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Proof step 218 from proof refine-write_inode (previous step)

cache_files[m] = mkfile(m0, md0, # links(m, cache_dirs), content), 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_files, cache_icache, cache_pcache), synced(cache_dirs, cache_icache, cache_pcache), m ∈ cache_files, ino ∈ cache_files ⊦ (ino = m ⊃ mkfile(m2, md, # links(m, cache_dirs), content ⊕ mkcontent(m, cache_pcache));((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino]) = ((cache_files[m, mkfile(m2, md, # links(m, cache_dirs), content)] ⊕ cache_pcache) ⊕ cache_icache)[ino], m ∈ cache_icache

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 219:
⊦ ino ∈ icache ∧ ¬ icache[ino].inode.directory → (files ⊕ icache)[ino] = mkfile(icache[ino].inode.size, icache[ino].inode.meta, icache[ino].inode.nlink, files[ino].content)
Proof step 220:
cache_files[m] = mkfile(m0, md0, # links(m, cache_dirs), 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), synced(cache_files, cache_icache, cache_pcache), ino ∈ cache_files, m ∈ cache_files ⊦ (ino = m ⊃ mkfile(m2, md, # links(m, cache_dirs), content ⊕ mkcontent(m, cache_pcache));((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino]) = ((cache_files[m, mkfile(m2, md, # links(m, cache_dirs), content)] ⊕ cache_pcache) ⊕ cache_icache)[ino], m ∈ cache_icache, ino ∈ cache_icache ∧ ¬ cache_icache[ino].inode.directory

Rule argument

spec: cache-base name: at-icache-overwrite seq: ⊦ ino ∈ icache ∧ ¬ icache[ino].inode.directory → (files ⊕ icache)[ino] = mkfile (icache[ino].inode.size, icache[ino].inode.meta, icache[ino].inode.nlink, files[ino].content) subst: [ino, icache, files] → [ino, cache_icache, cache_files [m, mkfile(m2, md, # links(m, cache_dirs), content) ] ⊕ cache_pcache] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ino ∈ icache ∧ ¬ icache[ino].inode.directory → (files ⊕ icache)[ino] = mkfile (icache[ino].inode.size, icache[ino].inode.meta, icache[ino].inode.nlink, files[ino].content); (s)%⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache)); (s)% ⊦ mkfile(m, md, m0, content).content = content; (s)% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s) Used terms: ino, cache_icache, cache_files[m, mkfile(m2, md, # links(m, cache_dirs), content)] ⊕ cache_pcache