Trust in a relationship specifically must mean not asking for the
other to prove something. If you have the proof, you would not need
the trust. It's to not know, yet believe.
So how do people build up the initial trust? As so often, we base
assumptions on the future by experiences of the past. There are two
very different approaches, one pessimist and doubtful, and one
optimist and hopeful. In real life, people are usually somewhere in
between the one or the other:
1. A person mistrusts another person, until eventually the other makes
it obvious over time the mistrust is unnecessary
2. A person trusts another person, until eventually the other makes it
obvious over time the trust is unjustified
You can build up the trust to be optimistic either outside of a
relationship (e.g. by seeing that you can trust your parents), or in a
relationship (by seeing that your partner does never let you down, or
lie to you).
Concerning relationships of love, how does jealousy fit into this
One can be jealous because of knowing oneself, and one's own desires,
which can be projected on the partner. But is jealousy always
implicating mistrust? Not necessarily.
One can also be jealous because of low self-esteem.Or because one
feels the partner imposes different measurements of what makes a
relationship, even when the partner does not lie or gives reason to
mistrust (for one it might be OK to flirt with other people, for the
other this might cross the border).
Should one be optimistic, and trust? Out in the real world, you need
to be careful, or you will be hurt. But also, mistrust can poison a
relationship, and become self-fulfilling.
So, you asked if it's OK to for another person to ask, "Prove it."
This question is not asked out of the blue in a relationship of trust
-- it must be a symptom of something else. The real reasons behind the
question should be discussed, by asking the following (as sincere, not
- "Do I give you reason to not trust me?"
Hope this helps.