Theorems · Theorem · order theory
ne_of_gt
∀ {α : Type u_1} [inst : Preorder α] {a b : α}, b < a → a ≠ b- Defined in
- Mathlib.Order.Defs.PartialOrder
- Cited by
- 637 results in Mathlib
- Foundations
- Depth 6 from the axioms, rests on 14 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.
Cited by637
Results whose statement or proof uses this declaration.
- LT.lt.ne'proof · cited by 1,417
- Nat.factorial_ne_zeroproof · cited by 56
- ENNReal.zero_rpow_of_posproof · cited by 36
- Filter.eventually_ne_atTopproof · cited by 35
- Real.rpow_def_of_posproof · cited by 35
- ENNReal.coe_rpow_of_nonnegproof · cited by 34
- LipschitzWith.uniformContinuousproof · cited by 33
- LE.le.lt_iff_ne'proof · cited by 16
- Fintype.card_ne_zeroproof · cited by 16
- Asymptotics.IsBigO.mul_isLittleOproof · cited by 15
- Real.rpow_lt_rpowproof · cited by 12
- Asymptotics.IsLittleO.mul_isBigOproof · cited by 11
Showing the 200 most cited of 637.