[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 21 from proof refine-write (previous step)

files0 -- of[fd].ino = files -- of[fd].ino, (content.stream to m).buf = splice(buf, 0, (content0.stream to m1).buf, of[fd].pos, n1), files0[of[fd].ino] = mkfile(m, md, m0, content), files[of[fd].ino] = mkfile(m1, md, # links(of[fd].ino, dirs), content0), fs = abs-files(files), ofh = abs-of(of), 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), fd ∈ of, of[fd].ino ∈ files, of[fd].ino ∈ files0, n1 ≤ # buf, n0 ≤ # buf, n1 ≤ n0, psynced → asynced, of[fd].mode = MODE_W ∨ of[fd].mode = MODE_RW ⊦ fd ∈ ofh ∧ (ofh[fd].mode = MODE_W ∨ ofh[fd].mode = MODE_RW) ∧ ⟨err0 := ESUCCESS; if err0 = ESUCCESS then let fh = ofh[fd] in let f = fs[fh.fid] in choose n with n ≤ n0 in {n0 := n; f.content := splice(buf, 0, f.content, fh.pos, n0); fs[fh.fid] := f; ofh[fd].pos := fh.pos + n0} else n0 := ?; psynced := ?⟩ (ofh = abs-of(of[fd, of[fd].pos:= (of[fd].pos + n0)]) ∧ fs = abs-files(files0) ∧ (psynced → asynced0) ∧ n1 = n0 ∧ ESUCCESS = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 22:
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), fs = abs-files(files), ofh = abs-of(of), 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, m2 ∈ files, fd ∈ of, n1 ≤ n0, n0 ≤ # buf, n1 ≤ # buf, psynced → asynced, mode = MODE_W ∨ mode = MODE_RW ⊦ fd ∈ ofh ∧ (ofh[fd].mode = MODE_W ∨ ofh[fd].mode = MODE_RW) ∧ ⟨err0 := ESUCCESS; if err0 = ESUCCESS then let fh = ofh[fd] in let f = fs[fh.fid] in choose n with n ≤ n0 in {n0 := n; f.content := splice(buf, 0, f.content, fh.pos, n0); fs[fh.fid] := f; ofh[fd].pos := fh.pos + n0} else n0 := ?; psynced := ?⟩ (ofh = abs-of(of[fd, of[fd].pos:= (m3 + n0)]) ∧ fs = abs-files(files0) ∧ (psynced → asynced0) ∧ n1 = n0 ∧ ESUCCESS = err0)

Rule argument

spec: file name: elim seq: ⊦ (m = file.ino ∧ mode = file.mode) ∧ m0 = file.pos ↔ file = mkfile(m, mode, m0) subst: [file, m, mode, m0] → [of[fd], m2, mode, m3]

Additional information

Used simplifier rules: ⊦ (m = file.ino ∧ mode = file.mode) ∧ m0 = file.pos ↔ file = mkfile(m, mode, m0); (elim) Used terms: of[fd], m2, mode, m3