Theorems · Theorem · commutative algebra

DividedPowerAlgebra.submodule_span_prod_dp_eq_top

∀ {R : Type u_4} {M : Type u_5} {ι : Type u_6} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  {v : ι → M},
  Submodule.span R (Set.range v) = ⊤ →
    Submodule.span R (Set.range fun n => n.prod fun i k => DividedPowerAlgebra.dp R k (v i)) = ⊤

Defined in

Mathlib.RingTheory.DividedPowerAlgebra.Init

Cited by

0 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModule