source: CIVL/mods/dev.civl.sarl/doc/ideasAndExamplesOfIntDivTranslation@ 1aaefd4

In the examples, those examples will be translating into same thing no matter their vars are quantified or not.

example 1:

a/b=3
will be translated to 
Exists q1, r1 : (b * q1 + r1 = a and |r1| < |b| and (sign(a) = sign(r1) || r1 = 0) and q1 = 3)

example2:

a/b + c%d = 5
will be translated into

Exists q1, r1, q2, r2: (
q1*b+r1 = a and |r1| < |b| and ( sign(a) = sign(r1) || r1 = 0 )   //this is the translation of a/b
and q2*d + r2 = c and |r2| < |d| and ( sign(c) = sign(r2) || r2 = 0) // this is the translation of c%d
and q1 + r2 = 5      // this is the translation of the whole boolean expression
)


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my basic idea is that:
1. when encounter a divide or modulo (a/b), you will get two things: constraints (b*q + r =a) and value of the expression (q).
2. when encounter a '+' or '-' or '*' or ..., the result the which is not a boolean expression (like the result of a+b is not a boolean), you will just merge the constraints and pop the value of the expression and the constraints up to the stack.
3.when you encounter a '=' or '<' or '<=', the result of which is a booleanExpression. you will generate a Exists expression just like those examples. Because we only conside expression within Forall and Exist, so finally we will reach to a BooleanExpression.