Theorems · Theorem · logic and foundations

PrimrecRel.forall_mem_list

∀ {α : Type u_1} {β : Type u_2} {R : α → β → Prop} [inst : Primcodable α] [inst_1 : Primcodable β],
  PrimrecRel R → PrimrecRel fun L b => ∀ a ∈ L, R a b

If R a b is decidable, then given L : List α and b : β, g L b ↔ ∀ a L, R a b is a primitive recursive relation.

Defined in

Mathlib.Computability.Primrec.List

Cited by

1 results in Mathlib

Foundations

Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PrimcodablePrimcodable