Theorems · Definition · logic and foundations
uniqueOfSubsingleton
{α : Sort u_1} → [Subsingleton α] → α → Unique αGiven an explicit a : α with Subsingleton α, we can construct
a Unique α instance. This is a def because the typeclass search cannot
arbitrarily invent the a : α term. Nevertheless, these instances are all
equivalent by Unique.Subsingleton.unique.
See note [reducible non-instances].
- Defined in
- Mathlib.Logic.Unique
- Cited by
- 9 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.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Uniquestatement · cited by 400
Cited by12
Results whose statement or proof uses this declaration.
- Matrix.det_eq_elem_of_subsingletonproof · cited by 4
- ContinuousMultilinearMap.norm_ofSubsingletonproof · cited by 4
- Fintype.sum_subsingletonproof · cited by 2
- LinearIndependent.of_subsingleton'proof · cited by 2
- Matrix.permanent_eq_elem_of_subsingletonproof · cited by 1
- card_linearIndependentproof · cited by 1
- Fintype.prod_subsingletonproof · cited by 1
- simply_connected_iff_paths_homotopicproof · cited by 1
- ConditionallyCompleteLinearOrderedField.uniqueOrderRingHomproof · cited by 0
- ConditionallyCompleteLinearOrderedField.uniqueOrderRingIsoproof · cited by 0
- CategoryTheory.equiv_punit_iff_uniqueproof · cited by 0
- Function.Surjective.uniqueOfSurjectiveConstproof · cited by 0