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Proof step 312 from proof refine-write_inode (previous step)

cache_icache[m] = mkientry(boolvar, mkinode(m3, md2, boolvar0, m4, m5, m6)), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, # links(m, cache_dirs), content), 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), m ∈ cache_files, m ∈ cache_icache ⊦ ⟨fail#(; ; err); asynced := ?⟩ ( dirs = cache_dirs0 ∧ files = (cache_files ⊕ cache_pcache) ⊕ cache_icache[m3, mkientry(true, mkinode(m3, md, boolvar0, m4, m5, m2))] ∧ (asynced ↔ asynced1) ∧ 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 ⊕ cache_pcache) ⊕ cache_icache[m3, mkientry(true, mkinode(m3, md, boolvar0, m4, m5, m2))] ∧ (asynced ↔ asynced1) ∧ ESUCCESS = err)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 313:
cache_files[m] = mkfile(m1, md1, # links(m, cache_dirs), content0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, # links(m, cache_dirs), content), cache_icache[m] = mkientry(boolvar, mkinode(m3, md2, boolvar0, m4, m5, m6)), 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), m ∈ cache_icache, m ∈ cache_files ⊦ ⟨fail#(; ; err); asynced := ?⟩ ( (cache_files ⊕ cache_pcache) ⊕ cache_icache = (cache_files ⊕ cache_pcache) ⊕ cache_icache[m3, mkientry(true, mkinode(m3, md, boolvar0, m4, m5, m2))] ∧ (asynced ↔ asynced1) ∧ ESUCCESS = err), ⟨afs_files := ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m, mkfile(m0, md, # links(m, cache_dirs), content)]; afs_files[m].size := m2; err := ESUCCESS; asynced := ?⟩ ( afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache[m3, mkientry(true, mkinode(m3, md, boolvar0, m4, m5, m2))] ∧ (asynced ↔ asynced1) ∧ ESUCCESS = err)

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).meta:= md0 = mkfile(m, md0, m0, content); (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (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)