[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 29 from proof inv-write_inode (previous step)

dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), ¬ asynced3, err = ESUCCESS, afs-cons(dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ dirs, asynced2 → synced(files, icache, pcache) ⊦ ⟪icache_get#(m, icache; asynced3, inode1, err); if err = ESUCCESS ∧ asynced3 then {inode1.meta := md; skip; icache_set#(inode1, false; err, icache)} else if false then err := EFAIL⟫ ( icache-cons(icache, dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files) ∧ dcache-cons(dcache, dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files) ∧ pcache-cons(pcache, dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files) ∧ synced(dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], icache, pcache) ∧ (asynced2 → synced(files, icache, pcache)))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 30:
asynced ↔ asynced3, dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), ¬ asynced3, err = ESUCCESS, ino = m, inode = inode1, afs-cons(dirs, files), afs-cons(dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ dirs, asynced2 → synced(files, icache, pcache) ⊦ ⟪if ino ∈ icache then {inode := icache[ino].inode; asynced := true} else asynced := false; err := ESUCCESS; if err = ESUCCESS ∧ asynced then {inode1 := inode.meta:= md; skip; icache_set#(inode1, false; err, icache)} else if false then err := EFAIL⟫ ( icache-cons(icache, dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files) ∧ dcache-cons(dcache, dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files) ∧ pcache-cons(pcache, dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files) ∧ synced(dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], icache, pcache) ∧ (asynced2 → synced(files, icache, pcache)))

Rule argument

pos: right 1

Additional information

Used simplifier rules: icache_get#(INO, ICACHE; HIT, INODE, ERR) {if INO ∈ ICACHE then {INODE := ICACHE[INO].inode; HIT := true} else HIT := false; ERR := ESUCCESS };