Theorems · Theorem · order theory
ne_iff_lt_iff_le
∀ {α : Type u_2} [inst : PartialOrder α] {a b : α}, (a ≠ b ↔ a < b) ↔ a ≤ b- Defined in
- Mathlib.Order.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrder
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.
- PartialOrderstatement and proof · cited by 6,410
- Decidable.ne_iff_lt_iff_leproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- NumberField.FinitePlace.hasFiniteMulSupport_intproof · cited by 3
- PairReduction.disjoint_smallBall_logSizeBallSeqproof · cited by 1
- Valuation.Integers.dvdNotUnit_iff_ltproof · cited by 1
- IsDedekindDomain.HeightOneSpectrum.intAdicAbv_eq_one_iffproof · cited by 1
- dist_lt_dist_add_dist_iffproof · cited by 0
- DyckWord.pos_iff_ne_zeroproof · cited by 0