Theorems · Theorem · commutative algebra
Submodule.neg_eq_self_iff_neg_le
∀ {R : Type u_2} {M : Type u_3} [inst : Semiring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {S : Submodule R M},
-S = S ↔ -S ≤ S- Cited by
- 0 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Quot.sound
- Assumes
- SemiringAddCommGroupModule
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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
- Semiringstatement and proof · cited by 13,802
- AddCommGroupstatement and proof · cited by 12,871
- Submodulestatement and proof · cited by 7,192
- le_of_eqproof · cited by 366
- Submodule.pointwiseNegstatement · cited by 20
- antisymmproof · cited by 13
- Submodule.neg_leproof · cited by 3
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