Theorems · Theorem · linear algebra
Submodule.span_int_eq_addSubgroupClosure
∀ {M : Type u_9} [inst : AddCommGroup M] (s : Set M), (Submodule.span ℤ s).toAddSubgroup = AddSubgroup.closure s- Defined in
- Mathlib.LinearAlgebra.Span.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- AddCommGroupstatement and proof · cited by 12,871
- AddSubgroupstatement · cited by 3,232
- Submodule.spanstatement and proof · cited by 1,504
- Submodule.subset_spanproof · cited by 234
- AddSubgroup.closurestatement and proof · cited by 156
- Submodule.toAddSubgroupstatement and proof · cited by 106
- Submodule.span_inductionproof · cited by 77
- AddSubgroup.subset_closureproof · cited by 49
- AddSubgroup.zero_memproof · cited by 23
- AddSubgroup.add_memproof · cited by 17
- AddSubgroup.zsmul_memproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- RootPairing.linearIndepOn_root_baseOfproof · cited by 3
- NumberField.Units.isMaxRank_iff_closure_finiteIndexproof · cited by 1
- NumberField.Units.span_basisOfIsMaxRankproof · cited by 1
- RootPairing.ncard_eq_finrank_of_linearIndepOn_ofproof · cited by 1
- Submodule.span_int_eqproof · cited by 0