I've been reading some material the provides a different perspective. It isn't so much as to remind us to do things because we have been redeemed but rather it is to remind us of how much we don't do and need to repent. Consequently when Christ tells us to "Go and sin no more." or "Sell all that you have and come follow me.", He actually means just that. He isn't playing word games. Our failings in directly obeying His commands underscores our weaknesses and should lead us to repent on a daily basis pleading for His divine help.
Yes, our failings are our own and prove our inability to keep all the law.
Likewise, our sanctification is by the will of God, in order to prove it all true..."And be not conformed to this world: but be ye transformed by the renewing of your mind, that ye may prove what is that good, and acceptable, and perfect, will of God." Romans 12:2
Our obedience proves the truth of Christ risen, proves the Holy Spirit within us, proves that God changes the dead heart into a heart of flesh that will obey and glorify His name.
Adiaireton8 asks how we can know our salvation is true? The answer is that if God "renews your mind," you will prove it true.
If not, you won't.