Mathlib Map

Theorems · Theorem · order theory

Order.le_two_iff

∀ {α : Type u_1} {x : α} [inst : LinearOrder α] [inst_1 : AddMonoidWithOne α] [SuccAddOrder α] [IsBotZeroClass α]
  [NeZero 1] [NoMaxOrder α], x ≤ 2 ↔ x = 0 ∨ x = 1 ∨ x = 2
Defined in
Mathlib.Algebra.Order.SuccPred
Cited by
1 results in Mathlib
Foundations
Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LinearOrderAddMonoidWithOneSuccAddOrderIsBotZeroClassNeZeroNoMaxOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Ordinal.isPrincipal_mul_of_le_two · cited by 2Ordinal.isPrincipal_mul_o…LinearOrder · cited by 8572LinearOrderNoMaxOrder · cited by 340NoMaxOrderAddMonoidWithOne · cited by 313AddMonoidWithOneSuccAddOrder · cited by 108SuccAddOrderIsBotZeroClass · cited by 71IsBotZeroClassle_iff_lt_or_eq · cited by 26le_iff_lt_or_eqOrder.le_one_iff · cited by 10Order.le_one_iffOrder.lt_two_iff · cited by 5Order.lt_two_iffOrder.le_two_iffCITED BYCITES

Cites8

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

Cited by1

Results whose statement or proof uses this declaration.