How to formulate and deal with two different linear equations in Gurobi

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Working on an optimization problem formulated as an MIP where I have two decision variables a[i,j] and b[u,v,x,y]. I have a couple of equations (EQ1,.., EQ10). For simplicity and abstraction levels I just mention EQ1 and EQ2.

For a special case I need to express this situation :

If x!=y and a[u,x] = 1 and a[v,y] =1 then 
consider linear equation EQ1 // EQ1 for the special case
otherwise consider EQ2. 

Does any one know how to deal with this situation ? Any help will be highly appreciated.

Regards

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