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Proof step 82 from proof refine-writepage (previous step)

# buf = VFS_PAGE_SIZE, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md, m1, 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), m ∈ cache_files ⊦ ∃ err0. ⌊err0⌋ ∧ ⟨err := err0; asynced1 := ?⟩ ( (cache_files ⊕ cache_pcache) ⊕ cache_icache = (cache_files ⊕ cache_pcache[datakey(m, pageno), mkpentry(true, buf)]) ⊕ cache_icache ∧ (asynced1 ↔ asynced0) ∧ ESUCCESS = err), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m, mkfile(m0, md, m1, content[pageno, buf])] = (cache_files ⊕ cache_pcache[datakey(m, pageno), mkpentry(true, buf)]) ⊕ cache_icache

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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