we denote the Askey-Wilson coefficients in a normalization specified by part 1 of Lemma \[normrules\].

The first part of the following theorem establishes the consistency of Askey-Wilson types for Leonard pairs and for Askey-Wilson relations.

\[classth\] Assume that $d\ge 3$. Let $(A,A^*)$ denote a Leonard pair on $V$, and let $AW$ denote the Askey-Wilson relations satisfied by $(A,A^*)$.

1.  The Askey-Wilson relations $AW$ have the same Askey-Wilson type as the Leonard pair $(A,A^*)$.

2.  If there is other Leonard pair on $V$ that satisfies AW, it has the same Askey-Wilson type as $(A,A^*)$.

3.  There exist unique affine translation which normalizes $AW$ according to the specifications of Lemma $\ref{normrules}$.

4.  The Askey-Wilson relations AW satisfy all inequalities in the last two columns of Table $\ref{elltab}$ on the corresponding line. All underlined equalities can be achieved after an affine translation, and such an affine translation is unique. The indicated nonzero coefficients can be normalized to any chosen values by an affine scaling.

[[**Proof.** ]{}]{}For the first statement, check the results in Section \[qpararrays1\] (or Section \[qpararrays2\]) and Section \[otherpararrays\], and observe that the Askey-Wilson relations associated to any parameter array have the same Askey-Wilson type as the parameter array, with the 