Theorems · Theorem · commutative algebra
Submodule.spanRank_eq_zero_iff_eq_bot
∀ {R : Type u_1} {M : Type u} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {I : Submodule R M},
I.spanRank = 0 ↔ I = ⊥- Defined in
- Mathlib.Algebra.Module.SpanRank
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 80 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.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Submodulestatement and proof · cited by 7,192
- Set.Elemproof · cited by 7,166
- Bot.botstatement and proof · cited by 4,720
- Cardinalstatement and proof · cited by 2,598
- le_reflproof · cited by 2,061
- Submodule.spanproof · cited by 1,504
- Cardinal.mkproof · cited by 942
- Submodule.spanRankstatement and proof · cited by 61
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.spanRank_botproof · cited by 0