Theorems · Theorem · linear algebra
Module.rank_self
∀ (R : Type u) [inst : Semiring R] [StrongRankCondition R], Module.rank R R = 1
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringStrongRankCondition
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Cardinalstatement and proof · cited by 2,598
- Cardinal.liftproof · cited by 583
- Module.rankstatement · cited by 496
- StrongRankConditionstatement and proof · cited by 286
- Cardinal.lift_injproof · cited by 38
- Module.Basis.singletonproof · cited by 15
- Module.Basis.mk_eq_rankproof · cited by 10
- Cardinal.mk_punitproof · cited by 2
Cited by17
Results whose statement or proof uses this declaration.
- Module.finrank_selfproof · cited by 24
- rank_fun'proof · cited by 6
- Module.finrank_piproof · cited by 5
- Subalgebra.LinearDisjoint.rank_inf_eq_one_of_commute_of_flat_of_injproof · cited by 3
- rank_finsupp_selfproof · cited by 3
- Subalgebra.rank_eq_one_iffproof · cited by 3
- Module.lift_rank_of_isLocalizedModule_of_freeproof · cited by 1
- rank_finsupp_self'proof · cited by 1
- rank_le_oneproof · cited by 1
- rank_matrixproof · cited by 1
- Module.rank_baseChangeproof · cited by 1
- Module.rank_linearMap_selfproof · cited by 1