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Proof step 27 from proof refine-unlink (previous step)

cache_files[entries[str]] = mkfile(m2, md0, # links(entries[str], cache_dirs), content0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str]] = mkfile(m0, md, m1, content), cache_dirs[m] = mkdir(m3, md1, # links(m, cache_dirs), m5, entries), cache_icache[entries[str]] = mkientry(boolvar0, mkinode(m4, md2, boolvar, m6, m7, m8)), 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, str ∈ entries, entries[str] ∈ cache_files, entries[str] ∈ cache_icache → m4 = entries[str] ∧ (boolvar0 ⊃ 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) ), cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ m1 = # links(entries[str], cache_dirs), entries[str] ∈ cache_icache ∧ ¬ cache_icache[entries[str]].inode.directory

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
cache_files[entries[str]] = mkfile(m2, md0, # links(entries[str], cache_dirs), content0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str]] = mkfile(m0, md, m1, content), cache_dirs[m] = mkdir(m3, md1, # links(m, cache_dirs), m5, entries), cache_icache[entries[str]] = mkientry(boolvar0, mkinode(m4, md2, boolvar, m6, m7, m8)), 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, str ∈ entries, entries[str] ∈ cache_files, entries[str] ∈ cache_icache → m4 = entries[str] ∧ (boolvar0 ⊃ 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) ), cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ m1 = # links(entries[str], cache_dirs), entries[str] ∈ cache_icache ∧ ¬ boolvar

Rule argument

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkientry(boolvar, inode).inode = inode; (s)