let R be Ring; :: thesis: for T being InsType of the InstructionsF of (SCM R) st T = 0 holds

JumpParts T = {0}

let T be InsType of the InstructionsF of (SCM R); :: thesis: ( T = 0 implies JumpParts T = {0} )

assume A1: T = 0 ; :: thesis: JumpParts T = {0}

assume a in {0} ; :: thesis: a in JumpParts T

then A4: a = 0 by TARSKI:def 1;

( InsCode (halt (SCM R)) = 0 & JumpPart (halt (SCM R)) = 0 ) ;

hence a in JumpParts T by A1, A4; :: thesis: verum

JumpParts T = {0}

let T be InsType of the InstructionsF of (SCM R); :: thesis: ( T = 0 implies JumpParts T = {0} )

assume A1: T = 0 ; :: thesis: JumpParts T = {0}

hereby :: according to TARSKI:def 3,XBOOLE_0:def 10 :: thesis: {0} c= JumpParts T

let a be object ; :: according to TARSKI:def 3 :: thesis: ( not a in {0} or a in JumpParts T )let a be object ; :: thesis: ( a in JumpParts T implies a in {0} )

assume a in JumpParts T ; :: thesis: a in {0}

then consider I being Instruction of (SCM R) such that

A2: a = JumpPart I and

A3: InsCode I = T ;

I = halt (SCM R) by A1, A3, Th11;

then a = {} by A2;

hence a in {0} by TARSKI:def 1; :: thesis: verum

end;assume a in JumpParts T ; :: thesis: a in {0}

then consider I being Instruction of (SCM R) such that

A2: a = JumpPart I and

A3: InsCode I = T ;

I = halt (SCM R) by A1, A3, Th11;

then a = {} by A2;

hence a in {0} by TARSKI:def 1; :: thesis: verum

assume a in {0} ; :: thesis: a in JumpParts T

then A4: a = 0 by TARSKI:def 1;

( InsCode (halt (SCM R)) = 0 & JumpPart (halt (SCM R)) = 0 ) ;

hence a in JumpParts T by A1, A4; :: thesis: verum