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Are quasiprojections idempotent?

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.

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