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Proof step 22 from proof refine-unlink (previous step)

cache_icache[entries[str]].inode = mkinode(m4, md2, boolvar, m6, m7, m8), cache_dirs[m] = mkdir(m3, md1, # links(m, cache_dirs), m5, entries), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str]] = mkfile(m0, md, m1, content), cache_files[entries[str]] = mkfile(m2, md0, # links(entries[str], cache_dirs), content0), 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), entries[str] ∈ cache_files, str ∈ entries, m ∈ cache_dirs, entries[str] ∈ cache_icache → m4 = entries[str] ∧ (cache_icache[entries[str]].dirty ⊃ m4 ∈ cache_files ∧ m6 = cache_files[m4].nlink ∧ m7 = 0 ∧ ¬ boolvar ; cache_icache[entries[str]].inode = (m4 ∈ cache_dirs ⊃ mkinode(m4, cache_dirs[m4].meta, true, cache_dirs[m4].nlink, cache_dirs[m4].nsubdirs, cache_dirs[m4].size) ;mkinode(m4, cache_files[m4].meta, false, cache_files[m4].nlink, 0, cache_files[m4].size) ) ), cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ m1 = # links(entries[str], cache_dirs)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
cache_icache[entries[str]].inode = mkinode(m4, md2, boolvar, m6, m7, m8), cache_dirs[m] = mkdir(m3, md1, # links(m, cache_dirs), m5, entries), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str]] = mkfile(m0, md, m1, content), cache_files[entries[str]] = mkfile(m2, md0, # links(entries[str], cache_dirs), content0), 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), entries[str] ∈ cache_files, str ∈ entries, m ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), entries[str] ∈ cache_icache → m4 = entries[str] ∧ (cache_icache[entries[str]].dirty ⊃ m6 = # links(entries[str], cache_dirs) ∧ m7 = 0 ∧ ¬ boolvar ;mkinode(entries[str], md2, boolvar, m6, m7, m8) = mkinode(entries[str], md0, false, # links(entries[str], cache_dirs), 0, m2) ), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ m1 = # links(entries[str], cache_dirs)

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).size = m; (s)% ⊦ mkfile(m, md, m0, content).meta = md; (s)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)