let i be natural Number ; :: thesis: for R, R1, R2 being Element of i -tuples_on REAL st R1 + R = R2 + R holds
R1 = R2
let R, R1, R2 be Element of i -tuples_on REAL; :: thesis: ( R1 + R = R2 + R implies R1 = R2 )
assume R1 + R = R2 + R ; :: thesis: R1 = R2
then R1 + (R + (- R)) = (R2 + R) + (- R) by FINSEQOP:28;
then A1: R1 + (R + (- R)) = R2 + (R + (- R)) by FINSEQOP:28;
R + (- R) = i |-> 0 by Th8, Th9, BINOP_2:2, FINSEQOP:73;
then R1 = R2 + (i |-> 0) by A1, BINOP_2:2, FINSEQOP:56;
hence R1 = R2 by BINOP_2:2, FINSEQOP:56; :: thesis: verum