Theorems · Theorem · order theory
lt_self_iff_false
∀ {α : Type u_2} [inst : Preorder α] (x : α), x < x ↔ False- Defined in
- Mathlib.Order.Basic
- Cited by
- 41 results in Mathlib
- Foundations
- Depth 6 from the axioms · 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.
Cited by41
Results whose statement or proof uses this declaration.
- abs_posproof · cited by 45
- Set.self_notMem_Ioiproof · cited by 5
- AddMonoid.exponent_ne_zeroproof · cited by 4
- Topology.RelCWComplex.disjoint_skeletonLT_openCellproof · cited by 4
- le_of_forall_pos_lt_addproof · cited by 3
- AddSubmonoid.apply_ne_zero_of_mem_or_neg_mem_closureproof · cited by 3
- Set.Icc_eq_Ico_same_iffproof · cited by 2
- Finset.sum_Iio_add_zero_commproof · cited by 2
- Finset.addEnergy_pos_iffproof · cited by 2
- Set.powersetCard.nontrivialproof · cited by 2
- Collinear.wbtw_of_dist_eq_of_dist_leproof · cited by 2
- Real.geom_mean_lt_arith_mean_weighted_iff_of_posproof · cited by 2