = mkdir(m0, md1, m10, m11, entries0), (m = m8 ⊃ mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str);mkdir(m7, md4, # links(m, dirs0), m9, entries2)) = mkdir(m1, md2, m4, m6, entries1), dirs0[m] = mkdir(m7, md4, # links(m, dirs0), m9, entries2), files[entries[str]] = mkfile(m3, md, # links(entries[str], dirs0), content0), dirs0[m8] = mkdir(m2 + 1, md3, # links(m8, dirs0), m5, entries), afs-cons (dirs0[m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0] [m, mkdir(m12, md5, m13, m14, entries3) ], files), afs-cons(dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache0, pcache), m8 ∈ dirs0, m ∈ dirs0, entries[str] ∈ files, str ∈ entries, m = m8 → md5 = md0, asynced2 → synced(files, icache0, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m8, dirs0) ≠ ∅ ∨ m8 = ROOT_INO ⊦ pcache-cons (pcache, dirs0 [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m, mkdir(m12, md5, m13, m14, entries3) ], files), str0 ∈ entries2, entries[str] ∈ dirs0

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 189:
⊦ pcache-cons(pcache, dirs, files) ↔ (∀ key. key ∈ pcache → key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ valid-file-ino(key.ino, dirs, files) ∧ (¬ pcache[key].dirty → key.part ∈ files[key.ino].content ∧ pcache[key].page = files[key.ino].content[key.part]))
Proof step 190:
# links (entries[str], dirs0 [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m, mkdir(m12, md5, m13, m14, entries3) ]) = # links(entries[str], dirs0), (m = m8 ⊃ mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str);mkdir(m7, md4, # links(m, dirs0), m9, entries2)) = mkdir(m1, md2, m4, m6, entries1), (m8 = m ⊃ mkdir(m1 + 1, md5, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md0, # links(m8, dirs0), m5, entries -- str)) = mkdir(m0, md1, m10, m11, entries0), (m = m8 ⊃ mkdir(m1 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])) = mkdir(m12, md6, m13, m14, entries3), dirs0[m8] = mkdir(m2 + 1, md3, # links(m8, dirs0), m5, entries), files[entries[str]] = mkfile(m3, md, # links(entries[str], dirs0), content0), dirs0[m] = mkdir(m7, md4, # links(m, dirs0), m9, entries2), afs-cons(dirs0, files), afs-cons (dirs0[m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0] [m, mkdir(m12, md5, m13, m14, entries3) ], files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache0, pcache), str ∈ entries, entries[str] ∈ files, m ∈ dirs0, m8 ∈ dirs0, asynced2 → synced(files, icache0, pcache), m = m8 → md5 = md0, links(m8, dirs0) ≠ ∅ ∨ m8 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries[str] ∈ dirs0, str0 ∈ entries2, ∀ key. key ∈ pcache → key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ valid-file-ino (key.ino, dirs0 [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m, mkdir(m12, md5, m13, m14, entries3) ], files) ∧ (¬ pcache[key].dirty → key.part ∈ files[key.ino].content ∧ pcache[key].page = files[key.ino].content[key.part])

Rule argument

spec: cache-base name: pcache-cons seq: ⊦ pcache-cons(pcache, dirs, files) ↔ (∀ key. key ∈ pcache → key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ valid-file-ino(key.ino, dirs, files) ∧ ( ¬ pcache[key].dirty → key.part ∈ files[key.ino].content ∧ pcache[key].page = files[key.ino].content[key.part])) subst: [pcache, dirs, files] → [pcache, dirs0 [m8, (m8 = m ⊃ mkdir (m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir (m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m, mkdir(m12, md5, m13, m14, entries3) ], files] flags: <all paths>

Additional information

Used terms: pcache, dirs0 [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]) ;mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str) ) .meta:= md0 ] [m, mkdir(m12, md5, m13, m14, entries3) ], files