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Proof step 41 from proof refine-seek (previous step)

err = ESUCCESS, 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, psynced → asynced ⊦ ⟪afs_iget#(of[fd].ino, dirs, files, asynced; inode, err); n := n0; if err = ESUCCESS then n := inode.size + n; ofh := abs-of(of); if err = ESUCCESS then of[fd].pos := n⟫ ⟨posix_seek#(fd, SEEK_END, user, root, abs-files(files); n0, err0, ofh)⟩ (ofh = abs-of(of) ∧ (psynced → asynced) ∧ n = n0 ∧ err = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 42:
of[fd] = mkfile(m, mode, m0), err = ESUCCESS, 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, psynced → asynced ⊦ ⟪afs_iget#(m, dirs, files, asynced; inode, err); n := n0; if err = ESUCCESS then n := inode.size + n; ofh := abs-of(of); if err = ESUCCESS then of[fd].pos := n⟫ ⟨posix_seek#(fd, SEEK_END, user, root, abs-files(files); n0, err0, ofh)⟩ (ofh = abs-of(of) ∧ (psynced → asynced) ∧ n = n0 ∧ err = 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], m, mode, m0]

Additional information

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