Proof of parameterized dinaturality

Proposition (Parameterized dinaturality) (for f : Z U(B) U(A) and g : X U(A) Y U(B) in C):

=
Tr(X Z) Y A ((idX symmZ U(A)); (g idZ); (idY (symmU(B) Z); f))) = Tr(X Z) Y B ((idX f); g)

Proof.

= (Yanking)
= (Naturality of Tr)
= (Naturality of symm)
= (Functoriality of )
= (Symmetry sliding)
= (Naturality of symm)
= (Naturality of Tr)
= (Yanking)

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