Theorems · Theorem · order theory
LE.le.lt_or_eq
∀ {α : Type u_1} [inst : PartialOrder α] {a b : α}, a ≤ b → a < b ∨ a = bAlias of lt_or_eq_of_le.
- Defined in
- Mathlib.Order.Basic
- Cited by
- 48 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 · cited by 6,410
- lt_or_eq_of_leproof · cited by 29
Cited by48
Results whose statement or proof uses this declaration.
- Nat.floor_of_nonposproof · cited by 9
- interior_closedBallproof · cited by 8
- SimplexCategory.σ₀Iter_succproof · cited by 5
- Wbtw.wOppSide₁₃proof · cited by 4
- wbtw_iff_left_eq_or_right_mem_image_Iciproof · cited by 4
- WellQuasiOrdered.exists_monotone_subseqproof · cited by 4
- SimpleGraph.Walk.getVert_takeUntilproof · cited by 4
- image_le_of_liminf_slope_right_lt_deriv_boundary'proof · cited by 4
- EuclideanGeometry.inner_pos_or_eq_of_dist_le_radiusproof · cited by 3
- CategoryTheory.ComposableArrows.exact_iff_δlastproof · cited by 3
- monotone_transfiniteIterateproof · cited by 3
- Metric.subsingleton_closedBallproof · cited by 3