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Proof step 124 from proof refine-create (previous step)

(∅)[ino] = mkientry(boolvar0, mkinode(m0, md, boolvar, m3, m4, m6)), cache_dirs[m1] = mkdir(m2, md1, # links(m1, cache_dirs), m5, entries0), (cache_files ++ m)[ino] = mkfile(m7, md3, m8, content), 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, 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(m7, md3, m8, content ⊕ mkcontent(ino, cache_pcache)), ino = m1, m = 0, ino ∈ cache_icache, 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)) ] ∧ 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 use patterns applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: heap, inst: file-heap name: at-alloc seq: ino ∈ files, ino0 ≠ 0, ¬ ino0 ∈ files ⊦ ino ≠ ino0 → (files ++ ino0)[ino] = files[ino] subst: [ino, files, ino0] → [ino, (cache_files ⊕ cache_pcache) ⊕ cache_icache, m] flags: <all paths>

Additional information

Used simplifier rules: ino ∈ files, ino0 ≠ 0, ¬ ino0 ∈ files ⊦ ino ≠ ino0 → (files ++ ino0)[ino] = files[ino]; (s)% ⊦ ¬ ino ∈ icache → (files ⊕ icache)[ino] = files[ino]; (s)%⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache)); (s)% ⊦ ino ∈ files ⊕ icache ↔ ino ∈ files; (s)% ⊦ ino ∈ files ⊕ pcache ↔ ino ∈ files; (s)%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% ⊦ mkfile(m, md, m0, content).size = m; (s)% ⊦ mkfile(m, md, m0, content).meta = md; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)% ⊦ mkfile(m, md, m0, content).content = content; (s) Used terms: ino, (cache_files ⊕ cache_pcache) ⊕ cache_icache, m