Theorems · Theorem · order theory
le_of_lt
∀ {α : Type u_1} [inst : Preorder α] {a b : α}, a < b → a ≤ b- Defined in
- Mathlib.Order.Defs.PartialOrder
- Cited by
- 1,175 results in Mathlib
- Foundations
- Depth 4 from the axioms, rests on 11 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
- lt_iff_le_not_geproof · cited by 35
Cited by1,175
Results whose statement or proof uses this declaration.
- LT.lt.leproof · cited by 2,189
- lt_of_lt_of_leproof · cited by 438
- lt_of_le_of_ltproof · cited by 432
- lt_transproof · cited by 165
- Real.rpow_nonnegproof · cited by 111
- Real.rpow_mulproof · cited by 67
- Set.Ioc_subset_Icc_selfproof · cited by 53
- lt_iff_le_and_neproof · cited by 47
- Metric.ball_subset_closedBallproof · cited by 46
- Set.Ico_subset_Icc_selfproof · cited by 41
- Real.rpow_le_rpowproof · cited by 38
- Real.rpow_def_of_posproof · cited by 35
Showing the 200 most cited of 1,175.