DEFINITION and5_rec()
TYPE =
       ΠP0:Prop
         .ΠP1:Prop
           .ΠP2:Prop
             .ΠP3:Prop
               .ΠP4:Prop
                 .ΠP:Set.(P0→P1→P2→P3→P4→P)→(and5 P0 P1 P2 P3 P4)→P
BODY =
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