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Proof step 30 from proof truncate-inv (previous step)

⟨afs_truncate_internal#(m0, m0 / VFS_PAGE_SIZE; inode, buf-opt, ino0, ino, isdir, err, dirs, files1; asynced)⟩ ( inode = inode0 ∧ buf-opt = buf-opt1 ∧ ino0 = ino2 ∧ ino = ino3 ∧ (isdir ↔ isdir0) ∧ err = err0 ∧ dirs = dirs0 ∧ files1 = files0 ∧ (asynced ↔ asynced1)), files1[ino1] = mkfile(m0, md, # links(ino1, dirs), content0), buf-opt = none, ino = 0, ino0 = 0, inode = mkinode(ino1, md, false, # links(ino1, dirs), 0, m0), afs-cons(dirs0, files0), afs-cons(dirs, files1), files1 ~ files0, ino1 ∈ files1, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ (err0 = ESUCCESS ⊃ files0[ino1].content.stream from m0 = σ⊥ ∧ (n0 ≤ # buf → ino1 ∈ files0 ∧ files0[ino1].size = m0) ∧ files1 -- ino1 = files0 -- ino1 ;⌊err0⌋ ) ∧ inode0 = mkinode(ino1, md, false, # links(ino1, dirs), 0, m0)

User applied rule call left

And obtained the following new goals

Proof step 31:
⟨ let ino = inode.ino, content = files[inode.ino].content, buf = ? in {ino1 := inode.size % VFS_PAGE_SIZE, ino0 := min(n, inode.size); isdir := inode.size ≤ n ∧ ino1 ≠ 0 ∧ (pageno ∈ content ∨ buf-opt.some?); if isdir then {if buf-opt.some? then buf := buf-opt.buf else buf := files[ino].content[pageno]; buf := fill(buf, zero, ino1, VFS_PAGE_SIZE - ino1); content[pageno] := buf; buf-opt := some(buf)}; files[ino].content := content upto ino0; 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 := ?⟩ ( inode = inode0 ∧ buf-opt = buf-opt1 ∧ ino1 = ino2 ∧ ino0 = ino3 ∧ (isdir ↔ isdir0) ∧ err = err0 ∧ dirs = dirs0 ∧ files = files0 ∧ (asynced ↔ asynced1)), files1[ino4] = mkfile(m0, md, # links(ino4, dirs), content0), buf-opt = none, files = files1, ino = 0, ino0 = ino, ino1 = ino5, ino5 = 0, inode = mkinode(ino4, md, false, # links(ino4, dirs), 0, m0), n = m0, pageno = m0 / VFS_PAGE_SIZE, afs-cons(dirs, files1), afs-cons(dirs0, files0), files1 ~ files0, ino4 ∈ files1, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ VFS_PAGE_SIZE = 0, (err0 = ESUCCESS ⊃ files0[ino4].content.stream from m0 = σ⊥ ∧ (n0 ≤ # buf → ino4 ∈ files0 ∧ files0[ino4].size = m0) ∧ files1 -- ino4 = files0 -- ino4 ;⌊err0⌋ ) ∧ inode0 = mkinode(ino4, md, false, # links(ino4, dirs), 0, m0)

Rule argument

pos: left 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 := ? };