Theorems · Theorem · order theory
eq_of_le_of_not_lt
∀ {α : Type u_2} [inst : PartialOrder α] {a b : α}, a ≤ b → ¬a < b → a = b- Defined in
- Mathlib.Order.Basic
- Cited by
- 28 results in Mathlib
- Foundations
- Depth 15 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
- LE.le.eq_or_ltproof · cited by 220
Cited by28
Results whose statement or proof uses this declaration.
- LE.le.eq_of_not_ltproof · cited by 25
- csSup_eq_of_forall_le_of_forall_lt_exists_gtproof · cited by 8
- LieAlgebra.IsKilling.chainTopCoeff_zero_rightproof · cited by 4
- IsCyclotomicExtension.Rat.nrComplexPlaces_eq_totient_div_twoproof · cited by 4
- csSup_mem_of_not_isSuccLimitproof · cited by 3
- Wbtw.trans_left_rightproof · cited by 3
- Ideal.mem_minimalPrimes_of_height_leproof · cited by 3
- Matroid.IsCircuit.eq_of_not_indep_subsetproof · cited by 3
- BoxIntegral.integrable_of_bounded_and_ae_continuousWithinAtproof · cited by 2
- Profinite.NobelingProof.GoodProducts.head!_eq_o_of_maxProductsproof · cited by 2
- CompleteLattice.WellFoundedGT.isSupFiniteCompactproof · cited by 2
- IsClosed.Icc_subset_of_forall_mem_nhdsGT_of_Icc_subsetproof · cited by 2