Theorems · Theorem · order theory
le_one_iff_eq_one
∀ {α : Type u_1} {a : α} [inst : PartialOrder α] [inst_1 : One α] [IsBotOneClass α], a ≤ 1 ↔ a = 1- Defined in
- Mathlib.Algebra.Order.IsBotOne
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- PartialOrderOneIsBotOneClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- LE.le.ge_iff_eq'proof · cited by 50
- IsBotOneClassstatement and proof · cited by 35
- one_leproof · cited by 23
Cited by2
Results whose statement or proof uses this declaration.
- eq_one_of_le_oneproof · cited by 1
- PNat.eq_one_of_lt_twoproof · cited by 0