Theorems · Theorem · number theory
LinearRecurrence.is_sol_iff_mem_solSpace
∀ {R : Type u_1} [inst : CommSemiring R] (E : LinearRecurrence R) (u : ℕ → R), E.IsSolution u ↔ u ∈ E.solSpaceDefining property of the solution space : u is a solution
iff it belongs to the solution space.
- Defined in
- Mathlib.Algebra.LinearRecurrence
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Submodulestatement · cited by 7,192
- LinearRecurrencestatement and proof · cited by 21
- LinearRecurrence.IsSolutionstatement · cited by 11
- LinearRecurrence.solSpacestatement · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- LinearRecurrence.eq_iff_eqOn_range_orderproof · cited by 2