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Proof step 55 from proof inv-seek (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 56:
of[n0] = mkfile(m, mode, m0), of[fd, of[fd].pos:= n][n0] = mkfile(m1, mode0, m2), dom of < ino, afs-cons(dirs, files), of-cons(of, dirs, files), fd ∈ of, n0 ∈ of[fd, of[fd].pos:= n], n0 ∈ of → m ∈ files ⊦ whence = SEEK_CUR, whence = SEEK_END, m1 ∈ 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[fd, of[fd].pos:= n][n0], m1, mode0, m2]

Additional information

Used simplifier rules: ⊦ (m = file.ino ∧ mode = file.mode) ∧ m0 = file.pos ↔ file = mkfile(m, mode, m0); (elim) Used terms: of[fd, of[fd].pos:= n][n0], m1, mode0, m2