Theorems · Theorem · order theory
le_of_not_gt
∀ {α : Type u_1} [inst : LinearOrder α] {a b : α}, ¬b < a → a ≤ b- Defined in
- Mathlib.Order.Defs.LinearOrder
- Cited by
- 430 results in Mathlib
- Foundations
- Depth 11 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
- le_or_gtproof · cited by 269
Cited by430
Results whose statement or proof uses this declaration.
- not_ltproof · cited by 306
- Nat.unpair_pairproof · cited by 30
- 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
- Real.exp_strictMonoproof · cited by 17
- StrictMonoOn.le_iff_leproof · cited by 17
- unitInterval.two_mul_sub_one_mem_iffproof · cited by 15
- minpoly.minproof · cited by 15
- Set.IsWF.min_leproof · cited by 14
- le_of_forall_lt_imp_le_of_denseproof · cited by 14
- Real.sin_pos_of_pos_of_lt_piproof · cited by 11
Showing the 200 most cited of 430.