Theorems · Theorem · linear algebra
Finsupp.supported_empty
∀ {α : Type u_1} {M : Type u_2} {R : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M],
Finsupp.supported M R ∅ = ⊥- Defined in
- Mathlib.LinearAlgebra.Finsupp.Supported
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 79 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- 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
- Submodulestatement · cited by 7,192
- Finsuppstatement and proof · cited by 5,255
- Bot.botstatement · cited by 4,720
- Finsupp.extproof · cited by 399
- eq_bot_iffproof · cited by 159
- Finsupp.supportedstatement and proof · cited by 77
- Submodule.mem_botproof · cited by 55
Cited by3
Results whose statement or proof uses this declaration.
- Finsupp.disjoint_supported_supportedproof · cited by 2
- Finsupp.lmapDomain_supportedproof · cited by 2
- exists_maximal_linearIndepOn'proof · cited by 1