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Proof step 511 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), icache-cons(icache0, 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, ∀ ino. 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 ] .inode .ino = 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)) ] [ino ] .dirty ⊃ valid-file-inode (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 ] .inode, dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files[entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content)]) ; valid-ino (ino, dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files[entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content)]) ∧ valid-inode (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 ] .inode, dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files[entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content)]) )

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 512:
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)]), icache-cons(icache0, dirs0, files), synced(dirs0, icache0, pcache), 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)) ], m3 ∈ dirs0, str0 ∈ entries, entries[str0] ∈ files, asynced2 → synced(files, icache0, pcache), links(m3, dirs0) ≠ ∅ ∨ m3 = ROOT_INO ⊦ entries[str0] ∈ dirs0, 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 ] .inode .ino = 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)) ] [ino ] .dirty ⊃ 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 ] .inode .ino ∈ files ∧ 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 ] .inode .nlink = ( 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 ] .inode .ino = entries[str0] ⊃ mkfile(m, md3, # links(entries[str0], dirs0), content) ;files [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 ] .inode .ino ] ) .nlink ∧ 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 ] .inode .nsubdirs = 0 ∧ ¬ 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 ] .inode .directory ; (ino ∈ dirs0 ∨ ino ∈ files) ∧ 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 ] .inode = ( 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 ] .inode .ino ∈ dirs0 ⊃ mkinode (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 ] .inode .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)) ] [ino ] .inode .ino = m3 ⊃ mkdir(m1, md2, # links(m3, dirs0), m4, entries) ;dirs0 [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 ] .inode .ino ] ) .meta, true, ( 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 ] .inode .ino = m3 ⊃ mkdir(m1, md2, # links(m3, dirs0), m4, entries) ;dirs0 [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 ] .inode .ino ] ) .nlink, ( 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 ] .inode .ino = m3 ⊃ mkdir(m1, md2, # links(m3, dirs0), m4, entries) ;dirs0 [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 ] .inode .ino ] ) .nsubdirs, ( 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 ] .inode .ino = m3 ⊃ mkdir(m1, md2, # links(m3, dirs0), m4, entries) ;dirs0 [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 ] .inode .ino ] ) .size) ;mkinode (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 ] .inode .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)) ] [ino ] .inode .ino = entries[str0] ⊃ mkfile(m, md3, # links(entries[str0], dirs0), content) ;files [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 ] .inode .ino ] ) .meta, false, ( 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 ] .inode .ino = entries[str0] ⊃ mkfile(m, md3, # links(entries[str0], dirs0), content) ;files [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 ] .inode .ino ] ) .nlink, 0, ( 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 ] .inode .ino = entries[str0] ⊃ mkfile(m, md3, # links(entries[str0], dirs0), content) ;files [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 ] .inode .ino ] ) .size) ) )

Rule argument

Additional information

Used simplifier rules: ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)%⊦ getinode(ino, dirs, files) = (ino ∈ dirs ⊃ mkinode (ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ); (s)%⊦ valid-inode(inode, dirs, files) ↔ inode = getinode(inode.ino, dirs, files); (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)% ⊦ 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)%⊦ valid-file-inode(inode, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory; (s)