If you want to keep Mno.const. you will have to control the equation TAS/LSS. How do u control TAS? With CAS.
In normal conditions when you descend keeping Mno. constant you will increase the CAS to increase the TAS so that it matches with the increase in LSS to keep Mno. cosnt.
But when you descend in an Inversion layer keeping Mno. const.with the LSS decreasing the TAS needs to decrease at the same rate as LSS to keep Mno. const. But since the reduction in TAS is at a higher rate (due to the additional density increase due to reduced temp.) compared to the reduction in LSS the Mno. will decrease. So to keep Mno. const. TAS needs to reduce at a slower rate (equal to LSS) for which the CAS has to increase. If you reduced CAS the TAS would reduce at a much greater rate than LSS and the Mno.would reduce.
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Hence TAS will be taken care of due to additional increase of density due to decreasing temp.
The additional increase in density will further reduce the TAS and therefore the TAS will actually start reducing at a much faster rate than the LSS
(The CAS/TAS variation due to density error is much greater than the LSS change due to temp. variations.)