[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 79 from proof refine-mkdir (previous step)

(ino0 ∈ cache_dirs0[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m2 + 1, entries[str, ino0])] ++ ino0 ⊃ mkinode (ino0, (ino0 = m1 ⊃ mkdir(m, md2, m3, m4, entries0);mkdir(0, md, 1, 0, ∅)).meta, true, (ino0 = m1 ⊃ mkdir(m, md2, m3, m4, entries0);mkdir(0, md, 1, 0, ∅)).nlink, (ino0 = m1 ⊃ mkdir(m, md2, m3, m4, entries0);mkdir(0, md, 1, 0, ∅)).nsubdirs, (ino0 = m1 ⊃ mkdir(m, md2, m3, m4, entries0);mkdir(0, md, 1, 0, ∅)).size) ;mkinode(ino0, cache_files[ino0].meta, false, cache_files[ino0].nlink, 0, cache_files[ino0].size) ) = mkinode(m5, md3, boolvar, m6, m7, m8), (cache_dirs[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs), m2 + 1, entries[str, ino0])] ++ ino0)[m1] = mkdir(m, md0, m3, m4, entries0), cache_dirs[m1] = mkdir(m0, md1, # links(m1, cache_dirs), m2, 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), m2, 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_mkdir#(md; p_inode0, p_inode1, dent0, err0, cache_dirs, afs_files; afs_asynced)⟩ ( cache_dirs = (cache_dirs0[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m2 + 1, entries[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m1, (m1 = ino0 ∧ ino0 ∈ cache_dirs0[ino0, mkdir(m0 + 1, md1, # links(ino0, cache_dirs0), m2 + 1, entries[str, ino0])] ++ ino0 ⊃ mkdir(0, md, 1, 0, ∅) ;(cache_dirs0[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m2 + 1, entries[str, ino0])] ++ ino0)[m1] ) .meta:= md2 ] ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache[m1, mkientry(false, mkinode(m1, md2, true, m3, m4, m))] [m5, mkientry (false, (ino0 ∈ cache_dirs0[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m2 + 1, entries[str, ino0])] ++ ino0 ⊃ mkinode (ino0, (ino0 = m1 ⊃ mkdir(m, md2, m3, m4, entries0);mkdir(0, md, 1, 0, ∅)).meta, true, (ino0 = m1 ⊃ mkdir(m, md2, m3, m4, entries0);mkdir(0, md, 1, 0, ∅)).nlink, (ino0 = m1 ⊃ mkdir(m, md2, m3, m4, entries0);mkdir(0, md, 1, 0, ∅)).nsubdirs, (ino0 = m1 ⊃ mkdir(m, md2, m3, m4, entries0);mkdir(0, md, 1, 0, ∅)).size) ;mkinode(ino0, cache_files[ino0].meta, false, cache_files[ino0].nlink, 0, cache_files[ino0].size) )) ] ∧ (afs_asynced ↔ asynced0) ∧ (m1 ∈ cache_dirs0[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m2 + 1, entries[str, ino0])] ++ ino0 ⊃ mkinode (m1, md2, true, (m1 = ino0 ⊃ mkdir(0, md, 1, 0, ∅) ;(cache_dirs0[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m2 + 1, entries[str, ino0])] ++ ino0)[m1] ) .nlink, (m1 = ino0 ⊃ mkdir(0, md, 1, 0, ∅) ;(cache_dirs0[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m2 + 1, entries[str, ino0])] ++ ino0)[m1] ) .nsubdirs, (m1 = ino0 ⊃ mkdir(0, md, 1, 0, ∅) ;(cache_dirs0[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m2 + 1, entries[str, ino0])] ++ ino0)[m1] ) .size) ;mkinode(m1, cache_files[m1].meta, false, cache_files[m1].nlink, 0, cache_files[m1].size) ) = p_inode0 ∧ (ino0 ∈ cache_dirs0[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m2 + 1, entries[str, ino0])] ++ ino0 ⊃ mkinode (ino0, (ino0 = m1 ⊃ mkdir(0, md2, 1, 0, ∅);mkdir(0, md, 1, 0, ∅)).meta, true, (ino0 = m1 ⊃ mkdir(0, md2, 1, 0, ∅);mkdir(0, md, 1, 0, ∅)).nlink, (ino0 = m1 ⊃ mkdir(0, md2, 1, 0, ∅);mkdir(0, md, 1, 0, ∅)).nsubdirs, (ino0 = m1 ⊃ mkdir(0, md2, 1, 0, ∅);mkdir(0, md, 1, 0, ∅)).size) ;mkinode(ino0, cache_files[ino0].meta, false, cache_files[ino0].nlink, 0, cache_files[ino0].size) ) = p_inode1 ∧ mkdentry(str, ino0) = dent0 ∧ ESUCCESS = err0), ino0 = 0, ino0 ∈ cache_dirs, ino0 ∈ cache_files, str ∈ entries

