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Theorems · Theorem · order theory

Finset.exists_maximalFor

∀ {ι : Type u_1} {α : Type u_2} [inst : LE α] [IsTrans α LE.le] (f : ι → α) (s : Finset ι),
  s.Nonempty → ∃ i, MaximalFor (fun x => x ∈ s) f i
Defined in
Mathlib.Order.Preorder.Finite
Cited by
2 results in Mathlib
Foundations
Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LEIsTrans
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Finset.exists_maximal · cited by 5Finset.exists_maximalSet.Finite.exists_maximalFor · cited by 3Finite.exists_maximalForFinset · cited by 13712FinsetFinset.Nonempty · cited by 1001Finset.NonemptyIsTrans · cited by 157IsTranstrans · cited by 111transFinset.Nonempty.cons_induction · cited by 35Nonempty.cons_inductionMaximalFor · cited by 25MaximalForFinset.mem_cons_self · cited by 16Finset.mem_cons_selfFinset.mem_cons_of_mem · cited by 16Finset.mem_cons_of_memFinset.exists_maximalForCITED BYCITES

Cites8

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

Cited by2

Results whose statement or proof uses this declaration.