Theorems · Theorem · order theory
lt_or_ge
∀ {α : Type u_1} [inst : LinearOrder α] (a b : α), a < b ∨ b ≤ a- Defined in
- Mathlib.Order.Defs.LinearOrder
- Cited by
- 182 results in Mathlib
- Foundations
- Depth 9 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_of_not_geproof · cited by 374
Cited by182
Results whose statement or proof uses this declaration.
- le_or_gtproof · cited by 269
- lt_trichotomyproof · cited by 178
- Cardinal.mul_eq_selfproof · cited by 13
- ENNReal.tsum_geometricproof · cited by 8
- Cardinal.add_lt_of_ltproof · cited by 7
- Odd.strictMono_powproof · cited by 7
- UpperHalfPlane.cmp_dist_eq_cmp_dist_coe_centerproof · cited by 5
- Cardinal.mul_lt_of_ltproof · cited by 5
- Nat.log_one_rightproof · cited by 5
- Set.Ico_subset_Ico_union_Icoproof · cited by 4
- EReal.mul_le_of_forall_lt_of_nonnegproof · cited by 4
- alternatingGroup.isMultiplyPretransitiveproof · cited by 4