
theorem Th20:
  for F being finite set,
      A being FinSequence of bool F, i being Element of NAT,
      x being set st i in dom A holds Cut (A,i,x) is Reduction of A,i
proof
  let F be finite set, A be FinSequence of bool F,
      i be Element of NAT, x be set;
  set f = Cut (A,i,x);
A1: dom f = dom A by Def2;
  then
A2: for j being Element of NAT st j in dom A & j <> i holds A.j = f.j by Def2;
  assume i in dom A;
  then f.i = A.i \ {x} by A1,Def2;
  hence thesis by A1,A2,Def5;
end;
