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Proof step 165 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))][ino] = mkientry(boolvar, mkinode(m0, md, false, 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), 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)), ino = m, m = 0, str ∈ entries0, m ∈ cache_files, m ∈ cache_dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 166:
cache_files[ino] = mkfile(m7, md3, # links(ino, cache_dirs), content), cache_icache[m1, mkientry(false, mkinode(m1, md2, true, # links(m1, cache_dirs), m5, m2 + 1))][ino] = mkientry(boolvar, mkinode(m0, md, false, 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), ino ∈ cache_files, ino ∈ cache_icache[m1, mkientry(false, mkinode(m1, md2, true, # links(m1, cache_dirs), m5, m2 + 1))], m1 ∈ cache_dirs, 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(m6, md, m3, content ⊕ mkcontent(ino, cache_pcache)), m = 0, str ∈ entries0, m ∈ cache_files, m ∈ cache_dirs

Rule argument

Additional information

Used simplifier rules: afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base%ino ∈ files, ino0 ≠ 0, ¬ ino0 ∈ files ⊦ ino ≠ ino0 → (files ++ ino0)[ino] = files[ino]; (s)% ⊦ ino ≠ ino0 → (ino ∈ icache[ino0, ie] ↔ ino ∈ icache); (s)