Section FIN_DISCR_DEC_SAT_FIN_DEC_EQ_NOSYMS_SAT.
Variable (Σ : fo_signature) (HΣ : finite_t (syms Σ) + discrete (syms  Σ)).
End FIN_DISCR_DEC_SAT_FIN_DEC_EQ_NOSYMS_SAT.
(* If the relation symbols in Σ have all their arities upper bounded by n and Σunif n is the signature with the same functions symbols and relations symbols as Σ except that the arity of relations is uniformly equal to n, then there is a reduction  SAT(Σ,𝔽,ℂ) ---> SAT(Σunif n,𝔽,ℂ) *)

Theorem FSAT_UNIFORM Σ n :
(forall r : rels Σ, ar_rels _ r <= n)
-> FSAT Σ ⪯ᵢ FSAT (Σunif Σ n).