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Proof step 140 from proof refine-mkdir (previous step)

cache_icache[ino] = mkientry(boolvar0, mkinode(m11, md5, false, m12, m13, m14)), cache_files[ino] = mkfile(m10, md4, # links(ino, cache_dirs), content), cache_icache[m1, mkientry(false, mkinode(m1, md2, true, m3, m4, m))][m5, mkientry(false, mkinode(m5, md3, true, 1, 0, 0))][ino] = mkientry(boolvar, mkinode(m0, md, true, m2, m7, m9)), cache_dirs[m1] = mkdir(m6, md1, # links(m1, cache_dirs), m8, entries1), (cache_dirs[m1, mkdir(m6 + 1, md1, # links(m1, cache_dirs), m8 + 1, entries1[str, m5])] ++ m5)[m1] = mkdir(m, md0, m3, m4, entries0), 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), ino ∈ cache_files, m1 ∈ cache_dirs, ino ∈ cache_icache[m1, mkientry(false, mkinode(m1, md2, true, m3, m4, m))][m5, mkientry(false, mkinode(m5, md3, true, 1, 0, 0))], ino ∈ cache_icache, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m1, cache_dirs) ≠ ∅ ∨ m1 = ROOT_INO ⊦ m5 = 0, mkfile(m14, md5, m12, content ⊕ mkcontent(ino, cache_pcache)) = mkfile(m10, md4, # links(ino, cache_dirs), content ⊕ mkcontent(ino, cache_pcache)), str ∈ entries1, m5 ∈ cache_files, m5 ∈ cache_dirs

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 141:
⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0
Proof step 142:
(cache_dirs[m1, mkdir(m6 + 1, md1, # links(m1, cache_dirs), m8 + 1, entries1[str, m5])] ++ m5)[m1] = mkdir(m, md0, m3, m4, entries0), cache_dirs[m1] = mkdir(m6, md1, # links(m1, cache_dirs), m8, entries1), cache_icache[m1, mkientry(false, mkinode(m1, md2, true, m3, m4, m))][m5, mkientry(false, mkinode(m5, md3, true, 1, 0, 0))][ino] = mkientry(boolvar, mkinode(m0, md, true, m2, m7, m9)), cache_files[ino] = mkfile(m10, md4, # links(ino, cache_dirs), content), cache_icache[ino] = mkientry(boolvar0, mkinode(m11, md5, false, m12, m13, m14)), 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, ino ∈ cache_icache[m1, mkientry(false, mkinode(m1, md2, true, m3, m4, m))][m5, mkientry(false, mkinode(m5, md3, true, 1, 0, 0))], m1 ∈ cache_dirs, ino ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m1, cache_dirs) ≠ ∅ ∨ m1 = ROOT_INO ⊦ m5 = 0, m5 ∈ cache_dirs, m5 ∈ cache_files, str ∈ entries1, m14 = m10 ∧ md5 = md4 ∧ m12 = # links(ino, cache_dirs) ∧ content ⊕ mkcontent(ino, cache_pcache) = content ⊕ mkcontent(ino, cache_pcache)

Rule argument

spec: abstract-file name: inj seq: ⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0 subst: [m, md, m0, content, m1, md0, m2, content0] → [m14, md5, m12, content ⊕ mkcontent(ino, cache_pcache), m10, md4, # links(ino, cache_dirs), content ⊕ mkcontent(ino, cache_pcache)] flags: <all paths>

Additional information

Used terms: m14, md5, m12, content ⊕ mkcontent(ino, cache_pcache), m10, md4, # links(ino, cache_dirs), content ⊕ mkcontent(ino, cache_pcache)