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Proof step 203 from proof refine-write_inode (previous step)

cache_files[m] = mkfile(m1, md1, # links(m, cache_dirs), content0), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_dirs0 = cache_dirs, dirs = cache_dirs, err = err0, files = afs_files, inode = mkinode(m, md, false, # links(m, cache_dirs), 0, m2), 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), pre-write-inode(inode, dirs, files), synced(cache_dirs, cache_icache, cache_pcache), synced(cache_files, cache_icache, cache_pcache), m ∈ cache_files ⊦ ⟨fail#(; ; err); asynced := ?⟩ ( dirs = cache_dirs0 ∧ files = (cache_files[m, (cache_files[m].meta:= md).size:= m2] ⊕ cache_pcache) ⊕ cache_icache ∧ (asynced ↔ asynced0) ∧ ESUCCESS = err), ⟨if inode.directory then dirs[inode.ino].meta := inode.meta else {files[inode.ino].meta := inode.meta; files[inode.ino].size := inode.size}; err := ESUCCESS; asynced := ?⟩ ( dirs = cache_dirs0 ∧ files = (cache_files[m, (cache_files[m].meta:= md).size:= m2] ⊕ cache_pcache) ⊕ cache_icache ∧ (asynced ↔ asynced0) ∧ ESUCCESS = err), m ∈ cache_icache

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 204:
# links(m, cache_dirs) = cache_files[m].nlink, cache_files[m] = mkfile(m1, md1, cache_files[m].nlink, content0), 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), synced(cache_files, cache_icache, cache_pcache), m ∈ cache_files, ¬ m ∈ cache_icache ⊦ ⟨fail#(; ; err); asynced := ?⟩ ( (cache_files ⊕ cache_pcache) ⊕ cache_icache = (cache_files[m, (cache_files[m].meta:= md).size:= m2] ⊕ cache_pcache) ⊕ cache_icache ∧ (asynced ↔ asynced0) ∧ ESUCCESS = err), ⟨afs_files := ((cache_files ⊕ cache_pcache) ⊕ cache_icache )[m, mkfile(cache_files[m].size, md, cache_files[m].nlink, cache_files[m].content ⊕ mkcontent(m, cache_pcache)) ]; afs_files[m].size := m2; err := ESUCCESS; asynced := ?⟩ (afs_files = (cache_files[m, (cache_files[m].meta:= md).size:= m2] ⊕ cache_pcache) ⊕ cache_icache ∧ (asynced ↔ asynced0) ∧ ESUCCESS = err)

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).meta:= md0 = mkfile(m, md0, m0, content); (s)%afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)%⊦ (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)% ⊦ ino ∈ files ⊕ pcache ↔ ino ∈ files; (s)% ⊦ ino ∈ files ⊕ icache ↔ 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)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ valid-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)%⊦ valid-dir-inode(inode, dirs, files) ↔ valid-dir-ino(inode.ino, dirs, files) ∧ inode.nlink = dirs[inode.ino].nlink ∧ inode.size = dirs[inode.ino].size ∧ inode.nsubdirs = dirs[inode.ino].nsubdirs ∧ inode.directory; (s)%⊦ valid-wb-inode(inode, dirs, files) ↔ valid-dir-inode(inode, dirs, files) ∨ valid-file-inode(inode, dirs, files); (s)%⊦ pre-write-inode(inode, dirs, files) ↔ valid-wb-inode(inode, dirs, files); (s)