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Proof step 113 from proof refine-readpage (previous step)

# buf0 = 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), content[pageno] = content0[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 ∈ content0, pageno ∈ content, m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ content0[pageno] = zeropage, datakey(m, pageno) ∈ cache_pcache, ∀ ino. ( ino ∈ (cache_files ⊕ cache_pcache) ⊕ cache_icache ↔ ino ∈ (cache_files ⊕ cache_pcache[datakey(m, pageno), mkpentry(false, content0[pageno])]) ⊕ cache_icache) ∧ ( ino ∈ (cache_files ⊕ cache_pcache) ⊕ cache_icache → ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino] = ((cache_files ⊕ cache_pcache[datakey(m, pageno), mkpentry(false, content0[pageno])]) ⊕ cache_icache)[ino])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 114:
# buf0 = VFS_PAGE_SIZE, content[pageno] = content0[pageno], cache_files[m] = mkfile(m3, md0, # links(m, cache_dirs), content), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md, m1, content0), 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), m ∈ cache_files, pageno ∈ content, pageno ∈ content0, ino ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ content0[pageno] = zeropage, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino] = ((cache_files ⊕ cache_pcache[datakey(m, pageno), mkpentry(false, content0[pageno])]) ⊕ cache_icache)[ino], datakey(m, pageno) ∈ cache_pcache

Rule argument

Additional information

Used simplifier rules: ⊦ ino ∈ files ⊕ pcache ↔ ino ∈ files; (s)% ⊦ ino ∈ files ⊕ icache ↔ ino ∈ files; (s)