let N be with_zero set ; :: thesis: for S being non empty with_non-empty_values IC-Ins-separated halting with_explicit_jumps AMI-Struct over N

for I being Instruction of S st I is ins-loc-free holds

JUMP I is empty

let S be non empty with_non-empty_values IC-Ins-separated halting with_explicit_jumps AMI-Struct over N; :: thesis: for I being Instruction of S st I is ins-loc-free holds

JUMP I is empty

let I be Instruction of S; :: thesis: ( I is ins-loc-free implies JUMP I is empty )

assume A1: JumpPart I is empty ; :: according to COMPOS_0:def 8 :: thesis: JUMP I is empty

A2: rng (JumpPart I) = {} by A1;

JUMP I c= rng (JumpPart I) by Def1;

hence JUMP I is empty by A2; :: thesis: verum

for I being Instruction of S st I is ins-loc-free holds

JUMP I is empty

let S be non empty with_non-empty_values IC-Ins-separated halting with_explicit_jumps AMI-Struct over N; :: thesis: for I being Instruction of S st I is ins-loc-free holds

JUMP I is empty

let I be Instruction of S; :: thesis: ( I is ins-loc-free implies JUMP I is empty )

assume A1: JumpPart I is empty ; :: according to COMPOS_0:def 8 :: thesis: JUMP I is empty

A2: rng (JumpPart I) = {} by A1;

JUMP I c= rng (JumpPart I) by Def1;

hence JUMP I is empty by A2; :: thesis: verum