[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 7 from proof refine-iget (previous step)

¬ asynced0, err = err0, inode = inode0, 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), ino ∈ cache_dirs ∨ ino ∈ cache_files ⊦ ⟪icache_get#(ino, cache_icache; asynced0, inode, err); afs_files := (cache_files ⊕ cache_pcache) ⊕ cache_icache; if ¬ asynced0 ∨ err ≠ ESUCCESS then {afs_iget#(ino, cache_dirs, cache_files, cache_asynced; inode, err); if err = ESUCCESS then icache_set#(inode, false; err, cache_icache)}⟫ ⟨afs_iget#(ino, cache_dirs, afs_files, cache_asynced; inode0, err0)⟩ (afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ inode = inode0 ∧ err = err0)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 8:
asynced ↔ asynced0, ¬ asynced0, err = err0, icache = cache_icache, inode = inode0, 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), ino ∈ cache_dirs ∨ ino ∈ cache_files ⊦ ⟪if ino ∈ icache then {inode := icache[ino].inode; asynced := true} else asynced := false; err := ESUCCESS; afs_files := (cache_files ⊕ cache_pcache) ⊕ cache_icache; if ¬ asynced ∨ err ≠ ESUCCESS then {afs_iget#(ino, cache_dirs, cache_files, cache_asynced; inode, err); if err = ESUCCESS then icache_set#(inode, false; err, cache_icache)}⟫ ⟨afs_iget#(ino, cache_dirs, afs_files, cache_asynced; inode0, err0)⟩ (afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ inode = inode0 ∧ err = err0)

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 };