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Familiar religious example: Luke 6:37 "Judge not, and ye shall not be judged: condemn not, and ye shall not be condemned: forgive, and ye shall be forgiven:"

Transitive (from mathematics) doesn't quite work because it's not really if A=B & B=C then A=C. If I forgive her and God forgives me, the God forgives her? Maybe theologically correct, but not the right meaning.
Transference in psychology doesn't quite fit either. "God is transferring His forgiveness for me to another person"--don't think so.
Causal is closer: "If I forgive him, God will forgive me"

Any other options?

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There is cast your bread upon the waters from Judeo-Christian thought (the book of Ecclesiates 11:1 to be exact) and good karma from Hindu/Yogic/Buddhist thought.

The best fit from English idioms, however, is probably what goes around comes around. This is often taken in its negative sense (do evil to others and evil will be done to you) but is equally applicable to the doing of good to others, particularly in the form of random acts of kindness.

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People in glass houses should not throw stones.

"Those who live in glass houses should not throw stones" is a proverb used in several European countries pertaining to hypocrisy. It means that "One who is vulnerable to criticism regarding a certain issue should not criticize others about the same issue." https://en.wikipedia.org/wiki/Those_who_live_in_glass_houses_should_not_throw_stones

See also:https://english.stackexchange.com/search?q=glass+houses

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