reserve a,b,c,d for positive Real,
  m,u,w,x,y,z for Real,
  n,k for Nat,
  s,s1 for Real_Sequence;

theorem
  (b+c-a)/a+(c+a-b)/b+(a+b-c)/c>=3
proof
A1: b/a+c/b+a/c>=3 by Th20;
  a/b+b/c+c/a>=3 by Th20;
  then (a/b+b/c+c/a)+(b/a+c/b+a/c)>=3+3 by A1,XREAL_1:7;
  then
A2: (a/b+b/c+c/a+b/a+c/b+a/c)-3>=6-3 by XREAL_1:9;
  (b+c-a)/a+(c+a-b)/b+(a+b-c)/c =(b+c)/a-a/a+(c+a-b)/b+(a+b-c)/c by
XCMPLX_1:120
    .=(b+c)/a-1+(c+a-b)/b+(a+b-c)/c by XCMPLX_1:60
    .=(b+c)/a-1+((c+a)/b-b/b)+(a+b-c)/c by XCMPLX_1:120
    .=(b+c)/a-1+((c+a)/b-1)+(a+b-c)/c by XCMPLX_1:60
    .=(b+c)/a-1+(c+a)/b-1+((a+b)/c-c/c) by XCMPLX_1:120
    .=(b+c)/a-1+(c+a)/b-1+((a+b)/c-1) by XCMPLX_1:60
    .=(b+c)/a+(c+a)/b+(a+b)/c-3
    .=b/a+c/a+(c+a)/b+(a+b)/c-3 by XCMPLX_1:62
    .=b/a+c/a+(c/b+a/b)+(a+b)/c-3 by XCMPLX_1:62
    .=b/a+c/a+(c/b+a/b)+(a/c+b/c)-3 by XCMPLX_1:62
    .=a/b+b/c+c/a+b/a+c/b+a/c-3;
  hence thesis by A2;
end;
