let i be Nat; :: thesis: for K being non empty right_complementable Abelian add-associative right_zeroed addLoopStr
for R, R1 being Element of i -tuples_on the carrier of K holds R1 = (R1 + R) - R
let K be non empty right_complementable Abelian add-associative right_zeroed addLoopStr ; :: thesis: for R, R1 being Element of i -tuples_on the carrier of K holds R1 = (R1 + R) - R
let R, R1 be Element of i -tuples_on the carrier of K; :: thesis: R1 = (R1 + R) - R
thus R1 = R1 + (i |-> (0. K)) by Lm2
.= R1 + (R - R) by Th41
.= (R1 + R) - R by Th44 ; :: thesis: verum