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Proof step 337 from proof refine-write_inode (previous step)

cache_files[m3] = mkfile(m1, md1, # links(m3, cache_dirs), content0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m3] = mkfile(m0, md0, # links(m3, cache_dirs), content), cache_icache[m3] = mkientry(boolvar, mkinode(m3, md2, false, # links(m3, cache_dirs), 0, 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), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), ino ∈ cache_files, m3 ∈ cache_icache, m3 ∈ cache_files, ¬ boolvar → mkinode(m3, md2, false, # links(m3, cache_dirs), 0, m6) = mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m1) ⊦ (ino = m3 ⊃ mkfile(m2, md, # links(m3, cache_dirs), content);((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino]) = ((cache_files ⊕ cache_pcache) ⊕ cache_icache[m3, mkientry(true, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m2))])[ino], ino ∈ cache_icache[m3, mkientry(true, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m2))] ∧ ¬ cache_icache[m3, mkientry(true, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m2))][ino].inode.directory

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 338:
cache_files[m3] = mkfile(m1, md1, # links(m3, cache_dirs), content0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m3] = mkfile(m0, md0, # links(m3, cache_dirs), content), cache_icache[m3] = mkientry(boolvar, mkinode(m3, md2, false, # links(m3, cache_dirs), 0, m6)), cache_icache[m3, mkientry(true, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m2))][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), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), ino ∈ cache_files, m3 ∈ cache_icache, m3 ∈ cache_files, ino ∈ cache_icache[m3, mkientry(true, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m2))], ¬ boolvar → mkinode(m3, md2, false, # links(m3, cache_dirs), 0, m6) = mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m1) ⊦ (ino = m3 ⊃ mkfile(m2, md, # links(m3, cache_dirs), content);((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))

Rule argument

Additional information

Used simplifier rules: ⊦ ino ∈ icache ∧ icache[ino].inode.directory → (files ⊕ icache)[ino] = files[ino]; (s)% ⊦ ino ∈ icache[ino0, ie] ↔ ino = ino0 ∨ ino ∈ icache; (ws)%⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache)); (s)% ⊦ ¬ ino ∈ icache → (files ⊕ icache)[ino] = files[ino]; (s)