[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 10 from proof refine-write_inode (previous step)

afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = err0, 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), cache_sync → synced(cache_files, cache_icache, cache_pcache), m ∈ cache_dirs ∧ m0 = cache_dirs[m].nlink ∧ m2 = cache_dirs[m].size ∧ m1 = cache_dirs[m].nsubdirs ∧ boolvar ∨ m ∈ cache_files ∧ m0 = ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m].nlink ∧ m1 = 0 ∧ ¬ boolvar, m ∈ cache_dirs ∧ m0 = cache_dirs[m].nlink ∧ m2 = cache_dirs[m].size ∧ m1 = cache_dirs[m].nsubdirs ∧ boolvar ∨ m ∈ cache_files ∧ m0 = cache_files[m].nlink ∧ m1 = 0 ∧ ¬ boolvar, cache_sync ∨ boolvar ⊦ ⟪afs_write_inode#(mkinode(m, md, boolvar, m0, m1, m2); err, cache_dirs, cache_files; asynced1); asynced0 := false; inode0 := mkinode(m, md, boolvar, m0, m1, m2); asynced := false; if err = ESUCCESS then icache_get#(inode0.ino, cache_icache; asynced, inode, err); if err = ESUCCESS ∧ asynced then {inode.meta := inode0.meta; if ¬ inode0.directory then inode.size := inode0.size; icache_set#(inode, asynced0; err, cache_icache)} else if asynced0 then err := EFAIL⟫ ⟨afs_write_inode#(mkinode(m, md, boolvar, m0, m1, m2); err0, afs_dirs, afs_files; afs_asynced)⟩ (afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced1) ∧ err = err0)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 11:
afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, dirs = cache_dirs, err = err0, files = cache_files, inode = mkinode(m, md, boolvar, m0, m1, m2), 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), cache_sync → synced(cache_files, cache_icache, cache_pcache), cache_sync ∨ boolvar, m ∈ cache_dirs ∧ m0 = cache_dirs[m].nlink ∧ m2 = cache_dirs[m].size ∧ m1 = cache_dirs[m].nsubdirs ∧ boolvar ∨ m ∈ cache_files ∧ m0 = cache_files[m].nlink ∧ m1 = 0 ∧ ¬ boolvar, m ∈ cache_dirs ∧ m0 = cache_dirs[m].nlink ∧ m2 = cache_dirs[m].size ∧ m1 = cache_dirs[m].nsubdirs ∧ boolvar ∨ m ∈ cache_files ∧ m0 = ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m].nlink ∧ m1 = 0 ∧ ¬ boolvar ⊦ ⟪if pre-write-inode(inode, dirs, files) then { {if inode.directory then dirs[inode.ino].meta := inode.meta else {files[inode.ino].meta := inode.meta; files[inode.ino].size := inode.size}; err := ESUCCESS} or fail#(; ; err); asynced := ?} else abort; asynced0 := false; inode0 := mkinode(m, md, boolvar, m0, m1, m2); asynced2 := false; if err = ESUCCESS then icache_get#(inode0.ino, cache_icache; asynced2, inode, err); if err = ESUCCESS ∧ asynced2 then {inode.meta := inode0.meta; if ¬ inode0.directory then inode.size := inode0.size; icache_set#(inode, asynced0; err, cache_icache)} else if asynced0 then err := EFAIL⟫ ⟨afs_write_inode#(mkinode(m, md, boolvar, m0, m1, m2); err0, afs_dirs, afs_files; afs_asynced)⟩ (afs_dirs = dirs ∧ afs_files = (files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced) ∧ err = err0)

Rule argument

pos: right 1

Additional information

Used simplifier rules: afs_write_inode#(INODE; ERR, DIRS, FILES; ASYNCED) {if pre-write-inode(INODE, DIRS, FILES) then { {if INODE.directory then DIRS[INODE.ino].meta := INODE.meta else {FILES[INODE.ino].meta := INODE.meta; FILES[INODE.ino].size := INODE.size}; ERR := ESUCCESS} or fail#(; ; ERR); ASYNCED := ?} else abort };