Theorems · Theorem · group theory
Finset.prod_eq_prod_iff_single
∀ {ι : Type u_1} {M : Type u_3} {s : Finset ι} [inst : CommMonoid M] [IsRightCancelMul M] {f g : ι → M} {i : ι},
i ∈ s → (∀ j ∈ s, j ≠ i → f j = g j) → (∏ j ∈ s, f j = ∏ j ∈ s, g j ↔ f i = g i)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidIsRightCancelMul
Around this declaration
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Finset.prodstatement and proof · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- Finset.prod_congrproof · cited by 646
- IsRightCancelMulstatement and proof · cited by 43
- Finset.prod_eq_mul_prod_sdiff_singleton_of_memproof · cited by 10
- mul_left_injproof · cited by 8
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