Theorems · Theorem · order theory
LE.le.eq_of_not_lt
∀ {α : Type u_2} [inst : PartialOrder α] {a b : α}, a ≤ b → ¬a < b → a = bAlias of eq_of_le_of_not_lt.
- Defined in
- Mathlib.Order.Basic
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 16 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 · cited by 6,410
- eq_of_le_of_not_ltproof · cited by 28
Cited by25
Results whose statement or proof uses this declaration.
- Ordinal.isPrincipal_add_iff_zero_or_omega0_opowproof · cited by 3
- sign_eq_zero_iffproof · cited by 3
- LE.le.eq_of_not_ssubsetproof · cited by 2
- CovBy.exists_multiset_consproof · cited by 2
- IsPrimitiveRoot.mk_of_ltproof · cited by 2
- exists_le_isAssociatedPrime_of_isNoetherianRingproof · cited by 2
- Finset.vaddAntidiagonal_min_vadd_minproof · cited by 1
- Set.VAddAntidiagonal.eq_of_fst_le_fst_of_snd_le_sndproof · cited by 1
- Set.PartiallyWellOrderedOn.subsetProdLexproof · cited by 1
- Finpartition.mem_parts_or_eq_sdiff_of_mem_extendOfLEproof · cited by 1
- sSup_eq_of_forall_le_of_forall_lt_exists_gtproof · cited by 1
- Set.uIoc_injective_rightproof · cited by 1