Where does “prostituens” come from?

prostituens (Latin) comes from Latin prōstituō, from Latin statuo, from Latin stātus, from Latin stō, from Proto-Italic staēō, from Proto-Indo-European sth₂éh₁yeti, from Proto-Indo-European *steh₂-.

Definitions

Ancestry of “prostituens”, step by step

Step	Language	Word	Meaning
1	Latin	prōstituō	to set up in public
2	Latin	statuo	I set up, station; I establish, determine, fix; I...
3	Latin	stātus	fixed, set, having been set
4	Latin	stō	to stand
5	Proto-Italic	staēō	stand
6	Proto-Indo-European	sth₂éh₁yeti	to stand
7	Proto-Indo-European	*steh₂-	—

Every word from Proto-Indo-European *steh₂- →Every word from Proto-Indo-European sth₂éh₁yeti →Every word from Proto-Italic staēō →