Remark ReplaceTermTermsTermMonotone :
 forall a s1 s2 : nat,
 s1 <= s2 ->
 ReplaceTermTerm a s1 <= ReplaceTermTerm a s2 /\
 ReplaceTermsTerm a s1 <= ReplaceTermsTerm a s2.

(* Specifications: *)
Lemma ReplaceTermTermMonotone : forall a s1 s2 : nat, s1 <= s2 -> ReplaceTermTerm a s1 <= ReplaceTermTerm a s2.
Lemma ReplaceTermsTermMonotone : forall a s1 s2 : nat, s1 <= s2 -> ReplaceTermsTerm a s1 <= ReplaceTermsTerm a s2.