[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 257 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), icache-cons(icache0, dirs0, files), synced(dirs0, icache0, pcache), ino ∈ icache0[m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0))][m, mkientry(false, mkinode(m, md5, true, m13, m14, m12))], 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 ⊦ str0 ∈ entries2, entries[str] ∈ dirs0, icache0[m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0))][m, mkientry(false, mkinode(m, md5, true, m13, m14, m12))][ino].inode.ino = ino ∧ (icache0[m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0))][m, mkientry(false, mkinode(m, md5, true, m13, m14, m12))][ino].dirty ⊃ icache0[m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0))][m, mkientry(false, mkinode(m, md5, true, m13, m14, m12))][ino].inode.ino ∈ files ∧ icache0[m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0))][m, mkientry(false, mkinode(m, md5, true, m13, m14, m12))][ino].inode .nlink = files [icache0[m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0))][m, mkientry(false, mkinode(m, md5, true, m13, m14, m12))][ino].inode.ino ] .nlink ∧ icache0[m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0))][m, mkientry(false, mkinode(m, md5, true, m13, m14, m12))][ino].inode .nsubdirs = 0 ∧ ¬ icache0[m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0))][m, mkientry(false, mkinode(m, md5, true, m13, m14, m12))][ino].inode .directory ; (ino ∈ dirs0 ∨ ino ∈ files) ∧ icache0[m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0))][m, mkientry(false, mkinode(m, md5, true, m13, m14, m12))][ino].inode = ( icache0[m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0))][m, mkientry(false, mkinode(m, md5, true, m13, m14, m12))][ino].inode .ino ∈ dirs0 ⊃ mkinode (icache0[m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0))][m, mkientry(false, mkinode(m, md5, true, m13, m14, m12))][ino].inode .ino, ( icache0[m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0))][m, mkientry(false, mkinode(m, md5, true, m13, m14, m12))][ino].inode .ino = m ⊃ mkdir(m12, md5, m13, m14, entries3) ;( icache0[m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0))][m, mkientry(false, mkinode(m, md5, true, m13, m14, m12))][ino] .inode .ino = m8 ⊃ mkdir(m2, md0, # links(m8, dirs0), m5, entries -- str) ;dirs0 [icache0[m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0))][m, mkientry(false, mkinode(m, md5, true, m13, m14, m12))][ino].inode .ino ] ) ) .meta, true, ( icache0[m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0))][m, mkientry(false, mkinode(m, md5, true, m13, m14, m12))][ino].inode .ino = m ⊃ mkdir(m12, md5, m13, m14, entries3) ;( icache0[m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0))][m, mkientry(false, mkinode(m, md5, true, m13, m14, m12))][ino] .inode .ino = m8 ⊃ mkdir(m2, md0, # links(m8, dirs0), m5, entries -- str) ;dirs0 [icache0[m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0))][m, mkientry(false, mkinode(m, md5, true, m13, m14, m12))][ino].inode .ino ] ) ) .nlink, ( icache0[m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0))][m, mkientry(false, mkinode(m, md5, true, m13, m14, m12))][ino].inode .ino = m ⊃ mkdir(m12, md5, m13, m14, entries3) ;( icache0[m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0))][m, mkientry(false, mkinode(m, md5, true, m13, m14, m12))][ino] .inode .ino = m8 ⊃ mkdir(m2, md0, # links(m8, dirs0), m5, entries -- str) ;dirs0 [icache0[m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0))][m, mkientry(false, mkinode(m, md5, true, m13, m14, m12))][ino].inode .ino ] ) ) .nsubdirs, ( icache0[m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0))][m, mkientry(false, mkinode(m, md5, true, m13, m14, m12))][ino].inode .ino = m ⊃ mkdir(m12, md5, m13, m14, entries3) ;( icache0[m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0))][m, mkientry(false, mkinode(m, md5, true, m13, m14, m12))][ino] .inode .ino = m8 ⊃ mkdir(m2, md0, # links(m8, dirs0), m5, entries -- str) ;dirs0 [icache0[m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0))][m, mkientry(false, mkinode(m, md5, true, m13, m14, m12))][ino].inode .ino ] ) ) .size) ;mkinode (icache0[m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0))][m, mkientry(false, mkinode(m, md5, true, m13, m14, m12))][ino].inode.ino, files [icache0[m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0))][m, mkientry(false, mkinode(m, md5, true, m13, m14, m12))][ino].inode .ino ] .meta, false, files [icache0[m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0))][m, mkientry(false, mkinode(m, md5, true, m13, m14, m12))][ino].inode .ino ] .nlink, 0, files [icache0[m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0))][m, mkientry(false, mkinode(m, md5, true, m13, m14, m12))][ino].inode .ino ] .size) ) )

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 258:
# 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), icache0[m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0))][m, mkientry(false, mkinode(m, md5, true, m13, m14, m12))][ino].inode = mkinode(m15, md7, boolvar, m16, m17, m18), (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), icache-cons(icache0, dirs0, files), synced(dirs0, icache0, pcache), str ∈ entries, entries[str] ∈ files, m ∈ dirs0, m8 ∈ dirs0, ino ∈ icache0[m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0))][m, mkientry(false, mkinode(m, md5, true, m13, m14, m12))], 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, m15 = ino ∧ (icache0[m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0))][m, mkientry(false, mkinode(m, md5, true, m13, m14, m12))][ino].dirty ⊃ m15 ∈ files ∧ m16 = files[m15].nlink ∧ m17 = 0 ∧ ¬ boolvar ; (ino ∈ dirs0 ∨ ino ∈ files) ∧ icache0[m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0))][m, mkientry(false, mkinode(m, md5, true, m13, m14, m12))][ino].inode = (m15 ∈ dirs0 ⊃ mkinode (m15, (m15 = m ⊃ mkdir(m12, md5, m13, m14, entries3);(m15 = m8 ⊃ mkdir(m2, md0, # links(m8, dirs0), m5, entries -- str);dirs0[m15])).meta, true, (m15 = m ⊃ mkdir(m12, md5, m13, m14, entries3);(m15 = m8 ⊃ mkdir(m2, md0, # links(m8, dirs0), m5, entries -- str);dirs0[m15])).nlink, (m15 = m ⊃ mkdir(m12, md5, m13, m14, entries3);(m15 = m8 ⊃ mkdir(m2, md0, # links(m8, dirs0), m5, entries -- str);dirs0[m15])) .nsubdirs, (m15 = m ⊃ mkdir(m12, md5, m13, m14, entries3);(m15 = m8 ⊃ mkdir(m2, md0, # links(m8, dirs0), m5, entries -- str);dirs0[m15])).size) ;mkinode(m15, files[m15].meta, false, files[m15].nlink, 0, files[m15].size) ) )

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [icache0 [m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0)) ] [m, mkientry(false, mkinode(m, md5, true, m13, m14, m12)) ] [ino ] .inode, m15, md7, boolvar, m16, m17, m18]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: icache0[m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0))] [m, mkientry(false, mkinode(m, md5, true, m13, m14, m12)) ] [ino ] .inode, m15, md7, boolvar, m16, m17, m18