Word search: tree of life

What's it about the tree that Adam lost in the fall? I did a search on the phrase "tree of life". Let us look at what the Bible says.

(Gen 2:9 MKJV)
And out of the ground Jehovah God caused to grow every tree that is pleasant to the sight, and good for food. The tree of life also was in the middle of the garden, and the tree of knowledge of good and evil.

(Gen 3:22 MKJV)
And Jehovah God said, Behold, the man has become as one of Us, to know good and evil. And now, lest he put forth his hand and take also of the tree of life, and eat, and live forever,

(Gen 3:24 MKJV)
And He drove out the man. And He placed cherubs at the east of the garden of Eden, and a flaming sword which turned every way, to guard the way to the tree of life.

(Pro 3:18 MKJV)
She is a tree of life to those who lay hold upon her; and happy is everyone who keeps her.

(Pro 11:30 MKJV)
The fruit of the righteous is a tree of life; and he who takes souls is wise.

(Pro 13:12 MKJV)
Hope put off makes the heart sick, but desire fulfilled is a tree of life.

(Pro 15:4 MKJV)
A wholesome tongue is a tree of life, but crookedness in it is a break in the spirit.

(Rev 2:7 MKJV)
He who has an ear, let him hear what the Spirit says to the churches. To him who overcomes I will give to eat of the Tree of Life, which is in the midst of the paradise of God.

(Rev 22:2 MKJV)
In the midst of its street, and of the river, from here and from there, was the Tree of Life, which bore twelve fruits, each yielding its fruit according to one month. And the leaves of the tree were for the healing of the nations.

(Rev 22:14 MKJV)
Blessed are they who do His commandments, that their authority will be over the Tree of Life, and they may enter in by the gates into the city.

Think there's a distinction between "tree of life" and "Tree of Life"

tree of life = wisdom, fruit of the righteous, desire fulfilled, wholesome tongue.