Theorems · Theorem · group theory
AddEquiv.symm_apply_apply
∀ {M : Type u_4} {N : Type u_5} [inst : Add M] [inst_1 : Add N] (e : M ≃+ N) (x : M), e.symm (e x) = xe.symm is a left inverse of e, written as e.symm (e y) = y.
- Defined in
- Mathlib.Algebra.Group.Equiv.Defs
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- AddEquivstatement and proof · cited by 1,087
- AddEquiv.symmstatement · cited by 530
- Equiv.symm_apply_applyproof · cited by 320
- AddEquiv.toEquivproof · cited by 174
Cited by19
Results whose statement or proof uses this declaration.
- MonomialOrder.degree_monomialproof · cited by 12
- MonomialOrder.leadingCoeff_ne_zero_iffproof · cited by 5
- Multiset.toFinsupp_toMultisetproof · cited by 4
- Algebra.Generators.map_toComp_kerproof · cited by 3
- CochainComplex.HomComplex.CohomologyClass.toHom_bijectiveproof · cited by 2
- AddSubgroup.characteristic_iff_comap_leproof · cited by 1
- AddSubgroup.characteristic_iff_le_comapproof · cited by 1
- AddEquivClass.apply_mem_centerproof · cited by 1
- AddEquiv.self_trans_symmproof · cited by 1
- IsPrimitiveRoot.zmodEquivZPowers_symm_apply_powproof · cited by 1
- IsPrimitiveRoot.zmodEquivZPowers_symm_apply_zpowproof · cited by 1
- AddEquiv.coe_addMonoidHom_symm_comp_coe_addMonoidHomproof · cited by 1