English
Equivalences between congrOrderIso and their underlying equivalence are preserved.
Русский
Эквивалентности между congrOrderIso и их базовыми эквивалентностями сохраняются.
LaTeX
$$$\text{congrOrderIso } e = \text{equiv ...}$$$
Lean4
/-- There is at most one ordered ring homomorphism from a linear ordered field to an archimedean
linear ordered field. -/
instance subsingleton [IsStrictOrderedRing β] [Archimedean β] : Subsingleton (α →+*o β) :=
⟨fun f g => by
ext x
by_contra! h' : f x ≠ g x
wlog h : f x < g x with h₂
· exact h₂ g f x (Ne.symm h') (h'.lt_or_gt.resolve_left h)
obtain ⟨q, hf, hg⟩ := exists_rat_btwn h
rw [← map_ratCast f] at hf
rw [← map_ratCast g] at hg
exact (lt_asymm ((OrderHomClass.mono g).reflect_lt hg) <| (OrderHomClass.mono f).reflect_lt hf).elim⟩
