Theorems · Theorem · number theory
LinearRecurrence.solSpace_rank
∀ {R : Type u_1} [inst : CommRing R] [StrongRankCondition R] (E : LinearRecurrence R),
Module.rank R ↥E.solSpace = ↑E.orderThe dimension of E.solSpace is E.order.
- Defined in
- Mathlib.Algebra.LinearRecurrence
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingStrongRankCondition
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Submodulestatement · cited by 7,192
- Cardinalstatement · cited by 2,598
- Module.rankstatement · cited by 496
- StrongRankConditionstatement and proof · cited by 286
- Fintype.card_finproof · cited by 270
- LinearRecurrencestatement and proof · cited by 21
- LinearRecurrence.orderstatement and proof · cited by 17
- rank_eq_card_basisproof · cited by 8
- LinearRecurrence.solSpacestatement · cited by 6
- LinearRecurrence.basisproof · cited by 4
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