Theorems · Theorem · order theory
not_le
∀ {α : Type u_1} [inst : LinearOrder α] {a b : α}, ¬a ≤ b ↔ b < a- Defined in
- Mathlib.Order.Defs.LinearOrder
- Cited by
- 328 results in Mathlib
- Foundations
- Depth 10 from the axioms, rests on 20 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_iff_not_geproof · cited by 22
Cited by328
Results whose statement or proof uses this declaration.
- norm_pos_iffproof · cited by 168
- sq_nonnegproof · cited by 106
- lt_iff_lt_of_le_iff_leproof · cited by 54
- tsub_pos_iff_ltproof · cited by 27
- Orientation.oangle_eq_angle_of_sign_eq_oneproof · cited by 25
- intervalIntegral.intervalIntegral_eq_integral_uIocproof · cited by 17
- Metric.closedBall_eq_emptyproof · cited by 15
- Set.compl_Iciproof · cited by 11
- Finset.sum_Ico_eq_sum_rangeproof · cited by 10
- Set.compl_Iicproof · cited by 10
- Order.pred_lt_iff_of_not_isMinproof · cited by 10
- Path.trans_applystatement and proof · cited by 9
Showing the 200 most cited of 328.