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C-h f indent-region

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  3) Indent each line via ‘indent-according-to-mode’.
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(indent-according-to-mode)

Indent line in proper way for current major mode.
*Normally*, this is done by calling the function specified by the
variable ‘indent-line-function’.

indent-line-function is a variable defined in ‘indent.el’.

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Setting this function is all you need to make TAB indent appropriately
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