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Proof step 230 from proof refine-read (previous step)

files[m] = mkfile(m1, md, # links(m, dirs), content), of[fd] = mkfile(m, mode, m0), root.dir?, m1 < m0, 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), m ∈ files, fd ∈ of, n0 ≤ # buf0, psynced → asynced ⊦ (¬ n ≤ n0 ∨ ¬ of[fd].pos + n ≤ files[of[fd].ino].size) ∧ ⟨n0 := 0⟩ ((psynced → asynced) ∧ 0 = n0), ∃ n1. n1 ≤ n0 ∧ of[fd].pos + n1 ≤ files[of[fd].ino].size ∧ ⟨n0 := n1; buf := copy((content.stream to m1).buf, m0, buf0, 0, n0); ofh := abs-of(of[fd, mkfile(m, mode, m0 + n0)])⟩ (ofh = abs-of(of) ∧ (psynced → asynced) ∧ buf0 = buf ∧ 0 = n0), mode ≠ MODE_R ∧ mode ≠ MODE_RW

Heuristic dl case distinction applied rule case distinction

And obtained the following new goals

Proof step 231:
of[fd] = mkfile(m, mode, m0), files[m] = mkfile(m1, md, # links(m, dirs), content), root.dir?, dom of < ino2, m1 < m0, 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, m ∈ files, n0 ≤ # buf0, psynced → asynced ⊦ ⟨n0 := 0⟩ ((psynced → asynced) ∧ 0 = n0), ∃ n1. n1 ≤ n0 ∧ of[fd].pos + n1 ≤ files[of[fd].ino].size ∧ ⟨n0 := n1; buf := copy((content.stream to m1).buf, m0, buf0, 0, n0); ofh := abs-of(of[fd, mkfile(m, mode, m0 + n0)])⟩ (ofh = abs-of(of) ∧ (psynced → asynced) ∧ buf0 = buf ∧ 0 = n0), mode ≠ MODE_R ∧ mode ≠ MODE_RW

Rule argument

pos: right 1

Additional information

Used simplifier rules: let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat% ⊦ mkfile(m, mode, m0).pos = m0; (s)% ⊦ mkfile(m, mode, m0).ino = m; (s)% ⊦ mkfile(m, md, m0, content).size = m; (s)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ ¬ m + n < m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic