let T be InsType of the InstructionsF of SCM; :: thesis: ( T = 6 implies dom () = {1} )
set i1 = the Element of NAT ;
assume A1: T = 6 ; :: thesis: dom () = {1}
hereby :: according to TARSKI:def 3,XBOOLE_0:def 10 :: thesis: {1} c= dom ()
let x be object ; :: thesis: ( x in dom () implies x in {1} )
InsCode (SCM-goto the Element of NAT ) = 6 ;
then A2: JumpPart (SCM-goto the Element of NAT ) in JumpParts T by A1;
assume x in dom () ; :: thesis: x in {1}
then x in DOM () by CARD_3:def 12;
then x in dom (JumpPart (SCM-goto the Element of NAT )) by ;
hence x in {1} by ; :: thesis: verum
end;
let x be object ; :: according to TARSKI:def 3 :: thesis: ( not x in {1} or x in dom () )
assume A3: x in {1} ; :: thesis: x in dom ()
for f being Function st f in JumpParts T holds
x in dom f
proof
let f be Function; :: thesis: ( f in JumpParts T implies x in dom f )
assume f in JumpParts T ; :: thesis: x in dom f
then consider I being Instruction of SCM such that
A4: f = JumpPart I and
A5: InsCode I = T ;
consider i1 being Nat such that
A6: I = SCM-goto i1 by ;
f = <*i1*> by A4, A6;
hence x in dom f by ; :: thesis: verum
end;
then x in DOM () by CARD_3:109;
hence x in dom () by CARD_3:def 12; :: thesis: verum