Theorems · Theorem · order theory

Submodule.mem_iInf

∀ {R : Type u_1} {M : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {ι : Sort u_4}
  (p : ι → Submodule R M) {x : M}, x ∈ ⨅ i, p i ↔ ∀ (i : ι), x ∈ p i

Defined in

Mathlib.Algebra.Module.Submodule.Lattice

Cited by

12 results in Mathlib

Foundations

Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModule