What's that word meaning 'thus more strongly for X'?

Question

What's that word meaning 'thus more strongly'? As in X applies to Y, and thus even more strongly to Z. E.g.:

The body's immune system needs warmth, so adequate heating is good for you (and [this conclusion follows with even more force] for sick people)

I seem to remember that there is such a word, and it's Latin, though I could be wrong.

Answer 1

a fortiori

(It has an entry in Wikipedia.)

In Hebrew, we call it a Kal Vachomer (if this is true in a lenient case, it is all the more true in a strict case).

Answer 2

Perhaps a simpler, non-Latin phrase?

Adequate heating is good for you, and particularly for sick people

or

Adequate heating is good for you, and doubly so for sick people

Answer 3

A further option in addition to those already posted:

Adequate heating is good for you, and moreso/more so for sick people.