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Theorem refine-truncate-buff-some

valid-file-inode(inode, afs_dirs, afs_files), pageno = inode.size / VFS_PAGE_SIZE, buf-opt.some?, # buf-opt.buf = VFS_PAGE_SIZE, afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, afs_asynced ↔ cache_asynced, afs-cons(afs_dirs, afs_files), icache-cons(cache_icache, cache_dirs, cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), cache_sync → synced(cache_files, cache_icache, cache_pcache), afs-cons(cache_dirs, cache_files), buf-opt = buf-opt0, inode = inode0, asynced ↔ asynced0, err = err0 ⊦ ⟪cache_truncate#(n, pageno; buf-opt, inode, asynced, err, cache_dirs, cache_files, cache_asynced, cache_icache, cache_pcache)⟫ ⟨afs_truncate#(n, pageno; buf-opt0, inode0, asynced0, err0, afs_dirs, afs_files, afs_asynced)⟩ ( (afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ cache_asynced)) ∧ buf-opt = buf-opt0 ∧ inode = inode0 ∧ (asynced ↔ asynced0) ∧ err = err0)

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