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Proof step 13 from proof refine-fsync (previous step)

((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, m1, content), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache), m ∈ cache_icache → cache_icache[m].inode.ino = m ∧ (cache_icache[m].dirty ⊃ valid-file-inode(cache_icache[m].inode, cache_dirs, cache_files) ;valid-ino(m, cache_dirs, cache_files) ∧ valid-inode(cache_icache[m].inode, cache_dirs, cache_files) ) ⊦ m1 = cache_files[m].nlink

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
cache_icache[m].inode.ino = m, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, m1, content), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), m ∈ cache_icache, m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache), (cache_icache[m].dirty ⊃ cache_icache[m].inode.nlink = cache_files[m].nlink ∧ cache_icache[m].inode.nsubdirs = 0 ∧ ¬ cache_icache[m].inode.directory ;cache_icache[m].inode = mkinode(m, cache_files[m].meta, false, cache_files[m].nlink, 0, cache_files[m].size) ) ⊦ m1 = cache_files[m].nlink

Rule argument

Additional information

Used simplifier rules: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)%⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)%⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache)); (s)% ⊦ ¬ ino ∈ icache → (files ⊕ icache)[ino] = files[ino]; (s)%⊦ getinode(ino, dirs, files) = (ino ∈ dirs ⊃ mkinode (ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ); (s)%⊦ valid-inode(inode, dirs, files) ↔ inode = getinode(inode.ino, dirs, files); (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)%⊦ valid-file-inode(inode, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory; (s)