Theorems · Theorem · order theory
Submodule.coe_finsetInf
∀ {R : Type u_1} {M : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {ι : Type u_4}
(s : Finset ι) (p : ι → Submodule R M), ↑(s.inf p) = ⋂ i ∈ s, ↑(p i)- Defined in
- Mathlib.Algebra.Module.Submodule.Lattice
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 64 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.
Cites19
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
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- SetLike.coestatement and proof · cited by 8,199
- Submodulestatement and proof · cited by 7,192
- Set.univproof · cited by 3,945
- Set.iInterstatement and proof · cited by 1,084
- Finset.infstatement and proof · cited by 219
- Set.iInter_congr_Propproof · cited by 170
- Finset.induction_onproof · cited by 167
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.mem_finsetInfproof · cited by 1