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Theorems · Theorem · order theory

Function.not_lt_argmin

∀ {α : Type u_1} {β : Type u_2} (f : α → β) [inst : LT β] [inst_1 : WellFoundedLT β] [inst_2 : Nonempty α] (a : α),
  ¬f a < f (Function.argmin f)
Defined in
Mathlib.Order.WellFounded
Cited by
1 results in Mathlib
Foundations
Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LTWellFoundedLTNonempty
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Around this declaration

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

Function.argmin_le · cited by 2Function.argmin_leSet.univ · cited by 3945Set.univWellFoundedLT · cited by 491WellFoundedLTSet.mem_univ · cited by 416Set.mem_univwellFounded_lt · cited by 22wellFounded_ltWellFounded.not_lt_min · cited by 20WellFounded.not_lt_minFunction.argmin · cited by 4Function.argminFunction.not_lt_argminCITED BYCITES

Cites6

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Cited by1

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