Theorems · Theorem · ring theory
geom_sum_mul_add
∀ {R : Type u_1} [inst : Semiring R] (x : R) (n : ℕ), (∑ i ∈ Finset.range n, (x + 1) ^ i) * x + 1 = (x + 1) ^ n- Defined in
- Mathlib.Algebra.Ring.GeomSum
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Finset.sumstatement and proof · cited by 5,195
- Finset.rangestatement and proof · cited by 1,341
- one_powproof · cited by 521
- Commute.one_rightproof · cited by 22
- Commute.geom_sum₂_mul_addproof · cited by 3
- geom_sum₂_with_oneproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Nat.geomSum_eqproof · cited by 3
- Behrend.sum_eqproof · cited by 1