reserve x for set;
reserve a, b, c for Real;
reserve m, n, m1, m2 for Nat;
reserve k, l for Integer;
reserve p, q for Rational;
reserve s1, s2 for Real_Sequence;

theorem Th79:
  a>0 implies (1/a) #R c = 1 / a #R c
proof
  assume
A1: a>0;
  1 = 1 #R c by Th73
    .= ((1/a)*a) #R c by A1,XCMPLX_1:106
    .= (1/a) #R c * a #R c by A1,Th78;
  then 1 / a #R c = (1/a) #R c * (a #R c / a #R c) by XCMPLX_1:74
    .= (1/a) #R c * 1 by A1,Lm9,XCMPLX_1:60;
  hence thesis;
end;
