Theorems · Theorem · order theory
le_or_gt
∀ {α : Type u_1} [inst : LinearOrder α] (a b : α), a ≤ b ∨ b < a- Defined in
- Mathlib.Order.Defs.LinearOrder
- Cited by
- 269 results in Mathlib
- Foundations
- Depth 10 from the axioms, rests on 26 definitions · uses no axioms
- Assumes
- LinearOrder
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.
- LinearOrderstatement and proof · cited by 8,572
- lt_or_geproof · cited by 182
Cited by269
Results whose statement or proof uses this declaration.
- le_of_not_gtproof · cited by 430
- sq_nonnegproof · cited by 106
- Real.sqrt_eq_rpowproof · cited by 25
- Ordinal.opow_log_le_selfproof · cited by 11
- StieltjesFunction.measure_Iccproof · cited by 8
- strictConvex_closedBallproof · cited by 8
- Cardinal.mul_eq_max_of_aleph0_le_leftproof · cited by 8
- ENNReal.sub_mulproof · cited by 8
- Real.abs_rpow_le_abs_rpowproof · cited by 7
- Nat.choose_le_middleproof · cited by 7
- Real.ediam_Iccproof · cited by 5
- MeasureTheory.Adapted.isStoppingTime_hittingBtwnproof · cited by 5
Showing the 200 most cited of 269.