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Theorems · Theorem · order theory

WithTop.sSup_of_top_mem

∀ {α : Type u_1} [inst : LE α] [inst_1 : SupSet α] {s : Set (WithTop α)}, ⊤ ∈ s → sSup s = ⊤
Defined in
Mathlib.Order.ConditionallyCompleteLattice.Basic
Cited by
2 results in Mathlib
Foundations
Depth 13 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LESupSet
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

WithTop.sSup_of_not_bddAbove · cited by 0WithTop.sSup_of_not_bddAb…WithTop.sSup_singleton_top · cited by 0WithTop.sSup_singleton_topSet · cited by 53352SetTop.top · cited by 9680Top.topWithTop · cited by 3754WithTopSupSet.sSup · cited by 954SupSet.sSupSupSet · cited by 154SupSetWithTop.sSup_of_top_memCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

  • Setstatement and proof · cited by 53,352
  • Top.topstatement and proof · cited by 9,680
  • WithTopstatement and proof · cited by 3,754
  • SupSet.sSupstatement · cited by 954
  • SupSetstatement and proof · cited by 154

Cited by2

Results whose statement or proof uses this declaration.