Theorems · Theorem · sequences and series
tprod_pnat_eq_tprod_of_eq_one
∀ {M : Type u_1} [inst : CommMonoid M] [inst_1 : TopologicalSpace M] {f : ℕ → M},
f 0 = 1 → ∏' (n : ℕ+), f ↑n = ∏' (n : ℕ), f n- Cited by
- 0 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidTopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- CommMonoidstatement and proof · cited by 2,264
- SummationFilter.unconditionalstatement · cited by 2,068
- PNatstatement · cited by 392
- Function.mulSupportproof · cited by 240
- tprodstatement · cited by 230
- PNat.valstatement · cited by 226
- Function.Injective.tprod_eqproof · cited by 6
- PNat.coe_injectiveproof · cited by 3
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