[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 36 from proof refine-fsync (previous step)

((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, # links(m, cache_dirs), content), cache_files[m] = mkfile(m3, md1, # links(m, cache_dirs), content0), (cache_files0 ⊕ cache_pcache0) ⊕ cache_icache0 = (cache_files ⊕ cache_pcache) ⊕ cache_icache, afs-cons(cache_dirs, cache_files0), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files0), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache0, cache_dirs, cache_files0), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache0, cache_dirs, cache_files0), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache0, cache_pcache0), synced(cache_dirs, cache_icache, cache_pcache), m ∈ cache_files, cache_sync → synced(cache_files0, cache_icache0, cache_pcache0), cache_sync → synced(cache_files, cache_icache, cache_pcache), err = ESUCCESS ∨ ⌊err⌋ ⊦ ⟨afs_fsync# (mkinode(m, md, false, # links(m, cache_dirs), 0, m2), asynced, cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache; ; afs_asynced, err0)⟩ ((afs_asynced ↔ cache_asynced) ∧ err = err0)

User applied rule call right

And obtained the following new goals

Proof step 37:
asynced0 ↔ asynced, cache_files[m] = mkfile(m3, md1, # links(m, cache_dirs), content0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, # links(m, cache_dirs), content), dirs = cache_dirs, files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, inode = mkinode(m, md, false, # links(m, cache_dirs), 0, m2), (cache_files0 ⊕ cache_pcache0) ⊕ cache_icache0 = (cache_files ⊕ cache_pcache) ⊕ cache_icache, afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, cache_files0), dcache-cons(cache_dcache, cache_dirs, cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files0), icache-cons(cache_icache, cache_dirs, cache_files), icache-cons(cache_icache0, cache_dirs, cache_files0), pcache-cons(cache_pcache, cache_dirs, cache_files), pcache-cons(cache_pcache0, cache_dirs, cache_files0), synced(cache_dirs, cache_icache, cache_pcache), synced(cache_dirs, cache_icache0, cache_pcache0), m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache), cache_sync → synced(cache_files0, cache_icache0, cache_pcache0), err1 = ESUCCESS ∨ ⌊err1⌋ ⊦ ⟨if valid-file-inode(inode, dirs, files) then {fail_or_success#(; ; err); choose bv with true in asynced := bv} else abort⟩ ((asynced ↔ cache_asynced) ∧ err1 = err)

Rule argument

pos: right 1

Additional information

Used simplifier rules: afs_fsync#(INODE, ISDATASYNC, DIRS, FILES; ; ASYNCED, ERR) {if valid-file-inode(INODE, DIRS, FILES) then {fail_or_success#(; ; ERR); choose bv with true in ASYNCED := bv} else abort };