Theorems · Theorem · linear algebra
Submodule.coe_sup
∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
(p p' : Submodule R M), ↑(p ⊔ p') = ↑p + ↑p'- Defined in
- Mathlib.LinearAlgebra.Span.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- SetLike.coestatement and proof · cited by 8,199
- Submodulestatement and proof · cited by 7,192
- Set.extproof · cited by 2,266
- Set.addstatement · cited by 338
- SetLike.mem_coeproof · cited by 302
- Submodule.mem_supproof · cited by 73
- Set.mem_addproof · cited by 25
Cited by3
Results whose statement or proof uses this declaration.
- LinearMap.coprod_map_prodproof · cited by 2
- Subrepresentation.coe_supproof · cited by 0
- HomogeneousIdeal.coe_supproof · cited by 0