Theorems · Theorem · number theory
LinearRecurrence.eq_iff_eqOn_range_order
∀ {R : Type u_1} [inst : CommSemiring R] (E : LinearRecurrence R) (u v : ℕ → R),
E.IsSolution u → E.IsSolution v → (u = v ↔ Set.EqOn u v ↑(Finset.range E.order))Two solutions are equal iff their initial conditions are equal.
- Defined in
- Mathlib.Algebra.LinearRecurrence
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 77 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.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Finsetstatement · cited by 13,712
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coestatement and proof · cited by 8,199
- Finsuppproof · cited by 5,255
- Finset.rangestatement and proof · cited by 1,341
- Set.EqOnstatement and proof · cited by 603
- Module.Basis.reprproof · cited by 498
- Finsupp.extproof · cited by 399
- LinearEquiv.injectiveproof · cited by 162
- Finset.mem_rangeproof · cited by 140
- LinearRecurrencestatement and proof · cited by 21
Cited by2
Results whose statement or proof uses this declaration.
- Real.coe_fib_eq'proof · cited by 1
- LinearRecurrence.sol_eq_of_eq_initproof · cited by 0