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Proof step 157 from proof refine-create (previous step)

(ino = m ⊃ mkfile(0, md0, 1, ∅);(cache_files ++ m)[ino]) = mkfile(m7, md3, m8, content), 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(boolvar, mkinode(m0, md, false, m3, m4, m6)), cache_dirs[m1] = mkdir(m2, md1, # links(m1, cache_dirs), m5, entries0), ino = m, 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), 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)) ], 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]) = mkfile(m6, md, m3, content ⊕ mkcontent(ino, cache_pcache)), m = 0, str ∈ entries0, m ∈ cache_files, m ∈ cache_dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 158:
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 ⊦ m = 0, ∅ = ∅ ⊕ mkcontent(m, cache_pcache), str ∈ entries0, m ∈ cache_files, m ∈ cache_dirs

Rule argument

Additional information

Used simplifier rules: ⊦ ino ∈ icache[ino, ie]; (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)%⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)%⊦ mkientry(boolvar, inode) = mkientry(boolvar0, inode0) ↔ (boolvar ↔ boolvar0) ∧ inode = inode0; (ws)% ⊦ icache[ino, ie][ino] = ie; (s)