I added the following theorems to Funcoids and Reloids article. The theorems are simple to prove but are surprising, as do something similar to inverting a binary relation which is generally neither monovalued nor injective.
Proposition Let ,
,
are binary relations. Then
.
Theorem Let ,
,
are sets,
,
,
. Then
Theorem Let ,
,
are sets,
,
,
. Then
The above theorems are the key for describing product funcoids, a task I previously got stuck. Now I can continue my research.