Theorems · Definition · group theory
AddEquiv.op
{α : Type u_3} → {β : Type u_4} → [inst : Add α] → [inst_1 : Add β] → α ≃+ β ≃ (αᵃᵒᵖ ≃+ βᵃᵒᵖ)An iso α ≃+ β can equivalently be viewed as an iso αᵃᵒᵖ ≃+ βᵃᵒᵖ.
- Defined in
- Mathlib.Algebra.Group.Equiv.Opposite
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Equivstatement · cited by 8,337
- AddEquivstatement and proof · cited by 1,087
- AddEquiv.symmproof · cited by 530
- AddOppositestatement and proof · cited by 452
- AddOpposite.opproof · cited by 192
- AddOpposite.unopproof · cited by 125
Cited by5
Results whose statement or proof uses this declaration.
- AddEquiv.unopproof · cited by 0
- AddEquiv.op_apply_applystatement and proof · cited by 0
- AddEquiv.op_apply_symm_applystatement and proof · cited by 0
- AddEquiv.op_symm_apply_applystatement and proof · cited by 0
- AddEquiv.op_symm_apply_symm_applystatement and proof · cited by 0