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Theorems · Theorem · order theory

WithBot.strictAnti_iff

∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Preorder β] {f : WithBot α → β},
  StrictAnti f ↔ (StrictAnti fun a => f ↑a) ∧ ∀ (x : α), f ↑x < f ⊥
Defined in
Mathlib.Order.WithBot
Cited by
1 results in Mathlib
Foundations
Depth 21 from the axioms · uses propext, Quot.sound
Assumes
PreorderPreorder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

EReal.neg_strictAnti · cited by 2EReal.neg_strictAntiPreorder · cited by 7952PreorderBot.bot · cited by 4720Bot.botWithBot · cited by 1498WithBotWithBot.some · cited by 541WithBot.someStrictAnti · cited by 204StrictAntiWithBot.strictMono_iff · cited by 2WithBot.strictMono_iffWithBot.strictAnti_iffCITED BYCITES

Cites6

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Cited by1

Results whose statement or proof uses this declaration.