Theorems · Theorem · linear algebra
LinearIndepOn.mono
∀ {ι : Type u'} {R : Type u_2} {M : Type u_4} {v : ι → M} [inst : Semiring R] [inst_1 : AddCommMonoid M]
[inst_2 : Module R M] {t s : Set ι}, LinearIndepOn R v s → t ⊆ s → LinearIndepOn R v t- Cited by
- 14 results in Mathlib
- Foundations
- Depth 82 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · 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
- LinearIndepOnstatement and proof · cited by 211
- Set.inclusionproof · cited by 145
- LinearIndependent.compproof · cited by 41
- Set.inclusion_injectiveproof · cited by 28
Cited by14
Results whose statement or proof uses this declaration.
- ZLattice.rankproof · cited by 5
- linearIndepOn_iUnion_of_directedproof · cited by 4
- exists_linearIndependent_cons_of_lt_rankproof · cited by 2
- RootPairing.Base.linearIndependent_pair_of_neproof · cited by 2
- linearIndepOn_union_iffproof · cited by 2
- Module.exists_set_linearIndependent_of_lt_lift_rankproof · cited by 2
- Module.le_rank_iff_exists_finsetproof · cited by 1
- MonoidAlgebra.isGroupLikeElem_iff_mem_range_single_oneproof · cited by 1
- AddMonoidAlgebra.isGroupLikeElem_iff_mem_range_single_oneproof · cited by 1
- linearIndepOn_iff_linearIndepOn_finsetproof · cited by 1
- le_of_span_le_spanproof · cited by 1
- le_rank_iff_exists_linearIndependentproof · cited by 1