COMMENT ⊗   VALID 00002 PAGES
C REC  PAGE   DESCRIPTION
C00001 00001
C00002 00002	DECLARE INDVAR X X0 X1 X2 Y Y0 Y1 Y2 Z Z0 Z1 Z2
C00004 ENDMK
C⊗;
DECLARE INDVAR X X0 X1 X2 Y Y0 Y1 Y2 Z Z0 Z1 Z2;
DECLARE INDVAR u u0 u1 u2 v v0 v1 v2 w w0 w1 w2 ε LIST;
DECLARE INDCONST nil ε LIST;
DECLARE INDVAR x x0 x1 x2 y y0 y1 y2 ε ELEMENT;

DECLARE OPCONST CONS 2;
DECLARE OPCONST CAR 1[R ← 600];
DECLARE OPCONST CDR 1[R ← 600];
DECLARE OPCONST cons(ELEMENT,LIST) = LIST;
DECLARE OPCONST car(LIST) = ELEMENT[R←600];
DECLARE OPCONST cdr(LIST) = LIST[R←600];

AXIOM CONS:
	∀x u.(cons(x,u) = CONS(x,u))
;;

AXIOM CAR: ∀u.(car u = CAR u);;

AXIOM CDR: ∀u.(cdr u = CDR u);;

AXIOM LIST:
	∀x u.(car cons(x,u) = x)
	∀x u.(cdr cons(x,u) = u)
	∀u.(¬u=nil ⊃ u = cons(car u,cdr u))
;;

DECLARE PREDPAR P 1;

AXIOM INDUCTION: P(nil) ∧ ∀u.(¬(u=nil) ∧ P(cdr u) ⊃ P(u)) ⊃ ∀u.P(u);;

DECLARE OPCONST APP 2[L←400 R←395];

DECLARE OPCONST app(LIST,LIST) = LIST[L←400 R←395];

AXIOM APPEND:
	∀X Y.(X APP Y = IF X = nil THEN Y ELSE CONS(CAR X, CDR X APP Y))
	∀u v.(u app v = IF ∃w.(u APP v = w) THEN u APP v ELSE nil)
	∀u v.(u app v = IF LIST(u APP v) THEN u APP v ELSE nil)
;;