According to the documentation, there should be a Lemma le_not_gt_iff in Coq.Structures.OrdersFacts, but I haven't succeeded in referencing it.
I am trying to prove 2 < 1 → False
as part of a proof. I tried Nat.order tactic but it didn't work.
So now I am looking into Coq.Structures.OrdersFacts to find another Lemma that can help, and found le_not_gt_iff.
The problem I have is that the import
Require Import Coq.Structures.OrdersFacts.
doesn't seem to be enough to have access to the Lemma. I see it seems to be encapsulated in a module definition OrderedTypeFullFacts, but I don't know how to import that.