let R be good Ring; :: thesis: for a being Data-Location of R
for i1 being Instruction-Location of SCM R holds JUMP (a =0_goto i1) = {i1}
let a be Data-Location of R; :: thesis: for i1 being Instruction-Location of SCM R holds JUMP (a =0_goto i1) = {i1}
let i1 be Instruction-Location of SCM R; :: thesis: JUMP (a =0_goto i1) = {i1}
set X = { (NIC (a =0_goto i1),il) where il is Instruction-Location of SCM R : verum } ;

now

let x be set ; :: thesis: ( ( x in meet { (NIC (a =0_goto i1),il) where il is Instruction-Location of SCM R : verum } implies x in {i1} ) & ( x in {i1} implies x in meet { (NIC (a =0_goto i1),il) where il is Instruction-Location of SCM R : verum } ) )

hereby :: thesis: ( x in {i1} implies x in meet { (NIC (a =0_goto i1),il) where il is Instruction-Location of SCM R : verum } )

assume A1: x in meet { (NIC (a =0_goto i1),il) where il is Instruction-Location of SCM R : verum } ; :: thesis: x in {i1}
reconsider il1 = il. 1, il2 = il. 2 as Instruction-Location of SCM R by AMI_1:def 4;
( NIC (a =0_goto i1),il1 in { (NIC (a =0_goto i1),il) where il is Instruction-Location of SCM R : verum } & NIC (a =0_goto i1),il2 in { (NIC (a =0_goto i1),il) where il is Instruction-Location of SCM R : verum } ) ;
then A2: ( x in NIC (a =0_goto i1),il1 & x in NIC (a =0_goto i1),il2 ) by A1, SETFAM_1:def 1;
( NIC (a =0_goto i1),il1 c= {i1,(Next il1)} & NIC (a =0_goto i1),il2 c= {i1,(Next il2)} ) by Th61;
then A3: ( ( x = i1 or x = Next il1 ) & ( x = i1 or x = Next il2 ) ) by A2, TARSKI:def 2;
thus x in {i1} by A3, TARSKI:def 1; :: thesis: verum

end;

assume x in {i1} ; :: thesis: x in meet { (NIC (a =0_goto i1),il) where il is Instruction-Location of SCM R : verum }
then A4: x = i1 by TARSKI:def 1;
A5: NIC (a =0_goto i1),i1 in { (NIC (a =0_goto i1),il) where il is Instruction-Location of SCM R : verum } ;

now

let Y be set ; :: thesis: ( Y in { (NIC (a =0_goto i1),il) where il is Instruction-Location of SCM R : verum } implies i1 in Y )
assume Y in { (NIC (a =0_goto i1),il) where il is Instruction-Location of SCM R : verum } ; :: thesis: i1 in Y
then ex il being Instruction-Location of SCM R st Y = NIC (a =0_goto i1),il ;
hence i1 in Y by Th61; :: thesis: verum

end;

hence x in meet { (NIC (a =0_goto i1),il) where il is Instruction-Location of SCM R : verum } by A4, A5, SETFAM_1:def 1; :: thesis: verum

end;

hence JUMP (a =0_goto i1) = {i1} by TARSKI:2; :: thesis: verum