[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 75 from proof refine-create (previous step)

cache_dirs[m1] = mkdir(m0, md1, # links(m1, cache_dirs), m4, entries), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_dirs0 = cache_dirs, dent0 = negdentry(str), p_inode0 = mkinode(m1, md2, true, # links(m1, cache_dirs), m4, m0), ino0 ≠ 0, afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), m1 ∈ cache_dirs, ¬ str ∈ entries, ¬ ino0 ∈ cache_files, ¬ ino0 ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m1, cache_dirs) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ⟨afs_create#(md; p_inode0, p_inode1, dent0, err0, cache_dirs, afs_files; afs_asynced)⟩ ( cache_dirs = cache_dirs0[m1, (m1 ∈ cache_dirs0 ⊃ mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m4, entries[str, ino0]);cache_dirs0[m1]).meta:= md2] ∧ afs_files = ((cache_files ++ ino0)[ino0, mkfile(0, md, 1, ∅)] ⊕ cache_pcache) ⊕ cache_icache[m1, mkientry(false, mkinode(m1, md2, true, # links(m1, cache_dirs0), m4, m0 + 1))] [(ino0 ∈ cache_dirs0 ⊃ mkinode (ino0, (ino0 = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[ino0]).meta, true, (ino0 = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[ino0]).nlink, (ino0 = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[ino0]).nsubdirs, (ino0 = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[ino0]).size) ;mkinode(ino0, md, false, 1, 0, 0) ) .ino, mkientry (false, (ino0 ∈ cache_dirs0 ⊃ mkinode (ino0, (ino0 = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[ino0]).meta, true, (ino0 = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[ino0]).nlink, (ino0 = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[ino0]).nsubdirs, (ino0 = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[ino0]).size) ;mkinode(ino0, md, false, 1, 0, 0) )) ] ∧ (afs_asynced ↔ asynced0) ∧ (m1 ∈ cache_dirs0 ⊃ mkinode(m1, md2, true, # links(m1, cache_dirs0), m4, m0 + 1) ;mkinode (m1, (m1 = ino0 ⊃ mkfile(0, md, 1, ∅);(cache_files ++ ino0)[m1]).meta, false, (m1 = ino0 ⊃ mkfile(0, md, 1, ∅);(cache_files ++ ino0)[m1]).nlink, 0, (m1 = ino0 ⊃ mkfile(0, md, 1, ∅);(cache_files ++ ino0)[m1]).size) ) = p_inode0 ∧ (ino0 ∈ cache_dirs0 ⊃ mkinode (ino0, (ino0 = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[ino0]).meta, true, (ino0 = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[ino0]).nlink, (ino0 = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[ino0]).nsubdirs, (ino0 = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[ino0]).size) ;mkinode(ino0, md, false, 1, 0, 0) ) = p_inode1 ∧ mkdentry(str, ino0) = dent0 ∧ ESUCCESS = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 76:
(ino0 ∈ cache_dirs0 ⊃ mkinode (ino0, (ino0 = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[ino0]).meta, true, (ino0 = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[ino0]).nlink, (ino0 = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[ino0]).nsubdirs, (ino0 = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[ino0]).size) ;mkinode(ino0, md, false, 1, 0, 0) ) = mkinode(m, md0, boolvar, m2, m3, m5), cache_dirs[m1] = mkdir(m0, md1, # links(m1, cache_dirs), m4, entries), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_dirs0 = cache_dirs, dent0 = negdentry(str), p_inode0 = mkinode(m1, md2, true, # links(m1, cache_dirs), m4, m0), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), m1 ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m1, cache_dirs) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ⟨afs_create#(md; p_inode0, p_inode1, dent0, err0, cache_dirs, afs_files; afs_asynced)⟩ ( cache_dirs = cache_dirs0[m1, (m1 ∈ cache_dirs0 ⊃ mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m4, entries[str, ino0]);cache_dirs0[m1]).meta:= md2] ∧ afs_files = ((cache_files ++ ino0)[ino0, mkfile(0, md, 1, ∅)] ⊕ cache_pcache) ⊕ cache_icache[m1, mkientry(false, mkinode(m1, md2, true, # links(m1, cache_dirs0), m4, m0 + 1))] [m, mkientry (false, (ino0 ∈ cache_dirs0 ⊃ mkinode (ino0, (ino0 = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[ino0]).meta, true, (ino0 = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[ino0]).nlink, (ino0 = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[ino0]).nsubdirs, (ino0 = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[ino0]).size) ;mkinode(ino0, md, false, 1, 0, 0) )) ] ∧ (afs_asynced ↔ asynced0) ∧ (m1 ∈ cache_dirs0 ⊃ mkinode(m1, md2, true, # links(m1, cache_dirs0), m4, m0 + 1) ;mkinode (m1, (m1 = ino0 ⊃ mkfile(0, md, 1, ∅);(cache_files ++ ino0)[m1]).meta, false, (m1 = ino0 ⊃ mkfile(0, md, 1, ∅);(cache_files ++ ino0)[m1]).nlink, 0, (m1 = ino0 ⊃ mkfile(0, md, 1, ∅);(cache_files ++ ino0)[m1]).size) ) = p_inode0 ∧ (ino0 ∈ cache_dirs0 ⊃ mkinode (ino0, (ino0 = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[ino0]).meta, true, (ino0 = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[ino0]).nlink, (ino0 = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[ino0]).nsubdirs, (ino0 = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[ino0]).size) ;mkinode(ino0, md, false, 1, 0, 0) ) = p_inode1 ∧ mkdentry(str, ino0) = dent0 ∧ ESUCCESS = err0), ino0 = 0, str ∈ entries, ino0 ∈ cache_files, ino0 ∈ cache_dirs

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] → [(ino0 ∈ cache_dirs0 ⊃ mkinode (ino0, (ino0 = m1 ⊃ mkdir (m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]) ;cache_dirs0[ino0] ) .meta, true, (ino0 = m1 ⊃ mkdir (m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]) ;cache_dirs0[ino0] ) .nlink, (ino0 = m1 ⊃ mkdir (m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]) ;cache_dirs0[ino0] ) .nsubdirs, (ino0 = m1 ⊃ mkdir (m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]) ;cache_dirs0[ino0] ) .size) ;mkinode(ino0, md, false, 1, 0, 0) ), m, md0, boolvar, m2, m3, m5]

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: (ino0 ∈ cache_dirs0 ⊃ mkinode (ino0, (ino0 = m1 ⊃ mkdir (m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]) ;cache_dirs0[ino0] ) .meta, true, (ino0 = m1 ⊃ mkdir (m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]) ;cache_dirs0[ino0] ) .nlink, (ino0 = m1 ⊃ mkdir (m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]) ;cache_dirs0[ino0] ) .nsubdirs, (ino0 = m1 ⊃ mkdir (m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]) ;cache_dirs0[ino0] ) .size) ;mkinode(ino0, md, false, 1, 0, 0) ), m, md0, boolvar, m2, m3, m5