Theorems · Theorem · order theory
LE.le.antisymm
∀ {α : Type u_1} [inst : PartialOrder α] {a b : α}, a ≤ b → b ≤ a → a = bAlias of le_antisymm.
- Defined in
- Mathlib.Order.Basic
- Cited by
- 507 results in Mathlib
- Foundations
- Depth 4 from the axioms, rests on 7 definitions · uses no axioms
- Assumes
- PartialOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement · cited by 6,410
- le_antisymmproof · cited by 2,068
Cited by507
Results whose statement or proof uses this declaration.
- top_uniqueproof · cited by 102
- eq_of_forall_le_iffproof · cited by 65
- IsOpen.interior_eqproof · cited by 58
- MeasureTheory.Measure.prod_prodproof · cited by 38
- GaloisInsertion.l_u_eqproof · cited by 37
- ENNReal.coe_invproof · cited by 27
- Cardinal.IsRegular.cof_ordproof · cited by 23
- interior_interproof · cited by 22
- Cardinal.mk_eq_aleph0proof · cited by 20
- GaloisConnection.u_l_u_eq_uproof · cited by 17
- OrderIso.map_infproof · cited by 17
- Polynomial.natDegree_eq_of_le_of_coeff_ne_zeroproof · cited by 15
Showing the 200 most cited of 507.