let R be good Ring; :: thesis: for i1 being Instruction-Location of SCM R holds JUMP (goto i1) = {i1}
let i1 be Instruction-Location of SCM R; :: thesis: JUMP (goto i1) = {i1}
set X = { (NIC (goto i1),il) where il is Instruction-Location of SCM R : verum } ;

now

let x be set ; :: thesis: ( ( x in meet { (NIC (goto i1),il) where il is Instruction-Location of SCM R : verum } implies x in {i1} ) & ( x in {i1} implies x in meet { (NIC (goto i1),il) where il is Instruction-Location of SCM R : verum } ) )

hereby :: thesis: ( x in {i1} implies x in meet { (NIC (goto i1),il) where il is Instruction-Location of SCM R : verum } )

assume A1: x in meet { (NIC (goto i1),il) where il is Instruction-Location of SCM R : verum } ; :: thesis: x in {i1}
reconsider il1 = il. 1 as Instruction-Location of SCM R by AMI_1:def 4;
NIC (goto i1),il1 in { (NIC (goto i1),il) where il is Instruction-Location of SCM R : verum } ;
then x in NIC (goto i1),il1 by A1, SETFAM_1:def 1;
hence x in {i1} by Th59; :: thesis: verum

end;

assume x in {i1} ; :: thesis: x in meet { (NIC (goto i1),il) where il is Instruction-Location of SCM R : verum }
then A2: x = i1 by TARSKI:def 1;
A3: NIC (goto i1),i1 in { (NIC (goto i1),il) where il is Instruction-Location of SCM R : verum } ;

now

let Y be set ; :: thesis: ( Y in { (NIC (goto i1),il) where il is Instruction-Location of SCM R : verum } implies i1 in Y )
assume Y in { (NIC (goto i1),il) where il is Instruction-Location of SCM R : verum } ; :: thesis: i1 in Y
then consider il being Instruction-Location of SCM R such that
A4: Y = NIC (goto i1),il ;
NIC (goto i1),il = {i1} by Th59;
hence i1 in Y by A4, TARSKI:def 1; :: thesis: verum

end;

hence x in meet { (NIC (goto i1),il) where il is Instruction-Location of SCM R : verum } by A2, A3, SETFAM_1:def 1; :: thesis: verum

end;

hence JUMP (goto i1) = {i1} by TARSKI:2; :: thesis: verum