Theorems · Theorem · nonassociative algebras
LieSubmodule.toSubmodule_inj
∀ {R : Type u} {L : Type v} {M : Type w} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : AddCommGroup M]
[inst_3 : Module R M] [inst_4 : LieRingModule L M] (N N' : LieSubmodule R L M), ↑N = ↑N' ↔ N = N'- Defined in
- Mathlib.Algebra.Lie.Submodule
- Cited by
- 34 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
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.
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Submodulestatement · cited by 7,192
- LieRingstatement and proof · cited by 1,548
- LieRingModulestatement and proof · cited by 727
- LieSubmodulestatement and proof · cited by 489
- LieSubmodule.toSubmodulestatement · cited by 150
- LieSubmodule.toSubmodule_injectiveproof · cited by 2
Cited by34
Results whose statement or proof uses this declaration.
- LieAlgebra.rootSpace_zero_eqproof · cited by 9
- LieSubmodule.subsingleton_iffproof · cited by 4
- LieIdeal.incl_idealRangeproof · cited by 3
- LieSubmodule.disjoint_toSubmoduleproof · cited by 3
- LieHom.idealRange_eq_top_of_surjectiveproof · cited by 3
- LieHom.ker_eq_botproof · cited by 3
- LieSubalgebra.normalizer_eq_self_of_isCartanSubalgebraproof · cited by 3
- LieSubmodule.lie_baseChangeproof · cited by 3
- LieSubmodule.coe_lieSpan_submodule_eq_iffproof · cited by 3
- LieSubmodule.map_bracket_eqproof · cited by 3
- LieSubmodule.iSup_toSubmodule_eq_topproof · cited by 2
- LieModule.ideal_oper_maxTrivSubmodule_eq_botproof · cited by 2