00100 GIVEAX(DISTINCT1,(∀ X)(∀ U)
00150 (DISTINCT U ∧ ¬LMEM(X,U) ≡ DISTINCT CONS(X,U)));
00200
00300 GIVEAX(DISTINCT2,DISTINCT NIL);
00350
00400
00500 GIVEAX(NIL1,NIL='NIL);
00600
00700 GIVEAX(NIL2,(∀ X)(¬LMEM(X,NIL)));
00800
00900 GIVEAX(CONS1,(∀ X)(∀ Y)(X=CAR CONS(X,Y))));
01000
01100 GIVEAX(CONS2,(∀ X) (∀ Y)(Y=CDR CONS(X,Y))));
01200
01300 GIVEAX(CONS3,(∀ X)(∀ Y)(NIL≠CONS(X,Y)));
01400 END;