reserve n,i,j,k,l for Nat;
reserve D for non empty set;
reserve c,d for Element of D;
reserve p,q,q9,r for FinSequence of D;
reserve RAS for MidSp-like non empty ReperAlgebraStr over n+2;
reserve a,b,d,pii,p9i for Point of RAS;
reserve p,q for Tuple of (n+1),RAS;
reserve m for Nat of n;
reserve W for ATLAS of RAS;
reserve v for Vector of W;
reserve x,y for Tuple of (n+1),W;
reserve RAS for ReperAlgebra of n;
reserve a,b,pm,p9m,p99m for Point of RAS;
reserve p for Tuple of (n+1),RAS;
reserve W for ATLAS of RAS;
reserve v for Vector of W;
reserve x for Tuple of (n+1),W;

theorem Th29:
  RAS has_property_of_zero_in m & RAS is_additive_in m implies RAS
  is_semi_additive_in m
proof
  assume that
A1: RAS has_property_of_zero_in m and
A2: RAS is_additive_in m;
  let a,pm,p;
  assume p.m = pm;
  then *'(a,(p+*(m,a@pm))) = *'(a,p)@*'(a,(p+*(m,a))) by A2
    .= a@*'(a,p) by A1;
  hence thesis;
end;
