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Proof step 23 from proof refine-truncate (previous step)

((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, m1, 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_dirs, cache_icache, cache_pcache), m ∈ cache_files, datakey(m, m2 / VFS_PAGE_SIZE) ∈ cache_pcache, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ buf-opt0 = none, buf-opt0.some?

User applied rule constructor cut

And closed the goal!

Rule argument

var: buf-opt0

Additional information

Used simplifier rules: buffer-opt freely generated by none, some;;% ⊦ some(buf) ≠ none; (s)% ⊦ some(buf).some?; (s)