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Proof step 438 from proof refine-readpage (previous step)

# buf0 = VFS_PAGE_SIZE, cache_icache[m] = mkientry(boolvar, mkinode(m0, md, false, m1, m2, m4)), cache_files[m] = mkfile(m3, md0, # links(m, cache_dirs), content), content[pageno] ≠ zeropage, content[pageno] ≠ (content ⊕ mkcontent(m, cache_pcache))[pageno], 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), pageno ∈ content, m ∈ cache_files, m ∈ cache_icache, pageno ∈ content ⊕ mkcontent(m, cache_pcache), ¬ datakey(m, pageno) ∈ cache_pcache, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ∃ err0. ⌊err0⌋ ∧ ⟨err := err0⟩ ( (cache_files ⊕ cache_pcache) ⊕ cache_icache = (cache_files ⊕ cache_pcache[datakey(m, pageno), mkpentry(false, content[pageno])]) ⊕ cache_icache ∧ content[pageno] = 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)% ⊦ ¬ key ∈ pcache → pcache[key] = (∅)[key]; (s)% ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache; (s)% ⊦ ¬ n ∈ content1 → (content0 ⊕ content1)[n] = content0[n]; (s) Used terms: pageno, mkcontent(m, cache_pcache), content