Theorems · Theorem · group theory
FaithfulSMul.trans
∀ (R : Type u_4) (S : Type u_5) (T : Type u_6) [inst : Monoid S] [inst_1 : MulOneClass T] [inst_2 : SMul R S] [IsScalarTower R S S] [inst_4 : MulAction S T] [IsScalarTower S T T] [inst_6 : SMul R T] [IsScalarTower R T T] [IsScalarTower R S T] [FaithfulSMul R S] [FaithfulSMul S T], FaithfulSMul R T
- Defined in
- Mathlib.Algebra.Group.Action.Faithful
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- IsScalarTowerstatement and proof · cited by 3,896
- Monoidstatement and proof · cited by 3,887
- one_smulproof · cited by 1,374
- MulActionstatement and proof · cited by 1,294
- MulOneClassstatement and proof · cited by 1,018
- FaithfulSMulstatement and proof · cited by 340
- smul_assocproof · cited by 150
- faithfulSMul_iff_injective_smul_oneproof · cited by 8
Cited by6
Results whose statement or proof uses this declaration.
- IsGaloisGroup.quotientproof · cited by 1
- IsGaloisGroup.algebraMap_restrictHom_smulproof · cited by 1
- LieModule.isNilpotent_derivedSeries_of_traceForm_eq_zeroproof · cited by 1
- IsStronglyTranscendental.iff_of_isFractionRingproof · cited by 0
- IsStronglyTranscendental.of_transcendentalproof · cited by 0
- Module.finrank_mul_finrank'proof · cited by 0