Remark ReplaceTermTermsTermIsPR : isPR 2 ReplaceTermTermsTerm.
Definition ReplaceTermTerm (t s : nat) : nat :=
cPairPi1 (ReplaceTermTermsTerm t s).
Definition ReplaceTermsTerm (t s : nat) : nat :=
cPairPi2 (ReplaceTermTermsTerm t s).

(* Specifications: *)
Lemma ReplaceTermTermIsPR : isPR 2 ReplaceTermTerm.
Lemma ReplaceTermsTermIsPR : isPR 2 ReplaceTermsTerm.
Remark ReplaceTermTermsTermMonotone :
forall a s1 s2 : nat,
s1 <= s2 ->
ReplaceTermTerm a s1 <= ReplaceTermTerm a s2 /\
ReplaceTermsTerm a s1 <= ReplaceTermsTerm a s2.
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.