Theorems · Theorem · logic and foundations
Function.Injective.subsingleton
∀ {α : Sort u_1} {β : Sort u_2} {f : α → β}, Function.Injective f → ∀ [Subsingleton β], Subsingleton αIf the codomain of an injective function is a subsingleton, then the domain is a subsingleton as well.
- Defined in
- Mathlib.Logic.Unique
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
- Assumes
- Subsingleton
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by16
Results whose statement or proof uses this declaration.
- Equiv.subsingletonproof · cited by 24
- HomogeneousLocalization.subsingletonproof · cited by 5
- Module.FaithfullyFlat.lTensor_reflects_trivialityproof · cited by 3
- AlgebraicGeometry.isFinite_iff_locallyOfFiniteType_of_jacobsonSpaceproof · cited by 1
- Polynomial.subsingleton_iff_subsingletonproof · cited by 1
- IsIsotypicOfType.of_subsingletonproof · cited by 1
- mdifferentiable_of_subsingletonproof · cited by 1
- Algebra.QuasiFiniteAt.of_isOpen_singletonproof · cited by 1
- PrimeSpectrum.subsingleton_iff_isField_of_isReducedproof · cited by 1
- Sublattice.subsingleton_iffproof · cited by 0
- Equiv.subsingleton.symmproof · cited by 0
- TopologicalSpace.NonemptyCompacts.subsingleton_iffproof · cited by 0