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Proof step 38 from proof inv-read (previous step)

of[fd] = mkfile(m, mode, m0), files[m] = mkfile(m1, md, # links(m, dirs), content), of[n0] = mkfile(m2, mode0, m3), dom of < ino2, afs-cons(dirs, files), of-cons(of, dirs, files), m2 ∈ files, n0 ∈ of, n0 ∈ of[fd, mkfile(m, mode, m0 + ino)], fd ∈ of, m ∈ files, n ≤ # buf, m0 ≤ m1 ⊦ ino = 0, of[fd, mkfile(m, mode, m0 + ino)][n0].ino ∈ files, mode ≠ MODE_R ∧ mode ≠ MODE_RW

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 39:
of[n0] = mkfile(m2, mode0, m3), files[m] = mkfile(m1, md, # links(m, dirs), content), of[fd] = mkfile(m, mode, m0), of[fd, mkfile(m, mode, m0 + ino)][n0] = mkfile(m4, mode1, m5), dom of < ino2, afs-cons(dirs, files), of-cons(of, dirs, files), m ∈ files, fd ∈ of, n0 ∈ of[fd, mkfile(m, mode, m0 + ino)], n0 ∈ of, m2 ∈ files, m0 ≤ m1, n ≤ # buf ⊦ ino = 0, m4 ∈ files, mode ≠ MODE_R ∧ mode ≠ MODE_RW

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, mkfile(m, mode, m0 + ino)][n0], m4, mode1, m5]

Additional information

Used simplifier rules: ⊦ (m = file.ino ∧ mode = file.mode) ∧ m0 = file.pos ↔ file = mkfile(m, mode, m0); (elim) Used terms: of[fd, mkfile(m, mode, m0 + ino)][n0], m4, mode1, m5