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Proof step 233 from proof refine-write_inode (previous step)

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, 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 ⊦ ⟪fail#(; ; err); asynced := ?; asynced0 := false; inode0 := mkinode(m, md, boolvar, m0, m1, m2); asynced2 := false; inode := mkinode(m, md, boolvar, m0, m1, m2); if err = ESUCCESS then icache_get#(inode0.ino, cache_icache; asynced2, inode, err); afs_files := (cache_files ⊕ cache_pcache) ⊕ cache_icache; 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⟫ ⟨cache_dirs0 := cache_dirs; afs_write_inode#(mkinode(m, md, boolvar, m0, m1, m2); err0, cache_dirs, afs_files; afs_asynced)⟩ (cache_dirs = cache_dirs0 ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced) ∧ err = err0)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 234:
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), 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, 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 ⊦ ⟪choose err0 with ⌊err0⌋ in err := err0; asynced := ?; asynced0 := false; inode0 := mkinode(m, md, boolvar, m0, m1, m2); asynced2 := false; inode := mkinode(m, md, boolvar, m0, m1, m2); if err = ESUCCESS then icache_get#(inode0.ino, cache_icache; asynced2, inode, err); afs_files := (cache_files ⊕ cache_pcache) ⊕ cache_icache; 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⟫ ⟨cache_dirs0 := cache_dirs; afs_write_inode#(mkinode(m, md, boolvar, m0, m1, m2); err0, cache_dirs, afs_files; afs_asynced)⟩ (cache_dirs = cache_dirs0 ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced) ∧ err = err0)

Rule argument

pos: right 1

Additional information

Used simplifier rules: fail#(; ; ERR){choose ERR0 with ⌊ERR0⌋ in ERR := ERR0};