Theorems · Theorem · linear algebra
nontrivial_of_hasRankNullity
∀ (R : Type u_1) [inst : Ring R] [HasRankNullity.{u, u_1} R], Nontrivial R- Cited by
- 0 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingHasRankNullity
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- Bot.botproof · cited by 4,720
- Nontrivialstatement · cited by 2,416
- HasQuotient.Quotientproof · cited by 2,301
- Module.rankproof · cited by 496
- subsingleton_or_nontrivialproof · cited by 161
- one_add_one_eq_twoproof · cited by 65
- HasRankNullitystatement and proof · cited by 26
- rank_subsingletonproof · cited by 19
- Submodule.rank_quotient_add_rankproof · cited by 8
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