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Proof step 430 from proof refine-rename-file-negdentry (previous step)

cache_dirs[m3] = mkdir(m0, md4, # links(m3, cache_dirs), m2, entries0), cache_dirs[m] = mkdir(m8, md3, # links(m, cache_dirs), m13, entries), cache_files[entries0[str]] = mkfile(m1, md1, # links(entries0[str], cache_dirs), content0), cache_icache[entries0[str]] = mkientry(boolvar, mkinode(m4, md2, false, m5, m6, m7)), 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), entries0[str] ∈ cache_icache, str ∈ entries0, m3 ∈ cache_dirs, entries0[str] ∈ cache_files, m ∈ cache_dirs, m = m3 → md = md0, cache_sync → synced(cache_files, cache_icache, cache_pcache), ∀ ino. ino ∈ cache_icache → cache_icache[ino].inode.ino = ino ∧ (cache_icache[ino].dirty ⊃ valid-file-inode(cache_icache[ino].inode, cache_dirs, cache_files) ;valid-ino(ino, cache_dirs, cache_files) ∧ valid-inode(cache_icache[ino].inode, cache_dirs, cache_files) ), links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ m5 = # links(entries0[str], cache_dirs), str0 ∈ entries

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 431:
cache_icache[entries0[str]] = mkientry(boolvar, mkinode(m4, md2, false, m5, m6, m7)), cache_files[entries0[str]] = mkfile(m1, md1, # links(entries0[str], cache_dirs), content0), cache_dirs[m] = mkdir(m8, md3, # links(m, cache_dirs), m13, entries), cache_dirs[m3] = mkdir(m0, md4, # links(m3, cache_dirs), m2, entries0), 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_dirs, entries0[str] ∈ cache_files, m3 ∈ cache_dirs, str ∈ entries0, entries0[str] ∈ cache_icache, cache_sync → synced(cache_files, cache_icache, cache_pcache), m = m3 → md = md0, ∀ ino. ino ∈ cache_icache → cache_icache[ino].inode.ino = ino ∧ (cache_icache[ino].dirty ⊃ cache_icache[ino].inode.ino ∈ cache_files ∧ cache_icache[ino].inode.nlink = cache_files[cache_icache[ino].inode.ino].nlink ∧ cache_icache[ino].inode.nsubdirs = 0 ∧ ¬ cache_icache[ino].inode.directory ; (ino ∈ cache_dirs ∨ ino ∈ cache_files) ∧ cache_icache[ino].inode = (cache_icache[ino].inode.ino ∈ cache_dirs ⊃ mkinode (cache_icache[ino].inode.ino, cache_dirs[cache_icache[ino].inode.ino].meta, true, cache_dirs[cache_icache[ino].inode.ino].nlink, cache_dirs[cache_icache[ino].inode.ino].nsubdirs, cache_dirs[cache_icache[ino].inode.ino].size) ;mkinode (cache_icache[ino].inode.ino, cache_files[cache_icache[ino].inode.ino].meta, false, cache_files[cache_icache[ino].inode.ino].nlink, 0, cache_files[cache_icache[ino].inode.ino].size) ) ), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO, links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO ⊦ m5 = # links(entries0[str], cache_dirs), str0 ∈ entries

Rule argument

Additional information

Used simplifier rules: ⊦ 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)