[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 39 from proof refine-write (previous step)

files0 -- m2 = files -- m2, (content.stream to m).buf = splice(buf, 0, (content0.stream to m1).buf, m3, n1), of[fd] = mkfile(m2, mode, m3), files0[m2] = mkfile(m, md, m0, content), files[m2] = mkfile(m1, md, # links(m2, dirs), content0), root.dir?, dom of < ino, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), of-cons(of, dirs, files), m2 ∈ files, fd ∈ of, m2 ∈ files0, n1 ≤ # buf, n0 ≤ # buf, n1 ≤ n0, psynced → asynced, mode = MODE_W ∨ mode = MODE_RW ⊦ ⟨f := mkfile(md, splice(buf, 0, (content0.stream to m1).buf, m3, n1)); fs := abs-files(files)[⌜m2⌝ , f]; ofh := abs-of(of[fd, mkfile(m2, mode, m3 + n1)]); psynced := ?⟩ (ofh = abs-of(of[fd, of[fd].pos:= (m3 + n1)]) ∧ fs = abs-files(files0) ∧ (psynced → asynced0) ∧ n1 = n1)

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 40:
files0 -- m2 = files -- m2, (content.stream to m).buf = splice(buf, 0, (content0.stream to m1).buf, m3, n1), files[m2] = mkfile(m1, md, # links(m2, dirs), content0), files0[m2] = mkfile(m, md, m0, content), of[fd] = mkfile(m2, mode, m3), root.dir?, dom of < ino, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), of-cons(of, dirs, files), m2 ∈ files0, fd ∈ of, m2 ∈ files, n1 ≤ n0, n0 ≤ # buf, n1 ≤ # buf, finp(content0.stream) → ⌜m1⌝ < # content0.stream ∨ ⌜m1⌝ = # content0.stream, psynced → asynced, mode = MODE_W ∨ mode = MODE_RW ⊦ ⟨fs := abs-files(files)[⌜m2⌝ , mkfile(md, splice(buf, 0, (content0.stream to m1).buf, m3, n1))]; ofh := abs-of(of[fd, mkfile(m2, mode, m3 + n1)]); psynced := ?⟩ (ofh = abs-of(of[fd, of[fd].pos:= (m3 + n1)]) ∧ fs = abs-files(files0) ∧ (psynced → asynced0) ∧ n1 = n1)

Rule argument

Additional information

Used simplifier rules: ⊦ # content.stream = ∞; (s)% ⊦ ⌜m⌝ ≠ ∞; (s)% ⊦ ⌜m⌝ < ∞; (s)