[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 259 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), 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 ⊃ ino ∈ files ∧ m16 = files[ino].nlink ∧ m17 = 0 ∧ ¬ boolvar ; (ino ∈ dirs0 ∨ ino ∈ files) ∧ mkinode(ino, md7, boolvar, m16, m17, m18) = (ino ∈ dirs0 ⊃ mkinode (ino, (ino = m ⊃ mkdir(m12, md5, m13, m14, entries3);(ino = m8 ⊃ mkdir(m2, md0, # links(m8, dirs0), m5, entries -- str);dirs0[ino])).meta, true, (ino = m ⊃ mkdir(m12, md5, m13, m14, entries3);(ino = m8 ⊃ mkdir(m2, md0, # links(m8, dirs0), m5, entries -- str);dirs0[ino])).nlink, (ino = m ⊃ mkdir(m12, md5, m13, m14, entries3);(ino = m8 ⊃ mkdir(m2, md0, # links(m8, dirs0), m5, entries -- str);dirs0[ino])) .nsubdirs, (ino = m ⊃ mkdir(m12, md5, m13, m14, entries3);(ino = m8 ⊃ mkdir(m2, md0, # links(m8, dirs0), m5, entries -- str);dirs0[ino])).size) ;mkinode(ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ) )

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 260:
# 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), icache0[m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0))][m, mkientry(false, mkinode(m, md5, true, m13, m14, m12))][ino] = mkientry(boolvar0, inode), inode = mkinode(m15, md7, boolvar, m16, m17, m18), 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, m15 = ino ∧ (boolvar0 ⊃ ino ∈ files ∧ m16 = files[ino].nlink ∧ m17 = 0 ∧ ¬ boolvar ; (ino ∈ dirs0 ∨ ino ∈ files) ∧ mkinode(ino, md7, boolvar, m16, m17, m18) = (ino ∈ dirs0 ⊃ mkinode (ino, (ino = m ⊃ mkdir(m12, md5, m13, m14, entries3);(ino = m8 ⊃ mkdir(m2, md0, # links(m8, dirs0), m5, entries -- str);dirs0[ino])).meta, true, (ino = m ⊃ mkdir(m12, md5, m13, m14, entries3);(ino = m8 ⊃ mkdir(m2, md0, # links(m8, dirs0), m5, entries -- str);dirs0[ino])).nlink, (ino = m ⊃ mkdir(m12, md5, m13, m14, entries3);(ino = m8 ⊃ mkdir(m2, md0, # links(m8, dirs0), m5, entries -- str);dirs0[ino])) .nsubdirs, (ino = m ⊃ mkdir(m12, md5, m13, m14, entries3);(ino = m8 ⊃ mkdir(m2, md0, # links(m8, dirs0), m5, entries -- str);dirs0[ino])).size) ;mkinode(ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ) )

Rule argument

spec: icache-entry name: elim seq: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode) subst: [ie, boolvar, inode] → [icache0 [m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0)) ] [m, mkientry(false, mkinode(m, md5, true, m13, m14, m12)) ] [ino ], boolvar0, inode]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode); (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 ], boolvar0, inode