[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 159 from proof refine-rmdir (previous step)

(entries3[str] = m6 ⊃ mkdir(m5, md, m3, m7, entries);mkdir(m5, md2, m3, m7, entries)) = mkdir(m, md4, m8, m9, entries1), (entries3[str] = m6 ⊃ mkdir(m0, md6, # links(entries3[str], cache_dirs), m1, entries3 -- str) ;mkdir(m2, md1, # links(entries3[str], cache_dirs), m13, ∅) ) = mkdir(m5, md2, m3 + 1, m7, entries), (m6 = entries3[str] ⊃ mkdir(m5, md0, m3, m7, entries);mkdir(m0, md, # links(m6, cache_dirs), m1, entries3 -- str)) = mkdir(m4, md3, m14, m15, entries0), cache_dirs[entries3[str]] = mkdir(m2, md1, # links(entries3[str], cache_dirs), m13, ∅), cache_dirs[m6] = mkdir(m0 + 1, md6, # links(m6, cache_dirs), m1 + 1, entries3), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, dirs = cache_dirs[entries3[str], mkdir(m5, md2, m3, m7, entries)] [m6, (m6 = entries3[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md6, # links(m6, cache_dirs), m1, entries3 -- str)).meta:= md ], files = afs_files, ino = inode.ino, inode = mkinode(entries3[str], md0, true, # links(entries3[str], cache_dirs), m13, m2), afs-cons (cache_dirs[m6, (m6 = entries3[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md6, # links(m6, cache_dirs), m1, entries3 -- str)).meta:= md] [entries3[str], mkdir(m, md0, m8, m9, entries1) ], cache_files), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons (cache_dcache -- dentrykey(m6, str), cache_dirs[m6, (m6 = entries3[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md6, # links(m6, cache_dirs), m1, entries3 -- str)).meta:= md] [entries3[str], mkdir(m, md0, m8, m9, entries1) ], cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons (cache_icache[entries3[str], mkientry(false, mkinode(entries3[str], md0, true, m8, m9, m))][m6, mkientry(false, mkinode(m6, md3, true, m14, m15, m4))], cache_dirs[m6, (m6 = entries3[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md6, # links(m6, cache_dirs), m1, entries3 -- str)).meta:= md] [entries3[str], mkdir(m, md0, m8, m9, entries1) ], cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons (cache_pcache, cache_dirs[m6, (m6 = entries3[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md6, # links(m6, cache_dirs), m1, entries3 -- str)).meta:= md] [entries3[str], mkdir(m, md0, m8, m9, entries1) ], cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), synced (cache_dirs[m6, (m6 = entries3[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md6, # links(m6, cache_dirs), m1, entries3 -- str)).meta:= md] [entries3[str], mkdir(m, md0, m8, m9, entries1) ], cache_icache[entries3[str], mkientry(false, mkinode(entries3[str], md0, true, m8, m9, m))][m6, mkientry(false, mkinode(m6, md3, true, m14, m15, m4))], cache_pcache), m6 ∈ cache_dirs, entries3[str] ∈ cache_dirs, str ∈ entries3, ino ∈ dirs, cache_sync → synced (cache_files, cache_icache[entries3[str], mkientry(false, mkinode(entries3[str], md0, true, m8, m9, m))] [m6, mkientry(false, mkinode(m6, md3, true, m14, m15, m4)) ], cache_pcache), cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m6, cache_dirs) ≠ ∅ ∨ m6 = ROOT_INO ⊦ entries3[str] = ROOT_INO, ino ∈ files, ∃ asynced. dirs[ino, dirs[ino].meta:= inode.meta] = cache_dirs [m6, (m6 = entries3[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md6, # links(m6, cache_dirs), m1, entries3 -- str)).meta:= md ] [entries3[str], (entries3[str] = m6 ⊃ mkdir(m5, md, m3, m7, entries);mkdir(m5, md2, m3, m7, entries)).meta:= md0 ] ∧ files = (cache_files ⊕ cache_pcache) ⊕ cache_icache[entries3[str], mkientry(false, mkinode(entries3[str], md0, true, m8, m9, m))] [m6, mkientry(false, mkinode(m6, md3, true, m14, m15, m4)) ] ∧ (asynced ↔ asynced0) ∧ mkinode(m6, md3, true, m14, m15, m4) = (m6 ∈ dirs[ino, dirs[ino].meta:= inode.meta] ⊃ mkinode (m6, dirs[ino, dirs[ino].meta:= inode.meta][m6].meta, true, dirs[ino, dirs[ino].meta:= inode.meta][m6].nlink, dirs[ino, dirs[ino].meta:= inode.meta][m6].nsubdirs, dirs[ino, dirs[ino].meta:= inode.meta][m6].size) ;mkinode(m6, files[m6].meta, false, files[m6].nlink, 0, files[m6].size) ) ∧ mkinode(entries3[str], md0, true, m8, m9, m) = getinode(entries3[str], dirs[ino, dirs[ino].meta:= inode.meta], files) ∧ ESUCCESS = ESUCCESS

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries).size = m; (s)% ⊦ mkdir(m, md, m0, m1, entries).nsubdirs = m1; (s)% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)% ⊦ mkdir(m, md, m0, m1, entries).meta = md; (s)% ⊦ (ad.meta:= md).size = ad.size; (s)% ⊦ (ad.meta:= md).nsubdirs = ad.nsubdirs; (s)% ⊦ (ad.meta:= md).nlink = ad.nlink; (s)% ⊦ (ad.meta:= md).meta = md; (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)% ⊦ dirs[ino, ad][ino0, ad0][ino, ad1] = dirs[ino0, ad0][ino, ad1]; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)%⊦ mkdir(m, md, m0, m1, entries).meta:= md0 = mkdir(m, md0, m0, m1, entries); (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)%⊦ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) ∧ str ∈ entries ∧ afs-cons(dirs, files) → (entries[str] ∈ files ↔ ¬ entries[str] ∈ dirs); (ss)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)