let T be InsType of SCM+FSA-Instr; ( ( T = 9 or T = 10 ) implies JumpParts T = {{}} )
assume A1:
( T = 9 or T = 10 )
; JumpParts T = {{}}
hereby TARSKI:def 3,
XBOOLE_0:def 10 {{}} c= JumpParts T
let x be
set ;
( x in JumpParts T implies x in {{}} )assume
x in JumpParts T
;
x in {{}}then consider I being
Element of
SCM+FSA-Instr such that A2:
x = JumpPart I
and A3:
InsCode I = T
;
I in { [J,{},<*c,f,b*>] where J is Element of Segm 13, c, b is Element of SCM-Data-Loc , f is Element of SCM+FSA-Data*-Loc : J in {9,10} }
by A1, A3, Th7;
then consider J being
Element of
Segm 13,
c,
b being
Element of
SCM-Data-Loc ,
f being
Element of
SCM+FSA-Data*-Loc such that A4:
(
I = [J,{},<*c,f,b*>] &
J in {9,10} )
;
x = {}
by A2, A4, RECDEF_2:def 2;
hence
x in {{}}
by TARSKI:def 1;
verum
end;
set a = the Element of SCM-Data-Loc ;
set f = the Element of SCM+FSA-Data*-Loc ;
let x be set ; TARSKI:def 3 ( not x in {{}} or x in JumpParts T )
T in {9,10}
by A1, TARSKI:def 2;
then A5:
[T,{},<* the Element of SCM-Data-Loc , the Element of SCM+FSA-Data*-Loc , the Element of SCM-Data-Loc *>] in SCM+FSA-Instr
by Th4;
assume
x in {{}}
; x in JumpParts T
then
x = {}
by TARSKI:def 1;
then A6:
x = JumpPart [T,{},<* the Element of SCM-Data-Loc , the Element of SCM+FSA-Data*-Loc , the Element of SCM-Data-Loc *>]
;
InsCode [T,{},<* the Element of SCM-Data-Loc , the Element of SCM+FSA-Data*-Loc , the Element of SCM-Data-Loc *>] = T
;
hence
x in JumpParts T
by A6, A5; verum