Theorems · Theorem · order theory
le_iff_eq_or_lt
∀ {α : Type u_2} [inst : PartialOrder α] {a b : α}, a ≤ b ↔ a = b ∨ a < b- Defined in
- Mathlib.Order.Basic
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 13 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
- le_iff_lt_or_eqproof · cited by 26
Cited by20
Results whose statement or proof uses this declaration.
- ENNReal.coe_rpow_of_nonnegproof · cited by 34
- Real.rpow_lt_rpowproof · cited by 12
- Order.le_succ_iff_eq_or_leproof · cited by 6
- Set.Iio_insertproof · cited by 5
- LieAlgebra.derivedSeriesOfIdeal_leproof · cited by 4
- Order.lt_succ_iff_eq_or_lt_of_not_isMaxproof · cited by 3
- Valuation.map_add_of_distinct_valproof · cited by 3
- PhragmenLindelof.horizontal_stripproof · cited by 3
- Order.lt_succ_iff_eq_or_ltproof · cited by 2
- IsAtom.le_iSupproof · cited by 2
- AddCircle.liftIoc_eq_liftIcoproof · cited by 1
- Order.le_iff_eq_or_succ_leproof · cited by 1