Theorems · Theorem · linear algebra
exists_mem_ne_zero_of_rank_pos
∀ {R : Type u_1} {M : Type u_2} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] [Nontrivial R]
{s : Submodule R M}, 0 < Module.rank R ↥s → ∃ b ∈ s, b ≠ 0- Defined in
- Mathlib.LinearAlgebra.Dimension.Finite
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
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- 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
- Bot.botproof · cited by 4,720
- Cardinalstatement and proof · cited by 2,598
- Nontrivialstatement and proof · cited by 2,416
- Module.rankstatement and proof · cited by 496
- lt_irreflproof · cited by 190
- Submodule.exists_mem_ne_zero_of_ne_botproof · cited by 9
- rank_botproof · cited by 6
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