Theorems · Theorem · order theory
LE.le.not_gt
∀ {α : Type u_1} [inst : Preorder α] {a b : α}, a ≤ b → ¬b < aAlias of not_lt_of_ge.
- Defined in
- Mathlib.Order.Defs.PartialOrder
- Cited by
- 189 results in Mathlib
- Foundations
- Depth 6 from the axioms, rests on 12 definitions · 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.
- Preorderstatement · cited by 7,952
- not_lt_of_geproof · cited by 52
Cited by189
Results whose statement or proof uses this declaration.
- ENNReal.rpow_oneproof · cited by 56
- minpoly.dvdproof · cited by 31
- ENNReal.mul_rpow_of_nonnegproof · cited by 23
- Finset.Ico_eq_empty_of_leproof · cited by 22
- lt_imp_lt_of_le_imp_leproof · cited by 18
- not_lt_zeroproof · cited by 11
- Nat.le_log_of_pow_leproof · cited by 8
- Nat.pair_unpairproof · cited by 8
- minpoly.uniqueproof · cited by 7
- Set.Ioc_eq_empty_of_leproof · cited by 6
- ProperSpace.of_locallyCompactSpaceproof · cited by 6
- Metric.thickening_of_nonposproof · cited by 6