[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 86 from proof inv-rmdir (previous step)

(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), asynced ↔ false, dirs0[m5] = mkdir(m0, md1, # links(m5, dirs0), m2, entries0), dirs0[entries0[str]] = mkdir(m1, md3, # links(entries0[str], dirs0), m4, ∅), err = ESUCCESS, icache = icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, true, m8, m9, m))], inode = ( m5 ∈ dirs0[m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md] ⊃ mkinode (m5, 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], dirs0[entries0[str], mkdir(m3, md2, m7, m6, entries)] [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] ] .meta:= md0 ] [m5 ] .meta, true, 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], dirs0[entries0[str], mkdir(m3, md2, m7, m6, entries)] [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] ] .meta:= md0 ] [m5 ] .nlink, 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], dirs0[entries0[str], mkdir(m3, md2, m7, m6, entries)] [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] ] .meta:= md0 ] [m5 ] .nsubdirs, 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], dirs0[entries0[str], mkdir(m3, md2, m7, m6, entries)] [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] ] .meta:= md0 ] [m5 ] .size) ;mkinode(m5, files[m5].meta, false, files[m5].nlink, 0, files[m5].size) ), 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), dcache-cons(dcache, dirs0, files), icache-cons(icache0, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache0, pcache), m5 ∈ dirs0, str ∈ entries0, entries0[str] ∈ dirs0, 1 ≤ m0, 1 ≤ m2, asynced1 → synced(files, icache0, pcache), (m5 = entries0[str] ⊃ true;m0 ≥ 1 ∧ m2 ≥ 1), (m5 ∈ dirs0[m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md] ⊃ ( (str ∈ entries0 ∧ (m5 = entries0[str] ⊃ true;m0 ≥ 1 ∧ m2 ≥ 1)) ∧ str ∈ entries0 ∧ (str ∈ entries0 ∧ str ∈ entries0 ∧ (m5 = entries0[str] ⊃ true;m0 ≥ 1 ∧ m2 ≥ 1)) ∧ str ∈ entries0) ∧ ( (str ∈ entries0 ∧ (m5 = entries0[str] ⊃ true;m0 ≥ 1 ∧ m2 ≥ 1)) ∧ str ∈ entries0 ∧ (str ∈ entries0 ∧ str ∈ entries0 ∧ (m5 = entries0[str] ⊃ true;m0 ≥ 1 ∧ m2 ≥ 1)) ∧ str ∈ entries0) ∧ ( (str ∈ entries0 ∧ (m5 = entries0[str] ⊃ true;m0 ≥ 1 ∧ m2 ≥ 1)) ∧ str ∈ entries0 ∧ (str ∈ entries0 ∧ str ∈ entries0 ∧ (m5 = entries0[str] ⊃ true;m0 ≥ 1 ∧ m2 ≥ 1)) ∧ str ∈ entries0) ∧ (str ∈ entries0 ∧ (m5 = entries0[str] ⊃ true;m0 ≥ 1 ∧ m2 ≥ 1)) ∧ str ∈ entries0 ∧ (str ∈ entries0 ∧ str ∈ entries0 ∧ (m5 = entries0[str] ⊃ true;m0 ≥ 1 ∧ m2 ≥ 1)) ∧ str ∈ entries0 ;true ), links(m5, dirs0) ≠ ∅ ∨ m5 = ROOT_INO ⊦ ⟪icache[inode.ino] := mkientry(asynced, inode); dcache_delete#(m5, mkdentry(str, entries0[str]).name; err, dcache)⟫ ( icache-cons (icache, 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], (entries0[str] = m5 ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)).meta:= md0 ], files) ∧ dcache-cons (dcache, 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], (entries0[str] = m5 ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)).meta:= md0 ], files) ∧ pcache-cons (pcache, 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], (entries0[str] = m5 ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)).meta:= md0 ], files) ∧ synced (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], (entries0[str] = m5 ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)).meta:= md0 ], icache, pcache) ∧ (asynced1 → synced(files, icache, pcache))), entries0[str] = ROOT_INO, m0 = 0, m2 = 0

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Rule argument

Additional information