Mathlib Map

Theorems · Theorem · logic and foundations

ZFSet.IsOrdinal.trichotomous

∀ {x : ZFSet.{u}}, x.IsOrdinal → Std.Trichotomous (Subrel (fun x1 x2 => x1 ∈ x2) fun x_1 => x_1 ∈ x)
Defined in
Mathlib.SetTheory.ZFC.Ordinal
Cited by
2 results in Mathlib
Foundations
Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ZFSet.isOrdinal_iff_trichotomous · cited by 1ZFSet.isOrdinal_iff_trich…ZFSet.IsOrdinal.isTrichotomous · cited by 0IsOrdinal.isTrichotomousZFSet · cited by 259ZFSetSubrel · cited by 53SubrelZFSet.IsOrdinal · cited by 34ZFSet.IsOrdinalZFSet.IsOrdinal.mem · cited by 7IsOrdinal.memZFSet.IsOrdinal.mem_trichotomous · cited by 1IsOrdinal.mem_trichotomousIsOrdinal.trichotomousCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.