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Theorems · Theorem · order theory

iSup_ne_of_notMem

∀ {α : Type u_5} [inst : CompleteLinearOrder α] {ι : Sort u_6} [Finite ι] {f : ι → α} {a : α},
  a ≠ ⊥ → (∀ (x : ι), f x ≠ a) → iSup f ≠ a
Defined in
Mathlib.Order.ConditionallyCompleteLattice.Finset
Cited by
2 results in Mathlib
Foundations
Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CompleteLinearOrderFinite
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Around this declaration

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

iSup_ne_top · cited by 1iSup_ne_topiInf_ne_of_notMem · cited by 0iInf_ne_of_notMemBot.bot · cited by 4720Bot.botFinite · cited by 3029FiniteiSup · cited by 2415iSupCompleteLinearOrder · cited by 126CompleteLinearOrderSet.finite_range · cited by 58Set.finite_rangesSup_ne_of_notMem · cited by 3sSup_ne_of_notMemiSup_ne_of_notMemCITED BYCITES

Cites6

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Cited by2

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