Theorems · Theorem · nonassociative algebras
LieSubalgebra.toSubmodule_inj
∀ {R : Type u} {L : Type v} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
(L₁' L₂' : LieSubalgebra R L), L₁'.toSubmodule = L₂'.toSubmodule ↔ L₁' = L₂'- Defined in
- Mathlib.Algebra.Lie.Subalgebra
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext
- Assumes
- CommRingLieRingLieAlgebra
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.
- CommRingstatement and proof · cited by 17,173
- Submodulestatement · cited by 7,192
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- LieSubalgebrastatement and proof · cited by 418
- LieSubalgebra.toSubmodulestatement · cited by 90
- LieSubalgebra.toSubmodule_injectiveproof · cited by 3
Cited by8
Results whose statement or proof uses this declaration.
- LieHom.range_eq_topproof · cited by 4
- LieSubalgebra.incl_rangeproof · cited by 2
- LieAlgebra.eq_rootSpace_zero_iff_isCartanproof · cited by 1
- LieHom.range_inlproof · cited by 1
- LieHom.range_inrproof · cited by 1
- LieDerivation.IsKilling.range_ad_eq_topproof · cited by 1
- LieSubalgebra.isCartanSubalgebra_iff_isUcsLimitproof · cited by 0
- LieSubalgebra.coe_lieSpan_submodule_eq_iffproof · cited by 0