Theorems · Theorem · order theory
eq_top_mono
∀ {α : Type u} [inst : PartialOrder α] [inst_1 : OrderTop α] {a b : α}, a ≤ b → a = ⊤ → b = ⊤- Defined in
- Mathlib.Order.BoundedOrder.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- PartialOrderOrderTop
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- PartialOrderstatement and proof · cited by 6,410
- OrderTopstatement and proof · cited by 493
- top_uniqueproof · cited by 102
Cited by12
Results whose statement or proof uses this declaration.
- iUnion_closure_compactCoveringproof · cited by 2
- NNReal.summable_schlomilch_iffproof · cited by 2
- ProbabilityTheory.Kernel.densityProcess_mono_setproof · cited by 1
- AddCircle.coe_image_Icc_eqproof · cited by 0
- ProbabilityTheory.Kernel.densityProcess_antitone_kernel_rightproof · cited by 0
- MeasureTheory.measure_eq_top_monoproof · cited by 0
- MonoidAlgebra.span_isGroupLikeElemproof · cited by 0
- ProbabilityTheory.Kernel.densityProcess_mono_kernel_leftproof · cited by 0
- eq_top_of_bot_eq_topproof · cited by 0
- eq_top_of_top_eq_botproof · cited by 0
- AddMonoidAlgebra.span_isGroupLikeElemproof · cited by 0