let R be Ring; :: thesis: for T being InsType of the InstructionsF of (SCM R) st T = 4 holds

JumpParts T = {{}}

let T be InsType of the InstructionsF of (SCM R); :: thesis: ( T = 4 implies JumpParts T = {{}} )

assume A1: T = 4 ; :: thesis: JumpParts T = {{}}

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

assume x in {{}} ; :: thesis: x in JumpParts T

then x = {} by TARSKI:def 1;

then A5: x = JumpPart (MultBy ( the Data-Location of R, the Data-Location of R)) ;

InsCode (MultBy ( the Data-Location of R, the Data-Location of R)) = 4 ;

hence x in JumpParts T by A5, A1; :: thesis: verum

JumpParts T = {{}}

let T be InsType of the InstructionsF of (SCM R); :: thesis: ( T = 4 implies JumpParts T = {{}} )

assume A1: T = 4 ; :: thesis: JumpParts T = {{}}

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

set a = the Data-Location of R;let x be object ; :: thesis: ( x in JumpParts T implies x in {{}} )

assume x in JumpParts T ; :: thesis: x in {{}}

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

A2: x = JumpPart I and

A3: InsCode I = T ;

consider a, b being Data-Location of R such that

A4: I = MultBy (a,b) by A1, A3, Th15;

x = {} by A2, A4;

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

end;assume x in JumpParts T ; :: thesis: x in {{}}

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

A2: x = JumpPart I and

A3: InsCode I = T ;

consider a, b being Data-Location of R such that

A4: I = MultBy (a,b) by A1, A3, Th15;

x = {} by A2, A4;

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

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

assume x in {{}} ; :: thesis: x in JumpParts T

then x = {} by TARSKI:def 1;

then A5: x = JumpPart (MultBy ( the Data-Location of R, the Data-Location of R)) ;

InsCode (MultBy ( the Data-Location of R, the Data-Location of R)) = 4 ;

hence x in JumpParts T by A5, A1; :: thesis: verum