Theorems · Theorem · number theory
geom_sum_ne_zero
∀ {R : Type u_1} [inst : Ring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] {n : ℕ} {x : R},
x ≠ -1 → n ≠ 0 → ∑ i ∈ Finset.range n, x ^ i ≠ 0- Defined in
- Mathlib.Algebra.Order.Ring.GeomSum
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- Ringstatement and proof · cited by 7,463
- Finset.sumstatement and proof · cited by 5,195
- IsStrictOrderedRingstatement and proof · cited by 2,490
- zero_addproof · cited by 2,366
- LT.lt.ne'proof · cited by 1,417
- Finset.rangestatement and proof · cited by 1,341
- pow_zeroproof · cited by 1,094
- LT.lt.neproof · cited by 872
- zero_lt_oneproof · cited by 598
- Evenproof · cited by 444
- LT.lt.transproof · cited by 370
Cited by1
Results whose statement or proof uses this declaration.
- geom_sum_eq_zero_iff_neg_oneproof · cited by 2