set GCD1 = ((((GBP := 0) ';' (SBP := 7)) ';' (saveIC (SBP,RetIC))) ';' (goto 2)) ';' (halt SCMPDS);
set GCD2 = (((((((((GBP := 0) ';' (SBP := 7)) ';' (saveIC (SBP,RetIC))) ';' (goto 2)) ';' (halt SCMPDS)) ';' ((SBP,3) <=0_goto 9)) ';' ((SBP,6) := (SBP,3))) ';' (Divide (SBP,2,SBP,3))) ';' ((SBP,7) := (SBP,3))) ';' ((SBP,(4 + RetSP)) := (GBP,1));
A1: card (((((GBP := 0) ';' (SBP := 7)) ';' (saveIC (SBP,RetIC))) ';' (goto 2)) ';' (halt SCMPDS)) = (card ((((GBP := 0) ';' (SBP := 7)) ';' (saveIC (SBP,RetIC))) ';' (goto 2))) + 1 by Th4
.= ((card (((GBP := 0) ';' (SBP := 7)) ';' (saveIC (SBP,RetIC)))) + 1) + 1 by Th4
.= (((card ((GBP := 0) ';' (SBP := 7))) + 1) + 1) + 1 by Th4
.= ((2 + 1) + 1) + 1 by Th5
.= 5 ;
A2: card ((((((((((GBP := 0) ';' (SBP := 7)) ';' (saveIC (SBP,RetIC))) ';' (goto 2)) ';' (halt SCMPDS)) ';' ((SBP,3) <=0_goto 9)) ';' ((SBP,6) := (SBP,3))) ';' (Divide (SBP,2,SBP,3))) ';' ((SBP,7) := (SBP,3))) ';' ((SBP,(4 + RetSP)) := (GBP,1))) = (card (((((((((GBP := 0) ';' (SBP := 7)) ';' (saveIC (SBP,RetIC))) ';' (goto 2)) ';' (halt SCMPDS)) ';' ((SBP,3) <=0_goto 9)) ';' ((SBP,6) := (SBP,3))) ';' (Divide (SBP,2,SBP,3))) ';' ((SBP,7) := (SBP,3)))) + 1 by Th4
.= ((card ((((((((GBP := 0) ';' (SBP := 7)) ';' (saveIC (SBP,RetIC))) ';' (goto 2)) ';' (halt SCMPDS)) ';' ((SBP,3) <=0_goto 9)) ';' ((SBP,6) := (SBP,3))) ';' (Divide (SBP,2,SBP,3)))) + 1) + 1 by Th4
.= (((card (((((((GBP := 0) ';' (SBP := 7)) ';' (saveIC (SBP,RetIC))) ';' (goto 2)) ';' (halt SCMPDS)) ';' ((SBP,3) <=0_goto 9)) ';' ((SBP,6) := (SBP,3)))) + 1) + 1) + 1 by Th4
.= ((((card ((((((GBP := 0) ';' (SBP := 7)) ';' (saveIC (SBP,RetIC))) ';' (goto 2)) ';' (halt SCMPDS)) ';' ((SBP,3) <=0_goto 9))) + 1) + 1) + 1) + 1 by Th4
.= ((((5 + 1) + 1) + 1) + 1) + 1 by A1, Th4
.= 10 ;
thus card GCD-Algorithm = (card ((((((((((((((GBP := 0) ';' (SBP := 7)) ';' (saveIC (SBP,RetIC))) ';' (goto 2)) ';' (halt SCMPDS)) ';' ((SBP,3) <=0_goto 9)) ';' ((SBP,6) := (SBP,3))) ';' (Divide (SBP,2,SBP,3))) ';' ((SBP,7) := (SBP,3))) ';' ((SBP,(4 + RetSP)) := (GBP,1))) ';' (AddTo (GBP,1,4))) ';' (saveIC (SBP,RetIC))) ';' (goto (- 7))) ';' ((SBP,2) := (SBP,6)))) + 1 by Th4
.= ((card (((((((((((((GBP := 0) ';' (SBP := 7)) ';' (saveIC (SBP,RetIC))) ';' (goto 2)) ';' (halt SCMPDS)) ';' ((SBP,3) <=0_goto 9)) ';' ((SBP,6) := (SBP,3))) ';' (Divide (SBP,2,SBP,3))) ';' ((SBP,7) := (SBP,3))) ';' ((SBP,(4 + RetSP)) := (GBP,1))) ';' (AddTo (GBP,1,4))) ';' (saveIC (SBP,RetIC))) ';' (goto (- 7)))) + 1) + 1 by Th4
.= (((card ((((((((((((GBP := 0) ';' (SBP := 7)) ';' (saveIC (SBP,RetIC))) ';' (goto 2)) ';' (halt SCMPDS)) ';' ((SBP,3) <=0_goto 9)) ';' ((SBP,6) := (SBP,3))) ';' (Divide (SBP,2,SBP,3))) ';' ((SBP,7) := (SBP,3))) ';' ((SBP,(4 + RetSP)) := (GBP,1))) ';' (AddTo (GBP,1,4))) ';' (saveIC (SBP,RetIC)))) + 1) + 1) + 1 by Th4
.= ((((card (((((((((((GBP := 0) ';' (SBP := 7)) ';' (saveIC (SBP,RetIC))) ';' (goto 2)) ';' (halt SCMPDS)) ';' ((SBP,3) <=0_goto 9)) ';' ((SBP,6) := (SBP,3))) ';' (Divide (SBP,2,SBP,3))) ';' ((SBP,7) := (SBP,3))) ';' ((SBP,(4 + RetSP)) := (GBP,1))) ';' (AddTo (GBP,1,4)))) + 1) + 1) + 1) + 1 by Th4
.= ((((10 + 1) + 1) + 1) + 1) + 1 by A2, Th4
.= 15 ; :: thesis: verum