Theorems · Theorem · order theory
le_refl
∀ {α : Type u_1} [inst : Preorder α] (a : α), a ≤ aThe relation ≤ on a preorder is reflexive.
- Defined in
- Mathlib.Order.Defs.PartialOrder
- Cited by
- 2,061 results in Mathlib
- Foundations
- Depth 3 from the axioms, rests on 4 definitions · uses no axioms
- Assumes
- Preorder
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.
- Preorderstatement and proof · cited by 7,952
- Preorder.le_reflproof · cited by 1
Cited by2,063
Results whose statement or proof uses this declaration.
- le_rflproof · cited by 1,558
- add_le_addproof · cited by 666
- le_of_eqproof · cited by 366
- mul_le_mul'proof · cited by 274
- Filter.tendsto_idproof · cited by 180
- Finset.sum_nonnegproof · cited by 91
- add_tsub_cancel_of_leproof · cited by 79
- ge_of_eqproof · cited by 67
- MeasureTheory.lintegral_monoproof · cited by 51
- MeasureTheory.Measure.prod_prodproof · cited by 38
- Real.rpow_le_rpowproof · cited by 38
- Ideal.dvd_iff_leproof · cited by 33
Showing the 200 most cited of 2,063.