In fact just to help out a little.
First point is that we are being warned as the last line you quoted said:
Heb 4:11 Let us therefore give diligence to enter into that rest, that no man fall after the same example of disobedience.
Notice the issue is disobedience due to a lack of faith as it is written:
Heb 3:15 While it is said, To day if ye will hear his voice, harden not your hearts, as in the provocation.
Heb 3:16 For some, when they had heard, did provoke: howbeit not all that came out of Egypt by Moses.
Heb 3:17 But with whom was he grieved forty years? was it not with them that had sinned, whose carcases fell in the wilderness?
Heb 3:18 And to whom sware he that they should not enter into his rest, but to them that believed not?
Heb 3:19 So we see that they could not enter in because of unbelief.
So the issue is they did not believe or have faith and disobeyed God. So what is the rest they did not enter? well the text told us it was those who died in the dessert which of course are those in Israel who did not enter the promised land.
Heb 4:3 For we which have believed do enter into rest, as he said, As I have sworn in my wrath, if they shall enter into my rest: although the works were finished from the foundation of the world.
This is a quote from the Psalms :
Psa 95:8 Harden not your heart, as in the provocation, and as in the day of temptation in the wilderness:
Psa 95:9 When your fathers tempted me, proved me, and saw my work.
Psa 95:10 Forty years long was I grieved with this generation, and said, It is a people that do err in their heart, and they have not known my ways:
Psa 95:11 Unto whom I sware in my wrath that they should not enter into my rest.
So we see it is about Israel not entering the promised land.
Heb 4:4 For he spake in a certain place of the seventh day on this wise, And God did rest the seventh day from all his works.
Heb 4:5 And in this place again, If they shall enter into my rest.
now notice that now the author directly connects the 7th day Sabbath with them not entering Gods rest. We see this in the words "in this wise"
Does the law teach us anything about Israel not obeying the Sabbath before going into the promised land?
Why yes see Exodus 16 and the manna, what was God's purpose in this test?
Exo 16:4 Then said the LORD unto Moses, Behold, I will rain bread from heaven for you; and the people shall go out and gather a certain rate every day, that I may prove them, whether they will walk in my law, or no.
Wow so the Sabbath was a test by God to see if obedience to His law would be done. was faith needed in this test?
Indeed read the rest of the story.
Why does the Author connect the 7th day Sabbath with their not entering into the promised land. Well for that one you whill have to study for yourself but I will give a hint:
Heb 9:3 And after the second veil, the tabernacle which is called the Holiest of all;
Heb 9:4 Which had the golden censer, and the ark of the covenant overlaid round about with gold, wherein was the golden pot that had manna, and Aaron's rod that budded, and the tables of the covenant;
Heb 9:5 And over it the cherubims of glory shadowing the mercyseat; of which we cannot now speak particularly.
Why is the manna in the Most Holy where judgment took place once a year?
one more clue:
Deu 8:1 All the commandments which I command thee this day shall ye observe to do, that ye may live, and multiply, and go in and possess the land which the LORD sware unto your fathers.
Deu 8:2 And thou shalt remember all the way which the LORD thy God led thee these forty years in the wilderness, to humble thee, and to prove thee, to know what was in thine heart, whether thou wouldest keep his commandments, or no.
Deu 8:3 And he humbled thee, and suffered thee to hunger, and fed thee with manna, which thou knewest not, neither did thy fathers know; that he might make thee know that man doth not live by bread only, but by every word that proceedeth out of the mouth of the LORD doth man live.
Anyway what else does the author of Hebrews say?
Heb 4:7 Again, he limiteth a certain day, saying in David, To day, after so long a time; as it is said, To day if ye will hear his voice, harden not your hearts.
Heb 4:8 For if Jesus had given them rest, then would he not afterward have spoken of another day.
Some people Get stuck on this passage but its actually really simple reasoning. The author is saying that the rest in the promised land that eventually came after all those died in the wilderness was led by Joshua, Yet David said a long time after Joshua, today if you hear my voice, so then there must be a promised land to us also. because if Joshua had given the true rest then David would not have spoken of another day namely "today" if you hear His voice.
In other words Today is the day you hear this, and David wrote it after the promised land thus there remains a promised land as the author clearly indicates:
Heb 11:39 And these all, having obtained a good report through faith, received not the promise:
Heb 11:40 God having provided some better thing for us, that they without us should not be made perfect.
SO we are traveling from type to anti-type and then the author reasons, If the true Day still remains then what else remains?
You guessed it the Sabbath remains because the true Promised land is yet to come.
Heb 4:9 There remaineth therefore a sabbath rest for the people of God.
And then the warning that we not fall after the same example of disobedience.
