Theorems · Theorem · order theory
NoMaxOrder.exists_gt
∀ {α : Type u_3} {inst : LT α} [self : NoMaxOrder α] (a : α), ∃ b, a < bFor each term a, there is some strictly greater b.
- Defined in
- Mathlib.Order.Max
- Cited by
- 62 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- NoMaxOrder
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.
- NoMaxOrderstatement and proof · cited by 340
Cited by62
Results whose statement or proof uses this declaration.
- not_isMaxproof · cited by 46
- Metric.uniformity_basis_distproof · cited by 25
- mem_nhds_iff_exists_Ioo_subsetproof · cited by 13
- Cardinal.mul_eq_selfproof · cited by 13
- Set.nonempty_Ioiproof · cited by 10
- Filter.atTop_basis_Ioiproof · cited by 10
- nhdsGT_basisproof · cited by 8
- hasFDerivAt_jacobiTheta₂proof · cited by 4
- Filter.not_isBoundedUnder_of_tendsto_atTopproof · cited by 4
- IsOrderBornology.atTop_le_coboundedproof · cited by 4
- Nat.exists_strictMono'proof · cited by 4
- mem_nhdsGT_iff_exists_Ioo_subsetproof · cited by 3