Hi

In the rules it states

"The attacking player assigns damage to his opponent first. Damage must be assigned to defending units before it can be assigned to the defending player’s capital. In other words, the attacking player must assign enough damage to destroy each defending unit before any damage can be assigned to the defending player’s capital. Note that more damage can be assigned to a unit at the attacker’s discretion, in anticipation of damage cancellation effects, but a minimum damage necessary to destroy each defending unit must be assigned before any damage can be assigned to the defender’s capital "

if I had a defending unit with 3 hit points and my opponent attacked me with 7 damage assigning 3 to my unit and the rest to my capitol and I play a card the reduces the damage he does to my defending unit so that it survives does the other 4 points of damage still get applied to the capitol as he applied damage in good fate

Yes. Only damage cancellation effects known at the time have to be considered. Once damage has been assigned, it will be applied, unless it is cancelled or redirected with a card effect.