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Theorems · Definition · order theory

InfHom.subtypeVal

{β : Type u_3} →
  [inst : SemilatticeInf β] → {P : β → Prop} → (Pinf : ∀ ⦃x y : β⦄, P x → P y → P (x ⊓ y)) → InfHom { x // P x } β

Subtype.val as an InfHom.

Defined in
Mathlib.Order.Hom.Lattice
Cited by
2 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Quot.sound
Assumes
SemilatticeInf
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

InfTopHom.subtypeVal · cited by 2InfTopHom.subtypeValInfHom.subtypeVal_apply · cited by 0InfHom.subtypeVal_applyInfHom.subtypeVal_coe · cited by 0InfHom.subtypeVal_coeSemilatticeInf · cited by 634SemilatticeInfInfHom · cited by 69InfHomSubtype.semilatticeInf · cited by 8Subtype.semilatticeInfInfHom.subtypeValCITED 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.