[Imprint][Data Privacy Statement][E-Mail]



View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 55 from proof write-prepost (previous step)

⟨afs_truncate#(m1, m1 / VFS_PAGE_SIZE; buf-opt, inode, isdir, err, dirs, files1, asynced)⟩ (buf-opt = buf-opt0 ∧ inode = inode0 ∧ (isdir ↔ isdir0) ∧ err = ESUCCESS ∧ dirs = dirs0 ∧ files1 = files0 ∧ (asynced ↔ asynced0)), files1 -- m = files0 -- m, files0[m] = mkfile(m2, md0, m3, content), of1[fd] = mkfile(m, mode, m0), files1[m] = mkfile(m1, md, # links(m, dirs), content0), buf-opt = none, err = ESUCCESS, files = files0, content.stream from m1 = σ⊥, ino0 = 0, inode = mkinode(m, md, false, # links(m, dirs), 0, m1), inode0 = mkinode(m, md, false, # links(m, dirs), 0, m1), n1 ≠ 0, afs-cons(dirs, files1), of-cons(of1, dirs, files1), write-inv(m0, m0 + n1, mkinode(m, md, false, # links(m, dirs), 0, m1), buf, 0, dirs0, files0, files0), files1 ~ files0, fd ∈ of1, m ∈ files1, n1 ≤ # buf ⊦ [vfs_write_loop#(of1[fd].pos, mkinode(m, md, false, # links(m, dirs), 0, m1), of1[fd].pos + n1, buf, dirs0; ino0, err, files0, asynced0)] ( write-inv(of1[fd].pos, of1[fd].pos + n1, mkinode(m, md, false, # links(m, dirs), 0, m1), buf, ino0, dirs0, files, files0) → [if ino0 ≠ 0 then err := ESUCCESS; of := of1; n := n1; if err = ESUCCESS then let ino = m1 in {n := ino0, ino1 := of1[fd].pos + ino0; if ino0 ≠ 0 ∧ ino < ino1 then {inode0 := mkinode(m, md, false, # links(m, dirs), 0, ino1); afs_check_commit#(dirs0, files0; err; asynced0); if err = ESUCCESS then afs_write_inode#(inode0; err, dirs0, files0; asynced0)}; ino2 := of1[fd].pos; if err ≠ ESUCCESS then n := (ino2 ≤ ino ⊃ ino - ino2;0), err := ESUCCESS; of[fd].pos := ino2 + n}; file := of1[fd]] (err = ESUCCESS ⊃ (files0[file.ino].content.stream to files0[file.ino].size).buf = splice(buf, 0, (files1[file.ino].content.stream to files1[file.ino].size).buf, file.pos, n) ∧ of = of1[fd, file.pos:= (file.pos + n)] ∧ n ≤ n1 ∧ file.ino ∈ files1 ∧ file.ino ∈ files0 ∧ files0[file.ino].meta = files1[file.ino].meta ∧ files0 -- file.ino = files1 -- file.ino ∧ (file.mode = MODE_W ∨ file.mode = MODE_RW) ;files0 ~ files1 ∧ of1 = of ∧ (err = EBADFD ∧ (fd ∈ of → file.mode ≠ MODE_W ∧ file.mode ≠ MODE_RW) ∨ ⌊err⌋ ) )), mode ≠ MODE_W ∧ mode ≠ MODE_RW

User applied rule insert program lemma

And obtained the following new goals

Rule argument

spec: vfs-asm name: write-loop-0 seq: files0 = files1 ⊦ [vfs_write_loop# (n0, inode, n1, buf, dirs; n, err, files0, asynced)] (n = 0 → files0 = files1) subst: [dirs, buf, n1, inode, n0, asynced, files0, err, n, files1] → [dirs0, buf, of1[fd].pos + n1, mkinode(m, md, false, # links(m, dirs), 0, m1), of1[fd].pos, asynced0, files0, err, ino0, files0] flags: <all paths>

Additional information