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Proof step 122 from proof refine-create (previous step)

cache_icache[m1, mkientry(false, mkinode(m1, md2, true, # links(m1, cache_dirs), m5, m2 + 1))] [m, mkientry(false, mkinode(m, md0, false, 1, 0, 0)) ] [ino ] = mkientry(boolvar0, mkinode(m0, md, boolvar, m3, m4, m6)), cache_dirs[m1] = mkdir(m2, md1, # links(m1, cache_dirs), m5, 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), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), m1 ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m1, cache_dirs) ≠ ∅ ∨ m1 = ROOT_INO, ino = m ∨ ino ∈ cache_files ⊦ (ino = m ⊃ mkfile(0, md0, 1, ∅);(((cache_files ⊕ cache_pcache) ⊕ cache_icache) ++ m)[ino]) = ((cache_files ++ m)[m, mkfile(0, md0, 1, ∅)] ⊕ cache_pcache)[ino], m = 0, str ∈ entries0, m ∈ cache_files, m ∈ cache_dirs, ino ∈ cache_icache[m1, mkientry(false, mkinode(m1, md2, true, # links(m1, cache_dirs), m5, m2 + 1))] [m, mkientry(false, mkinode(m, md0, false, 1, 0, 0)) ], ino ∈ cache_icache[m1, mkientry(false, mkinode(m1, md2, true, # links(m1, cache_dirs), m5, m2 + 1))] [m, mkientry(false, mkinode(m, md0, false, 1, 0, 0)) ] ∧ boolvar, ino ∈ cache_icache[m1, mkientry(false, mkinode(m1, md2, true, # links(m1, cache_dirs), m5, m2 + 1))] [m, mkientry(false, mkinode(m, md0, false, 1, 0, 0)) ] ∧ ¬ boolvar

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 123:
cache_dirs[m1] = mkdir(m2, md1, # links(m1, cache_dirs), m5, entries0), (∅)[ino] = mkientry(boolvar0, mkinode(m0, md, boolvar, m3, m4, m6)), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), m1 ∈ cache_dirs, ino ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m1, cache_dirs) ≠ ∅ ∨ m1 = ROOT_INO ⊦ (((cache_files ⊕ cache_pcache) ⊕ cache_icache) ++ m)[ino] = mkfile ((cache_files ++ m)[ino].size, (cache_files ++ m)[ino].meta, (cache_files ++ m)[ino].nlink, (cache_files ++ m)[ino].content ⊕ mkcontent(ino, cache_pcache)), ino = m1, m = 0, m ∈ cache_dirs, m ∈ cache_files, str ∈ entries0, ino ∈ cache_icache, ino ∈ cache_icache[m1, mkientry(false, mkinode(m1, md2, true, # links(m1, cache_dirs), m5, m2 + 1))] [m, mkientry(false, mkinode(m, md0, false, 1, 0, 0)) ] ∧ ¬ boolvar, ino ∈ cache_icache[m1, mkientry(false, mkinode(m1, md2, true, # links(m1, cache_dirs), m5, m2 + 1))] [m, mkientry(false, mkinode(m, md0, false, 1, 0, 0)) ] ∧ boolvar

Rule argument

Additional information

Used simplifier rules: ⊦ ino ∈ icache[ino0, ie] ↔ ino = ino0 ∨ ino ∈ icache; (ws)%ino ≠ 0, ¬ ino ∈ files ⊦ ino0 ∈ files ++ ino ↔ ino0 = ino ∨ ino0 ∈ files; (s)% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)%⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache)); (s)% ⊦ ¬ ino ∈ icache → icache[ino] = (∅)[ino]; (s)