Linear algebra, row reduced echelon form problem

I just saw that statement green says that first j columns in the full m rows are row reduced so why statement red is necessary.
I am not criticizing the author if I was I wouldn’t be reading his book. I just want to know why statement red is relevant while it is talking about first r-1 rows not all the rows. So is statement red is irrelevant if not please specify connection between statements green and red. Sorry again i don’t mean to criticize anyone
 
So what is your opinion please specify clearly how statement red is relevant to statement green or is statement red irrelevant after all
 
Dr Peterson I know it may seem that I am repeating the same question but I genuinely don’t understand why statement red is relevant to statement green I feel it was completely proven without it. It is a nice information to know but statement green doesn’t rely on statement red. It is as saying we can multiply all equations by two it is true but irrelevant for statement green. So can you explicitly where the reasoning will fall if we remove statement red or if it was actually irrelevant. Sorry but I want to have complete understanding of the proof before moving to the next
 
Maybe I made my question unclear. It is not about weather statement red is true or whether it is obvious. The question is whether the proof relies on it that the flow of reasoning will stop without it. Dr Peterson you said that statement green relies on it but how. Can you show me where the reasoning would fall if we removed statement red. Thanks
 
AbdelRahmanShady said:
Maybe I made my question unclear. It is not about weather statement red is true or whether it is obvious. The question is whether the proof relies on it that the flow of reasoning will stop without it. Dr Peterson you said that statement green relies on it but how. Can you show me where the reasoning would fall if we removed statement red. Thanks
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Please reread my posts #42 and #60. What did I say about whether it could be removed?

Are you always so obsessive?
 
I dont understand your reasoning about statement red you said it is used later by statement green but how. This proof didnt need statement red.
AbdelRahmanShady said:
By the way this how the proof could be without statement red. Since the new column j is to the right to each leading one and is below each leading statement 4 of definition RREF is true. And since there are only zeros in column j except row r then statement 3 is true and since it is 1 so statement 2 is true and statement 1 is true since the all zero rows are in r+1 to m rows so I proved statement green without needing to state statement red
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so is my proof missing something or is it the fact that statement red is needed only when the part of proof I made up is ommited.
 
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