Theorems · Theorem · order theory
Submodule.sub_mem_sup
∀ {R' : Type u_4} {M' : Type u_5} [inst : Ring R'] [inst_1 : AddCommGroup M'] [inst_2 : Module R' M']
{S T : Submodule R' M'} {s t : M'}, s ∈ S → t ∈ T → s - t ∈ S ⊔ T- Defined in
- Mathlib.Algebra.Module.Submodule.Lattice
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingAddCommGroupModule
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- sub_eq_add_negproof · cited by 1,023
- NegMemClass.neg_memproof · cited by 63
- Submodule.add_mem_supproof · cited by 6
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