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I think the author is saying these lines are all equal. The second term of the of the last 2 lines is saying "the expected value of Y given they did not get the treatment", it is just the notation that is changing.
After the following "...and we have that the causal impact on the treated is the same as in the untreated (because they are very similar)":
I do not understand why you write E[Y|T=0] since we don't have E[Y1|T=0] in the above lines.
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