English
Hausdorff's maximality principle: there exists a maximal totally ordered subset of α; i.e., IsMaxChain r (maxChain r).
Русский
Принцип максимальности Хаусдорфа: существует максимальная totally ordered подмножество α; IsMaxChain r (maxChain r).
LaTeX
$$$ IsMaxChain\, r\ (maxChain\, r) $$$
Lean4
/-- **Hausdorff's maximality principle**
There exists a maximal totally ordered set of `α`.
Note that we do not require `α` to be partially ordered by `r`. -/
theorem maxChain_spec : IsMaxChain r (maxChain r) :=
by_contradiction fun h =>
let ⟨_, H⟩ := chainClosure_maxChain.isChain.superChain_succChain h
H.ne (chainClosure_maxChain.succ_fixpoint_iff.mpr rfl).symm
