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Theorems · Theorem · order theory

Function.not_lt_argminOn

∀ {α : Type u_1} {β : Type u_2} (f : α → β) [inst : LT β] [inst_1 : WellFoundedLT β] (s : Set α) {a : α} (ha : a ∈ s),
  ¬f a < f (Function.argminOn f s ⋯)
Defined in
Mathlib.Order.WellFounded
Cited by
2 results in Mathlib
Foundations
Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LTWellFoundedLT
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Around this declaration

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

Function.argminOn_le · cited by 5Function.argminOn_leIntermediateField.exists_finset_maximalFor_isTranscendenceBasis_separableClosure · cited by 1IntermediateField.exists_…Set · cited by 53352SetWellFoundedLT · cited by 491WellFoundedLTwellFounded_lt · cited by 22wellFounded_ltWellFounded.not_lt_min · cited by 20WellFounded.not_lt_minFunction.argminOn · cited by 8Function.argminOnFunction.not_lt_argminOnCITED BYCITES

Cites5

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Cited by2

Results whose statement or proof uses this declaration.