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Proof step 821 from proof refine-truncate-buff-some (previous step)

# buf-opt0.buf = VFS_PAGE_SIZE, cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), ((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[m3] = mkfile(m0, md0, # links(m3, cache_dirs), content0), content = content0, ino = m3, buf-opt0.some?, 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), m3 ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ ⟨old_ino := m2 % VFS_PAGE_SIZE, size := min(m6, m2); asynced0 := m2 ≤ m6 ∧ old_ino ≠ 0 ∧ (m2 / VFS_PAGE_SIZE ∈ content ∨ buf-opt0.some?); buf-opt := buf-opt0; 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 ↔ asynced1) ∧ buf-opt0 = buf-opt ∧ mkinode(m3, md1, false, # links(m3, cache_dirs0), 0, m6) = inode ∧ ¬ asynced0 ∧ ESUCCESS = err), m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 822:
# buf-opt0.buf = 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), content = content0, ino = m3, old_ino = m2 % VFS_PAGE_SIZE, size = min(m6, m2), buf-opt0.some?, afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache0) ⊕ cache_icache), 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), m3 ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ ⟨asynced0 := m2 ≤ m6 ∧ old_ino ≠ 0 ∧ (m2 / VFS_PAGE_SIZE ∈ content ∨ buf-opt0.some?); buf-opt := buf-opt0; 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 ↔ asynced1) ∧ buf-opt0 = buf-opt ∧ mkinode(m3, md1, false, # links(m3, cache_dirs0), 0, m6) = inode ∧ ¬ asynced0 ∧ ESUCCESS = err), VFS_PAGE_SIZE = 0, m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0

Rule argument

Additional information

Used simplifier rules: ⊦ VFS_PAGE_SIZE ≠ 0; (s)