let k be natural number ; :: thesis: JUMP (goto k) = {k}
set X = { (NIC (goto k),il) where il is Instruction-Location of SCM : verum } ;

now

let x be set ; :: thesis: ( ( x in meet { (NIC (goto k),il) where il is Instruction-Location of SCM : verum } implies x in {k} ) & ( x in {k} implies x in meet { (NIC (goto k),il) where il is Instruction-Location of SCM : verum } ) )

hereby :: thesis: ( x in {k} implies x in meet { (NIC (goto k),il) where il is Instruction-Location of SCM : verum } )

set il1 = il. 1;
A1: NIC (goto k),(il. 1) in { (NIC (goto k),il) where il is Instruction-Location of SCM : verum } ;
assume x in meet { (NIC (goto k),il) where il is Instruction-Location of SCM : verum } ; :: thesis: x in {k}
then x in NIC (goto k),(il. 1) by A1, SETFAM_1:def 1;
hence x in {k} by Th46; :: thesis: verum

end;

assume x in {k} ; :: thesis: x in meet { (NIC (goto k),il) where il is Instruction-Location of SCM : verum }
then A2: x = k by TARSKI:def 1;

A3: now

let Y be set ; :: thesis: ( Y in { (NIC (goto k),il) where il is Instruction-Location of SCM : verum } implies k in Y )
assume Y in { (NIC (goto k),il) where il is Instruction-Location of SCM : verum } ; :: thesis: k in Y
then consider il being Instruction-Location of SCM such that
A4: Y = NIC (goto k),il ;
NIC (goto k),il = {k} by Th46;
hence k in Y by A4, TARSKI:def 1; :: thesis: verum

end;

k in NAT by ORDINAL1:def 13;
then reconsider k = k as Instruction-Location of SCM by AMI_1:def 4;
NIC (goto k),k in { (NIC (goto k),il) where il is Instruction-Location of SCM : verum } ;
hence x in meet { (NIC (goto k),il) where il is Instruction-Location of SCM : verum } by A2, A3, SETFAM_1:def 1; :: thesis: verum

end;

hence JUMP (goto k) = {k} by TARSKI:2; :: thesis: verum