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 80:
(cache_dirs[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs), m2 + 1, entries[str, m5])] ++ m5)[m1] = mkdir(m, md0, m3, m4, entries0), cache_dirs[m1] = mkdir(m0, md1, # links(m1, cache_dirs), m2, 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), m2, m0), m5 ≠ 0, 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, ¬ m5 ∈ cache_dirs, ¬ m5 ∈ cache_files, ¬ str ∈ entries, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m1, cache_dirs) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ⟨afs_mkdir#(md3; p_inode0, p_inode1, dent0, err0, cache_dirs, afs_files; afs_asynced)⟩ ( cache_dirs = (cache_dirs0[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m2 + 1, entries[str, m5])] ++ m5)[m5, mkdir(0, md3, 1, 0, ∅)] [m1, (m1 = m5 ∧ m5 ∈ cache_dirs0[m5, mkdir(m0 + 1, md1, # links(m5, cache_dirs0), m2 + 1, entries[str, m5])] ++ m5 ⊃ mkdir(0, md3, 1, 0, ∅) ;(cache_dirs0[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m2 + 1, entries[str, m5])] ++ m5)[m1] ) .meta:= md2 ] ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache[m1, mkientry(false, mkinode(m1, md2, true, m3, m4, m))] [m5, mkientry (false, (m5 ∈ cache_dirs0[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m2 + 1, entries[str, m5])] ++ m5 ⊃ mkinode (m5, (m5 = m1 ⊃ mkdir(m, md2, m3, m4, entries0);mkdir(0, md3, 1, 0, ∅)).meta, true, (m5 = m1 ⊃ mkdir(m, md2, m3, m4, entries0);mkdir(0, md3, 1, 0, ∅)).nlink, (m5 = m1 ⊃ mkdir(m, md2, m3, m4, entries0);mkdir(0, md3, 1, 0, ∅)).nsubdirs, (m5 = m1 ⊃ mkdir(m, md2, m3, m4, entries0);mkdir(0, md3, 1, 0, ∅)).size) ;mkinode(m5, cache_files[m5].meta, false, cache_files[m5].nlink, 0, cache_files[m5].size) )) ] ∧ (afs_asynced ↔ asynced0) ∧ (m1 ∈ cache_dirs0[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m2 + 1, entries[str, m5])] ++ m5 ⊃ mkinode (m1, md2, true, (m1 = m5 ⊃ mkdir(0, md3, 1, 0, ∅) ;(cache_dirs0[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m2 + 1, entries[str, m5])] ++ m5)[m1] ) .nlink, (m1 = m5 ⊃ mkdir(0, md3, 1, 0, ∅) ;(cache_dirs0[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m2 + 1, entries[str, m5])] ++ m5)[m1] ) .nsubdirs, (m1 = m5 ⊃ mkdir(0, md3, 1, 0, ∅) ;(cache_dirs0[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m2 + 1, entries[str, m5])] ++ m5)[m1] ) .size) ;mkinode(m1, cache_files[m1].meta, false, cache_files[m1].nlink, 0, cache_files[m1].size) ) = p_inode0 ∧ (m5 ∈ cache_dirs0[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m2 + 1, entries[str, m5])] ++ m5 ⊃ mkinode (m5, (m5 = m1 ⊃ mkdir(0, md2, 1, 0, ∅);mkdir(0, md3, 1, 0, ∅)).meta, true, (m5 = m1 ⊃ mkdir(0, md2, 1, 0, ∅);mkdir(0, md3, 1, 0, ∅)).nlink, (m5 = m1 ⊃ mkdir(0, md2, 1, 0, ∅);mkdir(0, md3, 1, 0, ∅)).nsubdirs, (m5 = m1 ⊃ mkdir(0, md2, 1, 0, ∅);mkdir(0, md3, 1, 0, ∅)).size) ;mkinode(m5, cache_files[m5].meta, false, cache_files[m5].nlink, 0, cache_files[m5].size) ) = p_inode1 ∧ mkdentry(str, m5) = dent0 ∧ ESUCCESS = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2) = mkinode(m3, md0, boolvar0, m4, m5, m6) ↔ m = m3 ∧ md = md0 ∧ (boolvar ↔ boolvar0) ∧ m0 = m4 ∧ m1 = m5 ∧ m2 = m6; (ws)% ⊦ 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)%ino ≠ 0, ¬ ino ∈ dirs ⊦ ino0 ∈ dirs ++ ino ↔ ino0 = ino ∨ ino0 ∈ dirs; (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)