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Proof step 37 from proof refine-rename-file-dentry (previous step)

cache_icache[entries0[str0]].inode = mkinode(m5, md7, boolvar, m6, m7, m9), cache_files[entries0[str0]] = mkfile(m1, md1, # links(entries0[str0], cache_dirs), content1), cache_dirs[m3] = mkdir(m0, md6, # links(m3, cache_dirs), m2, entries0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str]] = mkfile(m12, md3, m14, content), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str0]] = mkfile(m8, md4, m15, content0), cache_dirs[m] = mkdir(m11, md5, # links(m, cache_dirs), m17, entries), cache_files[entries[str]] = mkfile(m4, md2, # links(entries[str], cache_dirs), content2), 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), entries0[str0] ∈ cache_files, entries[str] ∈ cache_files, m3 ∈ cache_dirs, m ∈ cache_dirs, str0 ∈ entries0, str ∈ entries, entries0[str0] ∈ cache_icache → m5 = entries0[str0] ∧ (cache_icache[entries0[str0]].dirty ⊃ m5 ∈ cache_files ∧ m6 = cache_files[m5].nlink ∧ m7 = 0 ∧ ¬ boolvar ; cache_icache[entries0[str0]].inode = (m5 ∈ cache_dirs ⊃ mkinode(m5, cache_dirs[m5].meta, true, cache_dirs[m5].nlink, cache_dirs[m5].nsubdirs, cache_dirs[m5].size) ;mkinode(m5, cache_files[m5].meta, false, cache_files[m5].nlink, 0, cache_files[m5].size) ) ), cache_sync → synced(cache_files, cache_icache, cache_pcache), m = m3 → md = md0, links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ m15 = # links(entries0[str0], cache_dirs)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 38:
cache_icache[entries0[str0]].inode = mkinode(m5, md7, boolvar, m6, m7, m9), cache_files[entries0[str0]] = mkfile(m1, md1, # links(entries0[str0], cache_dirs), content1), cache_dirs[m3] = mkdir(m0, md6, # links(m3, cache_dirs), m2, entries0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str]] = mkfile(m12, md3, m14, content), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str0]] = mkfile(m8, md4, m15, content0), cache_dirs[m] = mkdir(m11, md5, # links(m, cache_dirs), m17, entries), cache_files[entries[str]] = mkfile(m4, md2, # links(entries[str], cache_dirs), content2), 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), entries0[str0] ∈ cache_files, entries[str] ∈ cache_files, m3 ∈ cache_dirs, m ∈ cache_dirs, str0 ∈ entries0, str ∈ entries, cache_sync → synced(cache_files, cache_icache, cache_pcache), m = m3 → md = md0, entries0[str0] ∈ cache_icache → m5 = entries0[str0] ∧ (cache_icache[entries0[str0]].dirty ⊃ m6 = # links(entries0[str0], cache_dirs) ∧ m7 = 0 ∧ ¬ boolvar ;mkinode(entries0[str0], md7, boolvar, m6, m7, m9) = mkinode(entries0[str0], md1, false, # links(entries0[str0], cache_dirs), 0, m1) ), links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ m15 = # links(entries0[str0], 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)