Theorems · Theorem · order theory
not_lt
∀ {α : Type u_1} [inst : LinearOrder α] {a b : α}, ¬a < b ↔ b ≤ a- Defined in
- Mathlib.Order.Defs.LinearOrder
- Cited by
- 306 results in Mathlib
- Foundations
- Depth 12 from the axioms, rests on 27 definitions · uses no axioms
- Assumes
- LinearOrder
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.
- LinearOrderstatement and proof · cited by 8,572
- le_of_not_gtproof · cited by 430
- not_lt_of_geproof · cited by 52
Cited by306
Results whose statement or proof uses this declaration.
- le_iff_le_iff_lt_iff_ltproof · cited by 25
- Metric.ball_eq_emptyproof · cited by 16
- Nat.finiteMultiplicity_iffproof · cited by 13
- Cardinal.infinite_iffproof · cited by 12
- PowerSeries.IsWeierstrassDivisorAt.isWeierstrassDivisionAt_div_modproof · cited by 10
- Order.pred_lt_iff_of_not_isMinproof · cited by 10
- MonomialOrder.degree_mul_leproof · cited by 10
- exists_lt_of_csInf_ltproof · cited by 10
- Module.finrank_of_not_finiteproof · cited by 8
- Set.compl_Iioproof · cited by 8
- Set.compl_Ioiproof · cited by 7
- Function.Periodic.intervalIntegral_add_eqproof · cited by 7
Showing the 200 most cited of 306.