Theorems · Definition · logic and foundations
Equiv.sumEmpty
(α : Type u_9) → (β : Type u_10) → [IsEmpty β] → α ⊕ β ≃ α
Sum with IsEmpty is equivalent to the original type.
- Defined in
- Mathlib.Logic.Equiv.Sum
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- IsEmpty
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivstatement · cited by 8,337
- IsEmptystatement and proof · cited by 759
- isEmptyElimproof · cited by 59
Cited by14
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Formula.equivSentenceproof · cited by 11
- Equiv.emptySumproof · cited by 4
- FirstOrder.Language.Formula.realize_equivSentence_symm_conproof · cited by 4
- FirstOrder.Language.BoundedFormula.constantsVarsEquivproof · cited by 4
- RelIso.sumLexEmptyproof · cited by 3
- Diffeomorph.sumEmptyproof · cited by 2
- Equiv.sumEmpty_symm_applystatement and proof · cited by 1
- FirstOrder.Language.BoundedFormula.realize_constantsVarsEquivproof · cited by 1
- Homeomorph.sumEmptyproof · cited by 1
- RelIso.emptySumLex_applystatement · cited by 0
- Equiv.sumEmpty.congr_simpstatement and proof · cited by 0