In "A formalization of set theory without variables" p.96 Tarski&Givant define quasi projections as relations satisfying
$ \breve{A} ; A \le 1' $
$ \breve{B} ; B \le 1' $
$ \breve{A} ; B = 1 $
Projections in general are idempotent operations, so are quasi projections $A$ and $B$ idempotent
$ A ; A = A $ ?
At the same page the manuscript defines (genuine?) projections with two additional conditions
$ (A;\breve{A})\cdot(B;\breve{B})≤1'$
$ A;1 = B;1 $
I'm unable to prove/refute idempotent property in either case.
