Theorems · Theorem · nonassociative algebras
LieSubalgebra.coe_lieSpan_submodule_eq_iff
∀ {R : Type u} {L : Type v} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] {p : Submodule R L},
(LieSubalgebra.lieSpan R L ↑p).toSubmodule = p ↔ ∃ K, K.toSubmodule = p- Defined in
- Mathlib.Algebra.Lie.Subalgebra
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingLieRingLieAlgebra
Around this declaration
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Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- SetLike.coestatement and proof · cited by 8,199
- Submodulestatement and proof · cited by 7,192
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- Bracket.bracketproof · cited by 642
- LieSubalgebrastatement and proof · cited by 418
- LieSubalgebra.toSubmodulestatement and proof · cited by 90
- LieSubalgebra.lieSpanstatement and proof · cited by 33
- LieSubalgebra.subset_lieSpanproof · cited by 19
- LieSubalgebra.lie_memproof · cited by 10
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