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But these gunmen WERE Muslims, the very worst of Muslims, to be certain, but as surely part of Islam as the highest of imams anywhere.

They were simply acting on their categorical imperatives, in the fullest sense they could.

Read the relevant verses of the Koran. Until these verses are vastly re-interpreted, or deleted, their meaning is pretty clear, and there was no mistake in their translation.

KORAN commands to kill infidels:

Allah is an enemy to unbelievers. - Sura 2:98

On unbelievers is the curse of Allah. - Sura 2:161

Slay them wherever ye find them and drive them out of the places whence they drove you out, for persecution is worse than slaughter. - Sura 2:191

Fight against them until idolatry is no more and Allah’s religion reigns supreme. (different translation: ) Fight them until there is no persecution and the religion is God’s entirely. - Sura 2:193 and Sura 8:39

Fighting is obligatory for you, much as you dislike it. - Sura 2:216
(different translation: ) Prescribed for you is fighting, though it is hateful to you.

..... martyrs.... Enter heaven - Sura 3:140-43

If you should die or be killed in the cause of Allah, His mercy and forgiveness would surely be better than all they riches they amass. If you should die or be killed, before Him you shall all be gathered. - Sura 3:157-8

You must not think that those who were slain in the cause of Allah are dead. They are alive, and well-provided for by their Lord. - Sura 3:169-71

Let those fight in the cause of God who sell the life of this world for the hereafter. To him who fights in the cause of God, whether he is slain or victorious, soon we shall give him a great reward. - Sura 4:74

Those who believe fight in the cause of God, and those who reject faith fight in the cause of evil. - Sura 4:76

But if they turn renegades, seize them and slay them wherever you find them. - Sura 4:89

Therefore, we stirred among them enmity and hatred, which shall endure till the Day of Resurrection, when Allah will declare to them all that they have done. - Sura 5:14

O believers, take not Jews and Christians as friends; they are friends of each other. Those of you who make them his friends is one of them. God does not guide an unjust people. - Sura 5:54

Make war on them until idolatry is no more and Allah’s religion reigns supreme - Sura 8:39

O Prophet! Exhort the believers to fight. If there are 20 steadfast men among you, they shall vanquish 200; and if there are a hundred, they shall rout a thousand unbelievers, for they are devoid of understanding. - Sura 8:65

It is not for any Prophet to have captives until he has made slaughter in the land. - Sura 8:67

Allah will humble the unbelievers. Allah and His apostle are free from obligations to idol-worshipers. Proclaim a woeful punishment to the unbelievers. - Sura 9:2-3

When the sacred months are over, slay the idolaters wherever you find them. Arrest them, besiege them, and lie in ambush everywhere for them. - Sura 9:5

Believers! Know that idolators are unclean. - Sura 9:28

Fight those who believe neither in God nor the Last Day, nor what has been forbidden by God and his messenger, nor acknowledge the religion of Truth, even if they are People of the Book, until they pay the tribute and have been humbled. - Sura 9:29 (another source: ) The unbelievers are impure and their abode is hell. (another source: ) Humiliate the non-Muslims to such an extent that they surrender and pay tribute.

Whether unarmed or well-equipped, march on and fight for the cause of Allah, with your wealth and your persons. - Sura 9:41

O Prophet! Make war on the unbelievers and the hypocrites. Be harsh with them. Their ultimate abode is hell, a hapless journey’s end. - Sura 9:73

Allah has purchased of their faithful lives and worldly goods, and in return has promised them the Garden. They will fight for His cause, kill and be killed. - Sura 9:111

Fight unbelievers who are near to you. Sura 9:123 (different translation:
Believers! Make war on the infidels who dwell around you. Let them find harshness in you. (another source: ) Ye who believe! Murder those of the disbelievers....

As for those who are slain in the cause of Allah, He will not allow their works to perish. He will vouchsafe them guidance and ennoble their state; He will admit them to the Paradise He has made known to them. - Sura 10:4-15

Allah has cursed the unbelievers and proposed for them a blazing hell. - Sura 33:60

Unbelievers are enemies of Allah and they will roast in hell. - Sura 41:14

When you meet the unbelievers, smite their necks, then when you have made wide slaughter among them, tie fast the bonds, then set them free, either by grace or ransom, until the war lays down its burdens. - Sura 47:4
(different translation: ) When you meet the unbelievers in the battlefield, strike off their heads, and when you have laid them low, bind your captives firmly.

Those who are slain in the way of Allah - he will never let their deeds be lost. Soon will he guide them and improve their condition, and admit them to the Garden, which he has announced for them. - Sura 47:5

Muslims are harsh against the unbelievers, merciful to one another. - Sura 48:25

There are more, but it is pretty plain from where these murderous thugs derive their justification and sanction.