Theorems · Theorem · ring theory
nontrivial_of_invariantBasisNumber
∀ (R : Type u) [inst : Semiring R] [InvariantBasisNumber R], Nontrivial R
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringInvariantBasisNumber
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Nontrivialstatement and proof · cited by 2,416
- zero_ne_oneproof · cited by 90
- InvariantBasisNumberstatement and proof · cited by 13
- LinearEquiv.ofSubsingletonproof · cited by 6
- eq_of_fin_equivproof · cited by 2
Cited by18
Results whose statement or proof uses this declaration.
- Module.Basis.mk_eq_rank''proof · cited by 23
- Module.Basis.mk_eq_rankproof · cited by 10
- rank_eq_card_basisproof · cited by 8
- rank_spanproof · cited by 6
- linearIndependent_le_basisproof · cited by 4
- rank_eq_oneproof · cited by 3
- LinearMap.charpoly_natDegreeproof · cited by 3
- lift_cardinalMk_eq_lift_cardinalMk_field_pow_lift_rankproof · cited by 2
- Submodule.rank_eq_spanRank_of_freeproof · cited by 2
- rank_eq_one_iffproof · cited by 1
- Module.Basis.le_spanproof · cited by 1
- mk_eq_mk_of_basisproof · cited by 1