Theorems · Theorem · commutative algebra
Submodule.neg_eq_self
∀ {R : Type u_2} {M : Type u_3} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] (p : Submodule R M),
-p = p- Cited by
- 3 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
- Assumes
- RingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- Submodule.extproof · cited by 204
- Submodule.pointwiseNegstatement · cited by 20
- Submodule.neg_mem_iffproof · cited by 11
Cited by3
Results whose statement or proof uses this declaration.
- Submodule.span_negproof · cited by 1
- PointedCone.sup_inf_assoc_of_le_submoduleproof · cited by 0
- PointedCone.inf_sup_assoc_of_le_of_submodule_leproof · cited by 0