extensional_of_trichotomous_of_irrefl

∀ {α : Sort u_1} (r : α → α → Prop) [Std.Trichotomous r] [Std.Irrefl r] {a b : α}, (∀ (x : α), r x a ↔ r x b) → a = b

In a trichotomous irreflexive order, every element is determined by the set of predecessors.

Defined in: Mathlib.Order.Defs.Unbundled
Cited by: 1 results in Mathlib
Foundations: Depth 12 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Std.Trichotomous Std.Irrefl

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