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Proof step 45 from proof refine-readpage (previous step)

# buf0 = VFS_PAGE_SIZE, cache_pcache[datakey(m, pageno)] = mkpentry(boolvar0, buf1), (∅)[m] = mkientry(boolvar1, mkinode(m2, md0, boolvar, m3, m4, m5)), cache_files[m] = mkfile(m0, md, # links(m, cache_dirs), content), buf1 ≠ (content ⊕ mkcontent(m, cache_pcache))[pageno], 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), pageno ∈ content ⊕ mkcontent(m, cache_pcache), m ∈ cache_files, datakey(m, pageno) ∈ cache_pcache, ¬ m ∈ cache_icache, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ∃ err0. ⌊err0⌋ ∧ ⟨err := err0⟩ (buf1 = buf0 ∧ ESUCCESS = err)

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] → [pageno, mkcontent(m, cache_pcache), content] flags: <all paths>

Additional information

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