Lte's prove what the [be] is for

Hi,I have a thought if I am uncertain as to whether it is right. That thought is that {what the [be] is for} is with what the subject acts. For example:1. In [Jack is in love.] , Jack exists in love / There is Jack in love.So, the [is] must show [exists] , because the [in] = being surrounded / contained / controled by 2. In {The proof of the pudding is in the eating.}, the [is] = identifies, because the [in] = attending for / on the purpose3. In {We believed in her innocence.} , [we believed] that activity is in her innocence.So, the [is] = exists, because the [in] = being surrounded / contained / controled by 4. In {what is in the mind.} , There is / exists what in the mind.The [is] = exists, because the [in] = being surrounded / contained / controled by the mind.5. In {what is on the mind.}, what is supported on the mind. And the mind is a supporter / receiver to take / to bear what , or [what] has a quality or a power to put itself on the mind.So, the [is] = has a quality / has a power, because the [on] = being supported by the mind. Thank you for your assistance.