[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 199 from proof inv-rmdir (previous step)

icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, true, m8, m9, m))][m5, mkientry(false, mkinode(m5, md5, true, m11, m12, m10))] [ino ] .inode = mkinode(m13, md6, boolvar, m14, m15, m16), (m5 = entries0[str] ⊃ mkdir(m3, md0, m7, m6, entries);mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str)) = mkdir(m10, md5, m11, m12, entries2), (entries0[str] = m5 ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)) = mkdir(m, md4, m8, m9, entries1), (entries0[str] = m5 ⊃ mkdir(m0 - 1, md1, # links(entries0[str], dirs0), m2 - 1, entries0 -- str) ;mkdir(m1, md3, # links(entries0[str], dirs0), m4, ∅) ) = mkdir(m3, md2, m7 + 1, m6, entries), dirs0[m5] = mkdir(m0, md1, # links(m5, dirs0), m2, entries0), dirs0[entries0[str]] = mkdir(m1, md3, # links(entries0[str], dirs0), m4, ∅), afs-cons (dirs0[m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], mkdir(m, md0, m8, m9, entries1) ], files), afs-cons(dirs0, files), icache-cons(icache0, dirs0, files), synced(dirs0, icache0, pcache), m5 ∈ dirs0, str ∈ entries0, entries0[str] ∈ dirs0, ino ∈ icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, true, m8, m9, m))][m5, mkientry(false, mkinode(m5, md5, true, m11, m12, m10))], 1 ≤ m0, 1 ≤ m2, asynced1 → synced(files, icache0, pcache), links(m5, dirs0) ≠ ∅ ∨ m5 = ROOT_INO ⊦ entries0[str] = ROOT_INO, m0 = 0, m2 = 0, m13 = ino ∧ (icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, true, m8, m9, m))][m5, mkientry(false, mkinode(m5, md5, true, m11, m12, m10))] [ino ] .dirty ⊃ ino ∈ files ∧ m14 = files[ino].nlink ∧ m15 = 0 ∧ ¬ boolvar ; (ino ∈ dirs0 ∨ ino ∈ files) ∧ mkinode(ino, md6, boolvar, m14, m15, m16) = (ino ∈ dirs0 ⊃ mkinode (ino, (ino = entries0[str] ⊃ mkdir(m, md0, m8, m9, entries1) ;(ino = m5 ⊃ mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str);dirs0[ino]) ) .meta, true, (ino = entries0[str] ⊃ mkdir(m, md0, m8, m9, entries1) ;(ino = m5 ⊃ mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str);dirs0[ino]) ) .nlink, (ino = entries0[str] ⊃ mkdir(m, md0, m8, m9, entries1) ;(ino = m5 ⊃ mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str);dirs0[ino]) ) .nsubdirs, (ino = entries0[str] ⊃ mkdir(m, md0, m8, m9, entries1) ;(ino = m5 ⊃ mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- 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 200:
(entries0[str] = m5 ⊃ mkdir(m0 - 1, md1, # links(entries0[str], dirs0), m2 - 1, entries0 -- str) ;mkdir(m1, md3, # links(entries0[str], dirs0), m4, ∅) ) = mkdir(m3, md2, m7 + 1, m6, entries), (entries0[str] = m5 ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)) = mkdir(m, md4, m8, m9, entries1), (m5 = entries0[str] ⊃ mkdir(m3, md0, m7, m6, entries);mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str)) = mkdir(m10, md5, m11, m12, entries2), dirs0[entries0[str]] = mkdir(m1, md3, # links(entries0[str], dirs0), m4, ∅), dirs0[m5] = mkdir(m0, md1, # links(m5, dirs0), m2, entries0), icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, true, m8, m9, m))][m5, mkientry(false, mkinode(m5, md5, true, m11, m12, m10))] [ino ] = mkientry(boolvar0, inode), inode = mkinode(m13, md6, boolvar, m14, m15, m16), afs-cons(dirs0, files), afs-cons (dirs0[m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], mkdir(m, md0, m8, m9, entries1) ], files), icache-cons(icache0, dirs0, files), synced(dirs0, icache0, pcache), ino ∈ icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, true, m8, m9, m))][m5, mkientry(false, mkinode(m5, md5, true, m11, m12, m10))], entries0[str] ∈ dirs0, str ∈ entries0, m5 ∈ dirs0, 1 ≤ m2, 1 ≤ m0, asynced1 → synced(files, icache0, pcache), links(m5, dirs0) ≠ ∅ ∨ m5 = ROOT_INO ⊦ entries0[str] = ROOT_INO, m0 = 0, m2 = 0, m13 = ino ∧ (boolvar0 ⊃ ino ∈ files ∧ m14 = files[ino].nlink ∧ m15 = 0 ∧ ¬ boolvar ; (ino ∈ dirs0 ∨ ino ∈ files) ∧ mkinode(ino, md6, boolvar, m14, m15, m16) = (ino ∈ dirs0 ⊃ mkinode (ino, (ino = entries0[str] ⊃ mkdir(m, md0, m8, m9, entries1) ;(ino = m5 ⊃ mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str);dirs0[ino]) ) .meta, true, (ino = entries0[str] ⊃ mkdir(m, md0, m8, m9, entries1) ;(ino = m5 ⊃ mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str);dirs0[ino]) ) .nlink, (ino = entries0[str] ⊃ mkdir(m, md0, m8, m9, entries1) ;(ino = m5 ⊃ mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str);dirs0[ino]) ) .nsubdirs, (ino = entries0[str] ⊃ mkdir(m, md0, m8, m9, entries1) ;(ino = m5 ⊃ mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- 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 [entries0[str], mkientry (false, mkinode(entries0[str], md0, true, m8, m9, m)) ] [m5, mkientry(false, mkinode(m5, md5, true, m11, m12, m10)) ] [ino ], boolvar0, inode]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode); (elim) Used terms: icache0 [entries0[str], mkientry(false, mkinode(entries0[str], md0, true, m8, m9, m)) ] [m5, mkientry(false, mkinode(m5, md5, true, m11, m12, m10)) ] [ino ], boolvar0, inode