Consider what I'd put in an old post, regarding what is meant when Jesus said (John 8:56), "Your father Abraham
rejoiced to see MY DAY: and he saw
it, and was glad"...
[quoting old post]
As for the Heb11:13 "these all died in faith"...
[quoting excerpt from Wm Kelly's Commentary on Hebrews 11--I tried to place his first paragraph here in such a way as to draw attention to the various Greek words (etc) used for what is most often translated simply as "by faith" in our English, but which are actually distinct Greek words...
(inserts in BLUE are mine)]
But "that day" is not yet come; and we return to their fathers. From the rising above difficulties insuperable save to God on whose word they relied (verses 11, 12), we have a summary in verses 13-16, which brings out the patriarchs refusing all temptation, and by faith holding on their pilgrim way to death consistently with the accomplishment of promise. This is the reason why the phraseology chances
[changes] in the beginning of verse 13.
It is no longer "in"
[en] faith, that is, in virtue (or the power) of faith as in verse 2, where such a force is requisite,
[...].
Nor further is it the proximate cause, the dynamic or instrumental dative as in verses 3, 4, 5, 7, 8, 9, 11, and again in 17, 20, 21, 22, 23, 24, 27, 29, 30, and 31.
Still less does it distinguish faith as the means "through"
[dia] which, as in 4, 7, 33.
Here (verse 13), if we say "in," we mean according to
[kata] faith, contrasted with sight or possession of the things promised. What indeed would be the sense of saying that "by" or "through" faith all these died?
Nor is it "in"
i.e. in virtue of faith, but according to
[kata] faith as in verse 7 of our chapter, where the precisely same phrase occurs
[that is, in v.7c].
[...] Conformity with faith is here predicated of Abraham and those patriarchs that followed, not for perseverance to the end though this was the fact, but in being content to wait for God's fulfilling the promises in due time.
"According to
[kata] faith died these all, not having received promises, but from afar having seen and saluted [or, embraced] them, and confessed that they were ["are," historical] strangers and sojourners on the earth [or, land]. For they that say such things clearly show that they seek after a fatherland. And if indeed they were* calling to mind whence they went out, they would have had opportunity to return; but now they desire a better, that is, a heavenly. Wherefore God is not ashamed of them to be called their God; for he prepared for them a city" (verses 13-16).
[...]
The aim in these verses is to present vividly that common pilgrim path in which the patriarchs walked, even to their death, before the Spirit takes up characteristic workings of faith, even in Abraham as well as in each of those that followed, as far as it bore on the subject in hand and the special help of those virtually addressed. How timely and needful it must have been we may gather, because they expand the truth already set forth briefly in verses 9, 10.
Neither death, nor the unseen state that succeeds, was the accomplishment of the promises. On the contrary their death without receiving what was promised was in accordance
[kata] with faith, and the witness of its single-eyed integrity.
And the accomplishment of the promises supposed, what they could not as yet understand any more than anticipate, the second advent of the Lord even more than the first, although the first was the far more solemn in itself,
and the righteous basis of the blessings and glories which await the second.
Hence the force of our Lord's word in John 8:56, "Abraham rejoiced that he should see my day, and he saw and was glad." Neither technically nor substantially was the first [advent] mainly in view as has been thought, but that day when God's word and oath shall be vindicated before a wondering and rejoicing world. The patristic dream, which some dream over again,
[i.e. the supposition] that it refers to what Abraham beheld after death when our Lord was here, is as unwarranted a perversion as the Socinian interpretation which Meyer justly stigmatises
[...]. The design of our Lord and of that chapter
[John 8] is to prove Himself the Light and Word and Son and God Himself; and hence the contrast between Abraham who believed and his seed who did not. Whatever glimpse Abraham may have had of the truth to which the sacrifice on Moriah pointed,
it was to the full accomplishment of the promise he looked, and saw by faith what still awaits fulfilment, the period of Christ's manifested glory, "My day." In this hope brightly breaking through the clouds Abraham exulted, and he saw, as faith ever sees, and rejoiced. He, like the rest, saw the promises in their accomplishment from afar off.
And so died these all in accordance with faith as they lived,
looking forward to Messiah's day for making good the promises.
--William Kelly, Commentary on Hebrews 11 (From BibleHub) -
https://biblehub.com/commentaries/kelly/hebrews/11.htm
[end quoting; bold, underline, and some bracketed inserts mine
(in BLUE)--including the particular Greek words he's referring to--; parentheses and some brackets original]
____________
bottom line: the phrase
"these [G3778] all died
according to faith" refers to those in vv.8-12
in particular.
[end quoting that post]
____________
Hope that helps you see my perspective on "Abraham rejoiced to see MY DAY" in John 8:56. = )