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Proof step 61 from proof refine-rename-file-dentry (previous step)

cache_files[entries[str]] = mkfile(m4, md2, # links(entries[str], cache_dirs), content2), cache_dirs[m] = mkdir(m11, md5, # links(m, cache_dirs), m17, entries), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str0]] = mkfile(m8, md4, m15, content0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str]] = mkfile(m12, md3, m14, content), cache_dirs[m3] = mkdir(m0, md6, # links(m3, cache_dirs), m2, entries0), cache_files[entries0[str0]] = mkfile(m1, md1, # links(entries0[str0], cache_dirs), content1), cache_icache[entries[str]] = mkientry(boolvar0, mkinode(entries[str], md7, boolvar, m6, m7, m9)), 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), str ∈ entries, str0 ∈ entries0, m ∈ cache_dirs, m3 ∈ cache_dirs, entries[str] ∈ cache_files, entries0[str0] ∈ cache_files, entries[str] ∈ cache_icache, m = m3 → md = md0, cache_sync → synced(cache_files, cache_icache, cache_pcache), (boolvar0 ⊃ m6 = # links(entries[str], cache_dirs) ∧ m7 = 0 ∧ ¬ boolvar ;mkinode(entries[str], md7, boolvar, m6, m7, m9) = mkinode(entries[str], md2, false, # links(entries[str], cache_dirs), 0, m4) ), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO, links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO ⊦ m14 = # links(entries[str], cache_dirs)

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 62:
cache_icache[entries[str]] = mkientry(boolvar0, mkinode(entries[str], 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), m6 = # links(entries[str], cache_dirs), 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), entries[str] ∈ cache_icache, 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, (boolvar0 ⊃ m6 = # links(entries[str], cache_dirs) ∧ m7 = 0 ∧ ¬ boolvar ;mkinode(entries[str], md7, boolvar, m6, m7, m9) = mkinode(entries[str], md2, false, # links(entries[str], cache_dirs), 0, m4) ), links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ m14 = # links(entries[str], cache_dirs)

Rule argument

fma: m6 = # links(entries[str], cache_dirs)

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2) = mkinode(m3, md0, boolvar0, m4, m5, m6) ↔ m = m3 ∧ md = md0 ∧ (boolvar ↔ boolvar0) ∧ m0 = m4 ∧ m1 = m5 ∧ m2 = m6; (ws) Used formulas: m6 = # links(entries[str], cache_dirs)