Theorems · Theorem · ring theory
geom_sum_two
∀ {R : Type u_1} [inst : Semiring R] {x : R}, ∑ i ∈ Finset.range 2, x ^ i = x + 1- Defined in
- Mathlib.Algebra.Ring.GeomSum
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 70 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 · cited by 5,195
- Finset.rangestatement · cited by 1,341
- pow_zeroproof · cited by 1,094
- pow_oneproof · cited by 894
- Finset.sum_singletonproof · cited by 251
- geom_sum_succ'proof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- Polynomial.cyclotomic_twoproof · cited by 4
- geom_sum_alternating_of_lt_neg_oneproof · cited by 2
- geom_sum_pos_and_lt_oneproof · cited by 1
- Projectivization.card_of_finrank_twoproof · cited by 0