reserve i,j,k for Nat;
reserve K for non empty addLoopStr,
  a for Element of K,
  p for FinSequence of the carrier of K,
  R for Element of i-tuples_on the carrier of K;
reserve K for left_zeroed right_zeroed add-associative right_complementable
  non empty addLoopStr,
  R,R1,R2 for Element of i-tuples_on the carrier of K;
reserve K for non empty addLoopStr,
  a1,a2 for Element of K,
  p1,p2 for FinSequence of the carrier of K,
  R1,R2 for Element of i-tuples_on the carrier of K;
reserve K for Abelian right_zeroed add-associative right_complementable non
  empty addLoopStr,
  R,R1,R2,R3 for Element of i-tuples_on the carrier of K;
reserve K for non empty multMagma,
  a,a9,a1,a2 for Element of K,
  p for FinSequence of the carrier of K,
  R for Element of i-tuples_on the carrier of K;

theorem Th53:
  a1*(i|->a2) = i|->(a1*a2)
proof
  thus a1*(i|->a2) = i|->(((the multF of K)[;](a1,id the carrier of K)).a2) by
FINSEQOP:16
    .= i|->(a1*a2) by Th48;
end;
