While it's true that a comma splice is a comma that separates two independent clauses without a conjunction, the sentence in question could be considered a comma splice if the sentence is taken in context.
"When was the crisis averted?"
"When he was able to crack the Trident code, that was deemed by many as his major achievement in his ...
Your first example does not have a comma splice. Your "supporter" is wrong. This would be a comma splice.
He was able to crack the Trident code, many deemed this the major achievement of his deciphering career.
Note: I repeat my suggestion (from my answer to your previous question) that "deciphering career" is awkward and likely not what you want to ...
When laid out step-by-step it could be considered a "formal proof", especially since you ask why a particular equation is valid.
In a less formal context this could be called "simplifying" the math by combining more complicated expressions and removing those that "cancel out". In this case you end up with a long equation, in the middle of which is
This is formally known as "A Proof", if it is indeed such. Something similar might be known as a theorem, but my maths certainly isn't good enough to tell you which this is.
I can't think of 'justification' ever being used in this sort of context (Mathematical / Scientific)
In U.S. English, a common way to refer to this hairstyle is that it's cut/angled/layered "to frame the face." See all of these youtube tutorials on how to cut hair like this.
While not an exact match for your sentence, a very natural way to express the same idea would be something like "locks/wisps of hair framed her face."
Tresses are long locks of hair which hang down from the head. It doesn't mean side of the head exclusively, but it does mean long hair hanging down.
Her dark brown tresses framed her pale face as she gazed into the distance.
This is part of the technical medical jargon. A syndrome is a collections of symptoms that seem to happen together. Back in the early 1980s, doctors in America started noticing that young men were being hospitalised and dying with some similar diseases: particular cancers combined with severe forms of other diseases that the immune system would normally ...
AIDS is a disease that makes other diseases much worse.
The name includes the word syndrome for historical reasons. A "syndrome" is a collection of symptoms that occur together. When doctors first notice such a collection of symptoms, they can call it a "syndrome", even if they have not proven that it is a communicable disease nor proven that it has an ...
I think you are looking for consonance. It is the consonant version of assonance, and alliteration is a more specific type of consonance.
However, I do not think I would characterize the end of "doubt" as having the same sound as the beginning of "truth".