let i be Nat; :: thesis: for K being non empty right_complementable Abelian add-associative right_zeroed addLoopStr
for R1, R2, R3 being Element of i -tuples_on the carrier of K holds R1 - (R2 - R3) = (R1 - R2) + R3
let K be non empty right_complementable Abelian add-associative right_zeroed addLoopStr ; :: thesis: for R1, R2, R3 being Element of i -tuples_on the carrier of K holds R1 - (R2 - R3) = (R1 - R2) + R3
let R1, R2, R3 be Element of i -tuples_on the carrier of K; :: thesis: R1 - (R2 - R3) = (R1 - R2) + R3
thus R1 - (R2 - R3) = R1 + (- (R2 - R3)) by FINSEQOP:84
.= R1 + ((- R2) + R3) by Th40
.= (R1 + (- R2)) + R3 by FINSEQOP:28
.= (R1 - R2) + R3 by FINSEQOP:84 ; :: thesis: verum