Theorems · Theorem · nonassociative algebras
LieSubmodule.coe_lieSpan_submodule_eq_iff
∀ {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] {p : Submodule R M},
↑(LieSubmodule.lieSpan R L ↑p) = p ↔ ∃ N, ↑N = p- Defined in
- Mathlib.Algebra.Lie.Submodule
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- SetLike.coestatement and proof · cited by 8,199
- Submodulestatement and proof · cited by 7,192
- LieRingstatement and proof · cited by 1,548
- LieRingModulestatement and proof · cited by 727
- Bracket.bracketproof · cited by 642
- LieSubmodulestatement and proof · cited by 489
- LieSubmodule.toSubmodulestatement and proof · cited by 150
- LieSubmodule.toSubmodule_injproof · cited by 34
Cited by3
Results whose statement or proof uses this declaration.
- LieIdeal.incl_idealRangeproof · cited by 3
- LieHom.idealRange_eq_top_of_surjectiveproof · cited by 3
- LieIdeal.coe_map_of_surjectiveproof · cited by 2