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Proof step 968 from proof refine-truncate-buff-none-cached (previous step)

# buf0 = VFS_PAGE_SIZE, ((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[m3] = mkfile(m0, md0, # links(m3, cache_dirs), content0), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), cache_pcache0[datakey(m3, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), 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), datakey(m3, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0, m3 ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ ⟨fail#(; ; err); asynced := ?⟩ ( (cache_files ⊕ cache_pcache0) ⊕ cache_icache = (cache_files[m3, mkfile(m6, md1, # links(m3, cache_dirs), content1 upto min(m6, m2))] ⊕ truncate(m3, min(m6, m2), cache_pcache0)) ⊕ cache_icache[m3, mkientry(false, mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m6))] ∧ ¬ asynced ∧ mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m6) = mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m2) ∧ ¬ asynced0 ∧ ESUCCESS = err), ⟨let ino = m3, content = content0, buf = ? in {old_ino := m2 % VFS_PAGE_SIZE, size := min(m6, m2); asynced0 := m2 ≤ m6 ∧ old_ino ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content; buf-opt := none; afs_files := (cache_files ⊕ cache_pcache0) ⊕ cache_icache; if asynced0 then {pageno := m2 / VFS_PAGE_SIZE; if buf-opt.some? then buf := buf-opt.buf else buf := afs_files[ino].content[pageno]; buf := fill(buf, zero, old_ino, VFS_PAGE_SIZE - old_ino); content[pageno] := buf; buf-opt := some(buf)}; afs_files[ino].content := content upto size; let new_inode = mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m2) in {new_inode.size := m6; cache_dirs0 := cache_dirs; afs_inode_sync#(new_inode; cache_dirs, afs_files)}; inode := (m3 ∈ cache_dirs ⊃ mkinode(m3, cache_dirs[m3].meta, true, cache_dirs[m3].nlink, cache_dirs[m3].nsubdirs, cache_dirs[m3].size) ;mkinode(m3, afs_files[m3].meta, false, afs_files[m3].nlink, 0, afs_files[m3].size) ); err := ESUCCESS}; asynced := ?⟩ ( cache_dirs = cache_dirs0 ∧ afs_files = (cache_files[m3, mkfile(m6, md1, # links(m3, cache_dirs0), content1 upto min(m6, m2))] ⊕ truncate(m3, min(m6, m2), cache_pcache0)) ⊕ cache_icache[m3, mkientry(false, mkinode(m3, md1, false, # links(m3, cache_dirs0), 0, m6))] ∧ ¬ asynced ∧ none = buf-opt ∧ mkinode(m3, md1, false, # links(m3, cache_dirs0), 0, m6) = inode ∧ ¬ asynced0 ∧ ESUCCESS = err), m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0

User applied rule weakening

And obtained the following new goals

Rule argument

poslist: right 1

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