question about multi-prime rsa

From <http://tools.ietf.org/html/rfc3447#page-8>:

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Each CRT coefficient t_i (i = 3, ..., u) is a positive integer less
than r_i satisfying

R_i * t_i == 1 (mod r_i) ,

where R_i = r_1 * r_2 * ... * r_(i-1).

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So t_3 satisfies the following:

R_i * t_i == 1 (mod r_3)

Where R_i = r_1 * r_2

And t_2, the following:

R_i * t_i == 1 (mod r_2)

Where R_i = r_1

ie. r_1 * t_i == 1 (mod r_2)

Problem is, this seems to contract this (from the previous page on the
RFC):

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In a valid RSA private key with the second representation, the two
factors p and q are the first two prime factors of the RSA modulus
n
(i.e., r_1 and r_2)
....
and the CRT coefficient qInv is a positive integer less than p
satisfying

q * qInv == 1 (mod p).

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Replacing p with r_1 and q with r_2 gets us this:

r_2 * qInv == 1 (mod r_1)

....but aren't qInv and t_2 essentially supposed to be the same thing?
As is, they're not:

qInv == r_2 ** -1 (mod r_1)
t_2 == r_1 ** -1 (mod r_2)
.