Theorems · Theorem · order theory
NoMinOrder.exists_lt
∀ {α : Type u_3} {inst : LT α} [self : NoMinOrder α] (a : α), ∃ b, b < aFor each term a, there is some strictly smaller b.
- Defined in
- Mathlib.Order.Max
- Cited by
- 41 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- NoMinOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NoMinOrderstatement and proof · cited by 247
Cited by41
Results whose statement or proof uses this declaration.
- not_isMinproof · cited by 42
- mem_nhds_iff_exists_Ioo_subsetproof · cited by 13
- Set.nonempty_Iioproof · cited by 10
- atBot_le_cocompactproof · cited by 4
- mem_nhdsLT_iff_exists_Ioo_subsetproof · cited by 4
- nhdsLT_basisproof · cited by 4
- locallyFinite_Icc_of_tendstoproof · cited by 3
- exists_seq_strictMono_tendstoproof · cited by 3
- ProbabilityTheory.Kernel.indep_limsup_atBot_selfproof · cited by 3
- Filter.atBot_basis_Iioproof · cited by 3
- intervalIntegral.continuous_primitiveproof · cited by 3
- Filter.Tendsto.add_atTopproof · cited by 3