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Proof step 111 from proof refine-seek (previous step)

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 ⊦ whence = SEEK_CUR, whence = SEEK_END, of[fd].ino ∈ files

Heuristic elimination applied rule insert elim lemma

And closed the goal!

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: ⊦ of-cons(of, dirs, files) ∧ fd ∈ of ∧ of[fd] = mkfile(ino, mode, n) → ino ∈ files; (ss)%⊦ (m = file.ino ∧ mode = file.mode) ∧ m0 = file.pos ↔ file = mkfile(m, mode, m0); (elim) Used terms: of[fd], m, mode, m0