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Proof step 38 from proof refine-writepage (previous step)

# buf = VFS_PAGE_SIZE, cache_files[m] = mkfile(m3, md0, # links(m, cache_dirs), content), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md, m1, content0), 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), m ∈ cache_files ⊦ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m, mkfile(m0, md, m1, content0[pageno, buf])] = (cache_files[m, mkfile(m3, md0, # links(m, cache_dirs), content[pageno, buf])] ⊕ cache_pcache[datakey(m, pageno), mkpentry(false, buf)]) ⊕ cache_icache

User applied rule apply lemma

And obtained the following new goals

Rule argument

spec: cache-base name: overwrite-write-page-clean seq: ⊦ ino ∈ files → ((files ⊕ pcache) ⊕ icache )[ino, ((files ⊕ pcache) ⊕ icache)[ino] .content:= ((files ⊕ pcache) ⊕ icache)[ino].content [m, buf ] ] = ( files [ino, files[ino].content:= files[ino].content[m, buf] ] ⊕ pcache[datakey(ino, m), mkpentry(false, buf)]) ⊕ icache subst: [ino, files, pcache, icache, m, buf] → [m, cache_files, cache_pcache, cache_icache, pageno, buf]

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).content = content; (s)%⊦ mkfile(m, md, m0, content).content:= content0 = mkfile(m, md, m0, content0); (s) Used terms: m, cache_files, cache_pcache, cache_icache, pageno, buf