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Proof step 182 from proof refine-read (previous step)

files[m3] = mkfile(m1, md, # links(m3, dirs), content), of[fd] = mkfile(m3, mode0, m4), abs-files(files)[⌜m3⌝ ] = mkfile(md0, buf), root.dir?, dom of < ino2, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), of-cons(of, dirs, files), read-inv(m4, m4 + n0, mkinode(m3, md, false, # links(m3, dirs), 0, m1), buf0, buf0, 0, dirs, files), read-inv(m4, m4 + n0, mkinode(m3, md, false, # links(m3, dirs), 0, m1), buf0, buf1, 0, dirs, files), m3 ∈ files, fd ∈ of, n0 ≤ # buf0, m4 ≤ m1, psynced → asynced ⊦ ∃ n1. n1 ≤ n0 ∧ of[fd].pos + n1 ≤ files[of[fd].ino].size ∧ ⟨n0 := n1; buf0 := copy(buf, m4, buf0, 0, n0); ofh := abs-of(of[fd, mkfile(m3, mode0, m4 + n0)])⟩ (ofh = abs-of(of[fd, of[fd].pos:= m4]) ∧ (psynced → asynced) ∧ buf1 = buf0 ∧ 0 = n0), mode0 ≠ MODE_R ∧ mode0 ≠ MODE_RW, abs-of(of) = abs-of(of[fd, of[fd].pos:= m4]) ∧ (psynced → asynced) ∧ buf1 = buf0 ∧ 0 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 183:
files[m3] = mkfile(m1, md, # links(m3, dirs), content), of[fd] = mkfile(m3, mode0, m4), buf1 ≠ buf0, root.dir?, dom of < ino2, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), of-cons(of, dirs, files), read-inv(m4, m4 + n0, mkinode(m3, md, false, # links(m3, dirs), 0, m1), buf0, buf0, 0, dirs, files), read-inv(m4, m4 + n0, mkinode(m3, md, false, # links(m3, dirs), 0, m1), buf0, buf1, 0, dirs, files), m3 ∈ files, fd ∈ of, n0 ≤ # buf0, m4 ≤ m1, psynced → asynced ⊦ ∃ n. n ≤ n0 ∧ of[fd].pos + n ≤ files[of[fd].ino].size ∧ ⟨n0 := n; buf0 := copy((content.stream to m1).buf, m4, buf0, 0, n0); ofh := abs-of(of[fd, mkfile(m3, mode0, m4 + n0)])⟩ (ofh = abs-of(of[fd, of[fd].pos:= m4]) ∧ (psynced → asynced) ∧ buf1 = buf0 ∧ 0 = n0), mode0 ≠ MODE_R ∧ mode0 ≠ MODE_RW

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).size = m; (s)% ⊦ mkfile(m, md, m0, content).content = content; (s)% ⊦ of[fd] = file ∧ fd ∈ of → of[fd, file] = of; (s)% ⊦ mkfile(m, mode, m0).pos:= m2 = mkfile(m, mode, m2); (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)