Theorems · Theorem · ring theory
CoalgEquiv.symm_apply_apply
∀ {R : Type u_1} {A : Type u_2} {B : Type u_3} [inst : CommSemiring R] [inst_1 : AddCommMonoid A]
[inst_2 : AddCommMonoid B] [inst_3 : Module R A] [inst_4 : Module R B] [inst_5 : CoalgebraStruct R A]
[inst_6 : CoalgebraStruct R B] (e : A ≃ₗc[R] B) (x : A), e.symm (e x) = x- Defined in
- Mathlib.RingTheory.Coalgebra.Equiv
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- CoalgebraStructstatement and proof · cited by 230
- LinearEquiv.symm_apply_applyproof · cited by 78
- CoalgEquivstatement and proof · cited by 77
- CoalgEquiv.symmstatement · cited by 26
- CoalgEquiv.toLinearEquivproof · cited by 13
Cited by1
Results whose statement or proof uses this declaration.
- isGroupLikeElem_map_equivproof · cited by 0