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Proof step 18 from proof inv-seek (previous step)

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

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: n = fd

Additional information

Used simplifier rules: ⊦ fd ≠ fd0 → of[fd0, file][fd] = of[fd]; (s)% ⊦ 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 formulas: n = fd