Theorems · Theorem · order theory
lt_irrefl
∀ {α : Type u_1} [inst : Preorder α] (a : α), ¬a < a- Defined in
- Mathlib.Order.Defs.PartialOrder
- Cited by
- 190 results in Mathlib
- Foundations
- Depth 5 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.
Cites3
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
- le_rflproof · cited by 1,558
- not_le_of_gtproof · cited by 97
Cited by190
Results whose statement or proof uses this declaration.
- ne_of_gtproof · cited by 637
- ne_of_ltproof · cited by 203
- LT.lt.falseproof · cited by 66
- lt_self_iff_falseproof · cited by 41
- le_of_forall_ltproof · cited by 25
- le_of_forall_gt_imp_ge_of_denseproof · cited by 21
- le_of_forall_gtproof · cited by 19
- lt_asymmproof · cited by 16
- le_of_forall_lt_imp_le_of_denseproof · cited by 14
- Finset.right_notMem_Icoproof · cited by 13
- MeasureTheory.MemLp.mono_exponentproof · cited by 11
- Finset.Ico_selfproof · cited by 8