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Proof step 561 from proof inv-write (previous step)

of[fd, mkfile(m, mode, m0 + n1)][n0] = mkfile(m5, mode1, m6), files[m] = mkfile(m2, md0, # links(m, dirs), content), of[fd] = mkfile(m, mode, m0), files0[m] = mkfile(n1 + m0, md, # links(m, dirs), content0), of[n0] = mkfile(m3, mode0, m4), n1 < ino4, dom of < ino3, afs-cons(dirs, files), afs-cons(dirs, files0), of-cons(of, dirs, files), of-cons(of, dirs, files0), n0 ∈ of[fd, mkfile(m, mode, m0 + n1)], m ∈ files0, fd ∈ of, m ∈ files, m3 ∈ files0, n0 ∈ of, n ≤ # buf0, ⌊err0⌋ ⊦ n = 0, m5 ∈ files, err1 = ESUCCESS ∧ ¬ isdir, (n1 + m0) % VFS_PAGE_SIZE ≠ 0 ∧ (n1 + m0) / VFS_PAGE_SIZE ∈ content0, mode ≠ MODE_W ∧ mode ≠ MODE_RW

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: store, inst: open-files name: At-other seq: ⊦ fd ≠ fd0 → of[fd0, file][fd] = of[fd] subst: [fd, file, fd0, of] → [n0, mkfile(m, mode, m0 + n1), fd, of] flags: <all paths>

Additional information

Used simplifier rules: ⊦ fd ≠ fd0 → (fd ∈ of[fd0, file] ↔ fd ∈ of); (s)%⊦ of-cons(of, dirs, files) ∧ fd ∈ of ∧ of[fd] = mkfile(ino, mode, n) → ino ∈ files; (ss)% ⊦ of[fd, file][fd] = file; (s)%⊦ mkfile(m, mode, m0) = mkfile(m1, mode0, m2) ↔ m = m1 ∧ mode = mode0 ∧ m0 = m2; (ws) Used terms: n0, mkfile(m, mode, m0 + n1), fd, of