Theorems · Theorem · linear algebra
Submodule.span_univ
∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M],
Submodule.span R Set.univ = ⊤- Defined in
- Mathlib.LinearAlgebra.Span.Defs
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Top.topstatement · cited by 9,680
- Submodulestatement · cited by 7,192
- Set.univstatement · cited by 3,945
- Submodule.spanstatement · cited by 1,504
- eq_top_iffproof · cited by 236
- Submodule.subset_spanproof · cited by 234
- SetLike.le_defproof · cited by 76
Cited by6
Results whose statement or proof uses this declaration.
- uniqueDiffWithinAt_univproof · cited by 16
- uniqueDiffWithinAt_iff_accPtproof · cited by 5
- Module.exists_dual_forall_apply_eq_oneproof · cited by 1
- Module.free_of_maximalIdeal_rTensor_injectiveproof · cited by 1
- Ideal.span_univproof · cited by 0
- ConvexCone.isGenerating_topproof · cited by 0