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Proof step 414 from proof refine-readpage (previous step)

# buf0 = VFS_PAGE_SIZE, cache_icache[ino] = mkientry(boolvar0, mkinode(m5, md1, false, m6, m7, m8)), content[pageno] = (content ⊕ mkcontent(m, cache_pcache))[pageno], cache_files[m] = mkfile(m3, md0, # links(m, cache_dirs), content), cache_icache[m] = mkientry(boolvar, mkinode(m0, md, false, m1, m2, m4)), cache_files[ino] = mkfile(m9, md2, # links(ino, cache_dirs), content0), cache_pcache[datakey(ino, n)] = mkpentry(boolvar1, buf), 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), datakey(ino, n) ∈ cache_pcache, ino ∈ cache_files, m ∈ cache_icache, m ∈ cache_files, pageno ∈ content, ino ∈ cache_icache, n ∈ content0 ⊕ mkcontent(ino, cache_pcache), cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ content[pageno] = zeropage, buf = (content0 ⊕ mkcontent(ino, cache_pcache[datakey(m, pageno), mkpentry(false, content[pageno])]))[n], datakey(m, pageno) ∈ cache_pcache

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: cache-base name: at-overwrite-content-new seq: ⊦ n ∈ content1 → (content0 ⊕ content1)[n] = content1[n] subst: [n, content1, content0] → [n, mkcontent (ino, cache_pcache [datakey(m, pageno), mkpentry(false, content[pageno]) ]), content0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ mkcontent(ino, pcache)[n] = pcache[datakey(ino, n)].page; (s)%⊦ key ∈ pcache ∧ ¬ key0 ∈ pcache → pcache[key0, pe][key] = pcache[key]; (s)% ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache; (s)% ⊦ mkpentry(boolvar, buf).page = buf; (s)% ⊦ ¬ n ∈ content1 → (content0 ⊕ content1)[n] = content0[n]; (s)% ⊦ key ∈ pcache[key0, pe] ↔ key = key0 ∨ key ∈ pcache; (ws) Used terms: n, mkcontent (ino, cache_pcache[datakey(m, pageno), mkpentry(false, content[pageno])]), content0