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Proof step 126 from proof refine-create (previous step)

cache_dirs[m1] = mkdir(m2, md1, # links(m1, cache_dirs), m5, entries0), 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_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 ] .inode .directory, 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_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)) ], cache_sync → synced(cache_files, cache_icache, cache_pcache), ino = m ∨ ino ∈ cache_files, links(m1, cache_dirs) ≠ ∅ ∨ m1 = ROOT_INO ⊦ (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, m ∈ cache_dirs, m ∈ cache_files, str ∈ entries0, 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 127:
cache_dirs[m1] = mkdir(m2, md1, # links(m1, cache_dirs), m5, entries0), cache_icache[m1, mkientry(false, mkinode(m1, md2, true, # links(m1, cache_dirs), m5, m2 + 1))][ino] = mkientry(boolvar0, mkinode(m0, md, true, 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_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_files, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m1, cache_dirs) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino] = mkfile(cache_files[ino].size, cache_files[ino].meta, cache_files[ino].nlink, cache_files[ino].content ⊕ mkcontent(ino, cache_pcache)), m = 0, m ∈ cache_dirs, m ∈ cache_files, str ∈ entries0

Rule argument

Additional information

Used simplifier rules: ino ∈ files, ino0 ≠ 0, ¬ ino0 ∈ files ⊦ ino ≠ ino0 → (files ++ ino0)[ino] = files[ino]; (s)% ⊦ ino ∈ files ⊕ pcache ↔ ino ∈ files; (s)% ⊦ ino ∈ files ⊕ icache ↔ ino ∈ files; (s)% ⊦ ino ≠ ino0 → icache[ino0, ie][ino] = icache[ino]; (s)%⊦ 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)%⊦ mkientry(boolvar, inode) = mkientry(boolvar0, inode0) ↔ (boolvar ↔ boolvar0) ∧ inode = inode0; (ws)% ⊦ icache[ino, ie][ino] = ie; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkientry(boolvar, inode).inode = inode; (s)%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)