Theorems · Theorem · order theory
le_iff_lt_or_eq
∀ {α : Type u_1} [inst : PartialOrder α] {a b : α}, a ≤ b ↔ a < b ∨ a = b- Defined in
- Mathlib.Order.Defs.PartialOrder
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext, Classical.choice, Quot.sound
- 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 and proof · cited by 6,410
- Decidable.le_iff_lt_or_eqproof · cited by 2
Cited by26
Results whose statement or proof uses this declaration.
- le_iff_eq_or_ltproof · cited by 20
- IsAtom.le_iffproof · cited by 10
- Order.le_one_iffproof · cited by 10
- Real.continuousAt_rpow_constproof · cited by 8
- Set.Iio_union_rightproof · cited by 3
- Metric.ball_union_sphereproof · cited by 3
- CauSeq.const_leproof · cited by 2
- Polynomial.isBigO_atTop_of_degree_leproof · cited by 2
- Odd.pow_nonpos_iffproof · cited by 2
- ChainCompletePartialOrder.IsExtremePt.setOfPred_isExtremePt_isAdmissibleproof · cited by 2
- Set.encard_le_one_iff_eqproof · cited by 2
- Odd.zpow_nonpos_iffproof · cited by 2