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Theorems · Definition · order theory

Pi.monotoneUncurry

(α : Type u_1) →
  (β : α → Type u_2) →
    (γ : (a : α) → β a → Type u_3) →
      [inst : (x : α) → (y : β x) → Preorder (γ x y)] →
        ((a : α) → (b : β a) → γ a b) →o (x : (a : α) × β a) → γ x.fst x.snd

Sigma.uncurry as a monotone function.

Defined in
Mathlib.Control.LawfulFix
Cited by
3 results in Mathlib
Foundations
Depth 12 from the axioms · uses no axioms
Assumes
Preorder
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Around this declaration

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

Pi.ωScottContinuous_uncurry · cited by 1Pi.ωScottContinuous_uncur…Pi.monotoneUncurry_coe · cited by 0Pi.monotoneUncurry_coePi.uncurry_curry_ωScottContinuous · cited by 0Pi.uncurry_curry_ωScottCo…Preorder · cited by 7952PreorderOrderHom · cited by 934OrderHomSigma.uncurry · cited by 21Sigma.uncurryPi.monotoneUncurryCITED BYCITES

Cites3

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

Cited by3

Results whose statement or proof uses this declaration.