set I = Load (<*> the Instructions of SCM+FSA );
take
Load (<*> the Instructions of SCM+FSA )
; Load (<*> the Instructions of SCM+FSA ) is pseudo-paraclosed
now let s be
State of
SCM+FSA ;
Load (<*> the Instructions of SCM+FSA ) is_pseudo-closed_on sA1:
card (Load (<*> the Instructions of SCM+FSA )) = 0
by CARD_1:47, SCMFSA_7:25;
A2:
for
n being
Element of
NAT st
n < 0 holds
IC (Comput (ProgramPart (s +* ((Load (<*> the Instructions of SCM+FSA )) +* (Start-At 0 ,SCM+FSA )))),(s +* ((Load (<*> the Instructions of SCM+FSA )) +* (Start-At 0 ,SCM+FSA ))),n) in dom (Load (<*> the Instructions of SCM+FSA ))
by NAT_1:2;
A3:
IC SCM+FSA in dom ((Load (<*> the Instructions of SCM+FSA )) +* (Start-At 0 ,SCM+FSA ))
by SF_MASTR:65;
IC (Comput (ProgramPart (s +* ((Load (<*> the Instructions of SCM+FSA )) +* (Start-At 0 ,SCM+FSA )))),(s +* ((Load (<*> the Instructions of SCM+FSA )) +* (Start-At 0 ,SCM+FSA ))),0 ) =
(s +* ((Load (<*> the Instructions of SCM+FSA )) +* (Start-At 0 ,SCM+FSA ))) . (IC SCM+FSA )
by AMI_1:13
.=
((Load (<*> the Instructions of SCM+FSA )) +* (Start-At 0 ,SCM+FSA )) . (IC SCM+FSA )
by A3, FUNCT_4:14
.=
card (Load (<*> the Instructions of SCM+FSA ))
by A1, SF_MASTR:66
.=
card (ProgramPart (Load (<*> the Instructions of SCM+FSA )))
by AMI_1:105
;
hence
Load (<*> the Instructions of SCM+FSA ) is_pseudo-closed_on s
by A2, Def3;
verum end;
hence
Load (<*> the Instructions of SCM+FSA ) is pseudo-paraclosed
by Def4; verum