Theorems · Theorem · commutative algebra
Submodule.iUnion_ssubset_of_forall_ne_top_of_card_lt
∀ {ι : Type u_1} {K : Type u_2} {M : Type u_3} [inst : Field K] [inst_1 : AddCommGroup M] [inst_2 : Module K M]
(s : Finset ι) (p : ι → Submodule K M), (∀ (i : ι), p i ≠ ⊤) → ↑s.card < ENat.card K → ⋃ i ∈ s, ↑(p i) ⊂ Set.univ- Defined in
- Mathlib.Algebra.Module.Submodule.Union
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites63
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 and proof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- Finsetstatement and proof · cited by 13,712
- AddCommGroupstatement and proof · cited by 12,871
- Top.topstatement and proof · cited by 9,680
- SetLike.coestatement and proof · cited by 8,199
- Fieldstatement and proof · cited by 7,404
- Submodulestatement and proof · cited by 7,192
- Set.Elemproof · cited by 7,166
- Set.ofPredproof · cited by 6,101
- Set.imageproof · cited by 5,609
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.exists_forall_notMem_of_forall_ne_topproof · cited by 1