; MINLOG: probestudstart.scm

; (load "~/minlog/init.scm")


(exload "Schueler/germanise.scm")


(define (zeige string)
  (display-global-assumptions string))

(set! COMMENT-FLAG #f)

(add-tvar-name "ℝ" "offen")
(add-var-name "x" "y" (py "ℝ"))
(add-var-name "f" "g" (py "ℝ => ℝ"))
(add-var-name "O" "U" "V" "W" (py "offen"))
(add-predconst-name "ee" (make-arity (py "ℝ") (py "offen") (py "boole")))
(add-token
 "in"
 'pred-infix
 (lambda (x y)
   ((string-and-arity-to-predconst-parse-function
	 "ee" (make-arity (py "ℝ") (py "offen")))
	(- 1) x y)))
(add-predconst-display "ee" 'pred-infix "in")

(libload "nat.scm")




(display "
nat.scm geladen
")

(av "l" (py "nat"))

; (add-token
;  "≤"
;  'rel-op
;  (lambda (x y)
;    (mk-term-in-app-form
;     (make-term-in-const-form (pconst-name-to-pconst "NatLe")) x y)))

; (add-display
;  (py "boole")
;  (lambda (x)
;    (let* ((op (term-in-app-form-to-final-op x))
; 	  (args (term-in-app-form-to-args x)))
;      (if (and (term-in-const-form? op)
; 	      (string=? "NatLe"
; 			(const-to-name (term-in-const-form-to-const op)))
; 	      (= 2 (length args)))
; 	 (list 'rel-op "≤"
; 	       (term-to-token-tree (car args))
; 	       (term-to-token-tree (cadr args)))
; 	 #f))))

(add-rewrite-rule (pt "n <= Succ n") (pt "True"))
(add-rewrite-rule (pt "n < Succ(Succ (n+k+l))") (pt "True"))
(aga "Hilfssatz1" (pf "all n,l. (n<l ->F) -> l<=n"))
(aga "Hilfssatz2"
     (pf "(all l,n.n<(l+1)*(l+1) -> Succ n<(l+1+1)*(l+1+1))
        & (all l,n.l*l<=n -> l*l<=Succ n)"))

(set! COMMENT-FLAG #t)



(display "
Ende von probestudstart.scm

")
