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Proof step 37 from proof inv-seek (previous step)

of[n0] = mkfile(m3, mode0, m4), of[fd] = mkfile(m, mode, m0), files[m] = mkfile(m1, md, m2, content), of[fd, mkfile(m, mode, m1 + n)][n0] = mkfile(m5, mode1, m6), dom of < ino0, afs-cons(dirs, files), of-cons(of, dirs, files), m3 ∈ files, n0 ∈ of, n0 ∈ of[fd, mkfile(m, mode, m1 + n)], fd ∈ of ⊦ m5 ∈ files

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, m1 + n), 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)% ⊦ fd ∈ of[fd, file]; (s) Used terms: n0, mkfile(m, mode, m1 + n), fd, of