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Proof step 1362 from proof refine-truncate-buff-none-uncached (previous step)

cache_icache[m] = mkientry(boolvar0, mkinode(m0, md0, false, # links(m, cache_dirs), m11, m12)), cache_files[m] = mkfile(m1, md2, # links(m, cache_dirs), content1), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache0) ⊕ 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_pcache0, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache0), m ∈ cache_icache, m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ datakey(m, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0, m2 ≤ m8 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content1 ⊕ mkcontent(m, cache_pcache0), m2 ≤ m8 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content1, ( n * VFS_PAGE_SIZE < min(m8, m2) ∧ n ∈ content1 ⊕ mkcontent(m, cache_pcache0) ↔ n ∈ (content1 upto min(m8, m2)) ⊕ mkcontent(m, truncate(m, min(m8, m2), cache_pcache0))) ∧ ( n * VFS_PAGE_SIZE < min(m8, m2) ∧ n ∈ content1 ⊕ mkcontent(m, cache_pcache0) → (content1 ⊕ mkcontent(m, cache_pcache0))[n] = ((content1 upto min(m8, m2)) ⊕ mkcontent(m, truncate(m, min(m8, m2), cache_pcache0)))[n])

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: right 4

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