let T be InsType of SCM-Instr; ( not not T = 1 & ... & not T = 5 implies JumpParts T = {{}} )
assume A1:
not not T = 1 & ... & not T = 5
; JumpParts T = {{}}
hereby TARSKI:def 3,
XBOOLE_0:def 10 {{}} c= JumpParts T
let x be
object ;
( x in JumpParts T implies x in {{}} )assume
x in JumpParts T
;
x in {{}}then consider I being
Element of
SCM-Instr such that A2:
x = JumpPart I
and A3:
InsCode I = T
;
I in { [J,{},<*b,c*>] where J is Element of Segm 9, b, c is Element of SCM-Data-Loc : J in {1,2,3,4,5} }
by A1, A3, Th9;
then consider J being
Element of
Segm 9,
b,
c being
Element of
SCM-Data-Loc such that A4:
I = [J,{},<*b,c*>]
and
J in {1,2,3,4,5}
;
x = {}
by A2, A4;
hence
x in {{}}
by TARSKI:def 1;
verum
end;
set a = the Element of SCM-Data-Loc ;
let x be object ; TARSKI:def 3 ( not x in {{}} or x in JumpParts T )
assume
x in {{}}
; x in JumpParts T
then A5:
x = {}
by TARSKI:def 1;
A6:
JumpPart [T,{},<* the Element of SCM-Data-Loc , the Element of SCM-Data-Loc *>] = {}
;
A7:
InsCode [T,{},<* the Element of SCM-Data-Loc , the Element of SCM-Data-Loc *>] = T
;
T in {1,2,3,4,5}
by A1, ENUMSET1:def 3;
then
[T,{},<* the Element of SCM-Data-Loc , the Element of SCM-Data-Loc *>] in SCM-Instr
by Th4;
hence
x in JumpParts T
by A5, A6, A7; verum