Avos drew life from the Tree of Life

במדרש יודע ה' ימי תמימים כו'.

In the Midrash: "Hashem knows the days of the wholehearted [temimim]," etc.

The Midrash on Chayei Sarah opens with the verse describing how Hashem knows the "days of the wholehearted" — connecting Sarah's righteous years to a deeper truth about time.

כבר כתבנו פי' תמימים להיות מתאימים הימים שלמטה באורות המיוחדים להם למעלה.

We have already written the meaning of "temimim" — that the days below are matched [mas'imim] with the lights designated for them above.

"Temimim" (whole/perfect) is read as "mas'imim" (matched): the days of a tzaddik's life below correspond exactly to their unique spiritual lights above, each day drawing down the illumination meant for it.

דאיתא כימי השמים על הארץ שימי האבות היו ת"ק שנה כמו מן השמים לארץ דהנה איתא עץ החיים מהלך ת"ק שנה.

For it is taught "like the days of heaven upon the earth" — that the days of the Avos were five hundred years, like the distance from heaven to earth; for it is taught that the Eitz HaChaim (Tree of Life) is a journey of five hundred years.

Chazal speak of the span "from heaven to earth" as five hundred years, the same measure given for the Eitz HaChaim. The Avos' lifespans correspond to this measure, linking their lives to the channel of life that runs from above to below.

והאבות בימי חייהם המשיכו החיים מעץ החיים.

And the Avos, during the days of their lives, drew down the life from the Eitz HaChaim.

Throughout their lives the Avos served as conduits, drawing the flow of true, eternal life from the Eitz HaChaim down into the world.

ופי' מהלך ת"ק שנה מי שהוא עובד ה' כל ת"ק שנה בלי פני' הוא מוציא החיים שיוכל להתגלות בעולם.

And the meaning of "a journey of five hundred years" is that one who serves Hashem for the full five hundred years without any ulterior motive [pniyah] brings forth the life so that it can be revealed in the world.

The "journey of five hundred years" describes a complete avodah: one who serves Hashem with total purity, free of any self-interest, across that full span draws the hidden life-force into open revelation in this world.

וכן עשו האבות.

And so the Avos did.

The Avos accomplished exactly this — a life of unblemished service that opened the channel of life for all generations.

ויתכן כי בודאי עץ החיים אין לו שיעור והוא בבחי' העומדים.

It may be that surely the Eitz HaChaim has no measure, and it is of the category of "those who stand [omdim]."

In itself the Eitz HaChaim is infinite and unbounded — belonging to the realm of the "standing" (the fixed, unchanging spiritual world above time and motion).

אבל מהלך ת"ק שנה הוא ההארות שיכולין להשיג בחי' מהלכים שהוא האדם בעוה"ז.

But "a journey of five hundred years" refers to the illuminations that can be attained by those of the category of "walkers [mehalchim]" — that is, man in this world.

The "journey" is the measure of what a human being — a "walker," one who progresses and grows in olam hazeh (this world) — is able to reach of those infinite lights. The Tree itself is limitless; the journey is our finite access to it.

וע"ז נאמר כימי העץ ימי עמי היינו עץ החיים.

And about this it is said, "as the days of the tree shall be the days of My people" — meaning the Eitz HaChaim.

The prophet's promise that the people's days will be "as the days of the tree" refers to this Eitz HaChaim: Bnei Yisrael's days are bound to and measured by that channel of eternal life.

והאבות בימי חייהם המשיכו הכל בשלימות וז"ש ונחלתם לעולם תהיה:

And the Avos, during the days of their lives, drew everything down in perfection; and this is the meaning of "and their inheritance shall be forever."

Because the Avos drew this life down completely and perfectly, the inheritance they opened is permanent — an everlasting bequest of connection to the Eitz HaChaim for their descendants.

Summary: The "wholehearted" days of the Avos were perfectly matched to their spiritual lights above; through a lifetime of pure, selfless avodah they drew the infinite life of the Eitz HaChaim into revealed form in this world, leaving an eternal inheritance of that life-connection for Bnei Yisrael.