Theorems · Theorem · group theory
Finset.prod_pair
∀ {ι : Type u_1} {M : Type u_4} [inst : CommMonoid M] {f : ι → M} [inst_1 : DecidableEq ι] {a b : ι},
a ≠ b → ∏ x ∈ {a, b}, f x = f a * f b- Cited by
- 5 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- Finset.prodstatement · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- Finset.prod_insertproof · cited by 109
- Finset.prod_singletonproof · cited by 78
- Finset.notMem_singletonproof · cited by 13
Cited by5
Results whose statement or proof uses this declaration.
- Finset.prod_eq_mul_of_memproof · cited by 1
- Nat.binomial_eqproof · cited by 1
- lt_hasProdproof · cited by 0
- Finset.prod_Icc_of_even_eq_rangeproof · cited by 0
- Nat.binomial_specproof · cited by 0