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Proof step 35 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), files[m2] = mkfile(m1, md, # links(m2, dirs), content0), files0[m2] = mkfile(m, md, m0, content), of[fd] = mkfile(m2, mode, m3), abs-files(files)[⌜m2⌝ ] = mkfile(md0, buf0), 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, psynced → asynced, mode = MODE_W ∨ mode = MODE_RW ⊦ ∃ n. n ≤ n0 ∧ ⟨n0 := n; f := mkfile(md0, splice(buf, 0, buf0, m3, n0)); fs := abs-files(files)[⌜m2⌝ , f]; ofh := abs-of(of[fd, mkfile(m2, mode, m3 + n0)]); psynced := ?⟩ (ofh = abs-of(of[fd, of[fd].pos:= (m3 + n0)]) ∧ fs = abs-files(files0) ∧ (psynced → asynced0) ∧ n1 = n0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 36:
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, psynced → asynced, mode = MODE_W ∨ mode = MODE_RW ⊦ ∃ n. n ≤ n0 ∧ ⟨n0 := n; f := mkfile(md, splice(buf, 0, (content0.stream to m1).buf, m3, n0)); fs := abs-files(files)[⌜m2⌝ , f]; ofh := abs-of(of[fd, mkfile(m2, mode, m3 + n0)]); psynced := ?⟩ (ofh = abs-of(of[fd, of[fd].pos:= (m3 + n0)]) ∧ fs = abs-files(files0) ∧ (psynced → asynced0) ∧ n1 = n0)

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).size = m; (s)% ⊦ mkfile(m, md, m0, content).content = content; (s)% ⊦ mkfile(m, md, m0, content).meta = md; (s)% ⊦ mkfile(md, buf) = mkfile(md0, buf0) ↔ md = md0 ∧ buf = buf0; (ws)%⊦ ino ∈ files → abs-files(files)[⌜ino⌝ ] = mkfile (files[ino].meta, (files[ino].content.stream to files[ino].size).buf); (s)