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Proof step 115 from proof refine-truncate-buff-none-uncached (previous step)

VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, cache_files[m1] = mkfile(m3, md1, # links(m1, cache_dirs), content), ((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[m1] = mkfile(m0, md0, # links(m1, cache_dirs), content0), afs_files = (cache_files ⊕ cache_pcache0) ⊕ cache_icache, buf-opt = none, cache_dirs0 = cache_dirs, inode = mkinode(m1, md, false, # links(m1, cache_dirs), 0, m2), old_ino = 0, size = 0, m2 % VFS_PAGE_SIZE ≠ 0, 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), m2 / VFS_PAGE_SIZE ∈ content, m1 ∈ cache_files, m2 ≤ m, ¬ datakey(m1, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ ⟨afs_truncate_internal#(m, m2 / VFS_PAGE_SIZE; inode, buf-opt, old_ino, size, asynced0, err, cache_dirs, afs_files; asynced)⟩ ( cache_dirs = cache_dirs0 ∧ afs_files = ( cache_files [m1, mkfile (m, md, # links(m1, cache_dirs0), content[m2 / VFS_PAGE_SIZE, fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] ⊕ truncate(m1, m2, cache_pcache0) [datakey(m1, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)) ]) ⊕ cache_icache[m1, mkientry(false, mkinode(m1, md, false, # links(m1, cache_dirs0), 0, m))] ∧ ¬ asynced ∧ some(fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)) = buf-opt ∧ (m1 ∈ cache_dirs0 ⊃ mkinode(m1, cache_dirs0[m1].meta, true, cache_dirs0[m1].nlink, cache_dirs0[m1].nsubdirs, cache_dirs0[m1].size) ;mkinode(m1, md, false, # links(m1, cache_dirs0), 0, m) ) = inode ∧ asynced0 ∧ ESUCCESS = err)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 116:
VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, ((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[m1] = mkfile(m0, md0, # links(m1, cache_dirs), content0), cache_files[m1] = mkfile(m3, md1, # links(m1, cache_dirs), content), afs_files = (cache_files ⊕ cache_pcache0) ⊕ cache_icache, buf-opt = none, cache_dirs0 = cache_dirs, dirs = cache_dirs, files = afs_files, inode = mkinode(m1, md, false, # links(m1, cache_dirs), 0, m2), n = m, old_ino = 0, pageno = m2 / VFS_PAGE_SIZE, size = 0, 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), m1 ∈ cache_files, m2 / VFS_PAGE_SIZE ∈ content, m2 ≤ m, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ ⟨ let ino = inode.ino, content = files[inode.ino].content, buf = ? in {old_ino := inode.size % VFS_PAGE_SIZE, size := min(n, inode.size); asynced0 := inode.size ≤ n ∧ old_ino ≠ 0 ∧ (pageno ∈ content ∨ buf-opt.some?); if asynced0 then {if buf-opt.some? then buf := buf-opt.buf else buf := files[ino].content[pageno]; buf := fill(buf, zero, old_ino, VFS_PAGE_SIZE - old_ino); content[pageno] := buf; buf-opt := some(buf)}; files[ino].content := content upto size; let new_inode = inode in {new_inode.size := n; afs_inode_sync#(new_inode; dirs, files)}; inode := getinode(inode.ino, dirs, files); err := ESUCCESS} or fail#(; ; err); asynced := ?⟩ ( dirs = cache_dirs0 ∧ files = ( cache_files [m1, mkfile (m, md, # links(m1, cache_dirs0), content[m2 / VFS_PAGE_SIZE, fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] ⊕ truncate(m1, m2, cache_pcache0) [datakey(m1, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)) ]) ⊕ cache_icache[m1, mkientry(false, mkinode(m1, md, false, # links(m1, cache_dirs0), 0, m))] ∧ ¬ asynced ∧ some(fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)) = buf-opt ∧ (m1 ∈ cache_dirs0 ⊃ mkinode(m1, cache_dirs0[m1].meta, true, cache_dirs0[m1].nlink, cache_dirs0[m1].nsubdirs, cache_dirs0[m1].size) ;mkinode(m1, md, false, # links(m1, cache_dirs0), 0, m) ) = inode ∧ asynced0 ∧ ESUCCESS = err), m2 % VFS_PAGE_SIZE = 0, VFS_PAGE_SIZE = 0, datakey(m1, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0

Rule argument

pos: right 1

Additional information

Used simplifier rules: afs_truncate_internal# (N, PAGENO ; INODE, PBUF-OPT, OFFSET, SIZE, MODIFIED, ERR, DIRS, FILES ; ASYNCED ) { let INO = INODE.ino, CONTENT = FILES[INODE.ino].content, PBUF = ? in {OFFSET := INODE.size % VFS_PAGE_SIZE, SIZE := min(N, INODE.size); MODIFIED := INODE.size ≤ N ∧ OFFSET ≠ 0 ∧ (PAGENO ∈ CONTENT ∨ PBUF-OPT.some?); if MODIFIED then {if PBUF-OPT.some? then PBUF := PBUF-OPT.buf else PBUF := FILES[INO].content[PAGENO]; PBUF := fill(PBUF, zero, OFFSET, VFS_PAGE_SIZE - OFFSET); CONTENT[PAGENO] := PBUF; PBUF-OPT := some(PBUF)}; FILES[INO].content := CONTENT upto SIZE; let NEW_INODE = INODE in {NEW_INODE.size := N; afs_inode_sync#(NEW_INODE; DIRS, FILES)}; INODE := getinode(INODE.ino, DIRS, FILES); ERR := ESUCCESS} or fail#(; ; ERR); ASYNCED := ? };% ⊦ VFS_PAGE_SIZE ≠ 0; (s)