You guys are mixing up the clauses in the fifth amendment.
The portion you are bolding and red-ing in the first clause applies to those who are serving in our armed forces. Awlaki was not a member of our military.
The "due process" clause is later and distinct from the first clause. That still applies to the rest of us citizens who aren't in the U.S. military. No exception is given in that clause for times of war or public danger.
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Actually the semi-colon at the end of the first clause sets conditions applicable to all following clauses each subsequent clause is set under the conditions joined to the first clause.
During time of war the military is not subject to the same conditions for Due Process as civilian courts. It would not be practical on the battlefield to:
(a) Detain each combatant without use of deadly force,
(b) Determine the status of each combatant,
(c) If the combatant is found to be a citizen, then continue detainment,
(d) Proceed with investigation,
(e) Convene a Grand Jury,
(f) Pending results of Grand Jury, then issue an arrest warrant,
(g) Try the person in court,
(h) Execute if found convicted of a Capital Offense (which treason is).
The difference is that in a tactical situation you have to react within a specified time window or an opportunity is lost.
This war will not be won with typical courtroom proceedings, this war will be won by cutting the head off the snake and when a new one starts to grow you cut that off next, and you keep going until there is nothing left but the tail that will wither and die.
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