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Proof step 34 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), ((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, 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 ⊦ ⟨fail#(; ; err); asynced0 := ?⟩ ( (cache_files ⊕ cache_pcache) ⊕ cache_icache = ( cache_files[m, mkfile(m3, md0, # links(m, cache_dirs), content[pageno, buf])] ⊕ cache_pcache[datakey(m, pageno), mkpentry(false, buf)]) ⊕ cache_icache ∧ ¬ asynced0 ∧ ESUCCESS = err)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 35:
# buf = VFS_PAGE_SIZE, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md, m1, content0), cache_files[m] = mkfile(m3, md0, # links(m, cache_dirs), content), 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_files, cache_icache, cache_pcache), synced(cache_dirs, cache_icache, cache_pcache), m ∈ cache_files ⊦ ⟨choose err0 with ⌊err0⌋ in err := err0; asynced0 := ?⟩ ( (cache_files ⊕ cache_pcache) ⊕ cache_icache = ( cache_files[m, mkfile(m3, md0, # links(m, cache_dirs), content[pageno, buf])] ⊕ cache_pcache[datakey(m, pageno), mkpentry(false, buf)]) ⊕ cache_icache ∧ ¬ asynced0 ∧ ESUCCESS = err), ((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

Rule argument

pos: right 1

Additional information

Used simplifier rules: fail#(; ; ERR){choose ERR0 with ⌊ERR0⌋ in ERR := ERR0};