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Proof step 14 from proof inv-seek (previous step)

dom of < ino, afs-cons(dirs, files), of-cons(of, dirs, files), fd ∈ of, n ∈ of[fd, of[fd].pos:= (of[fd].pos + n0)], n ∈ of → of[n].ino ∈ files ⊦ of[fd, of[fd].pos:= (of[fd].pos + n0)][n].ino ∈ files

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 15:
of[n] = mkfile(m, mode, m0), dom of < ino, afs-cons(dirs, files), of-cons(of, dirs, files), n ∈ of[fd, of[fd].pos:= (of[fd].pos + n0)], fd ∈ of, n ∈ of → m ∈ files ⊦ of[fd, of[fd].pos:= (of[fd].pos + n0)][n].ino ∈ files

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[n], 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[n], m, mode, m0