
theorem Th3:
  for X be set for p be FinSequence of bool X for q be FinSequence
of BOOLEAN for i be Nat st i in dom p & q.i = FALSE holds MergeSequence(p,q).i
  = X\p.i
proof
  let X be set;
  let p be FinSequence of bool X;
  let q be FinSequence of BOOLEAN;
  let i be Nat;
  assume that
A1: i in dom p and
A2: q.i = FALSE;
  thus MergeSequence(p,q).i = IFEQ(q.i,TRUE,p.i,X\p.i) by A1,Def1
    .= X\p.i by A2,FUNCOP_1:def 8;
end;
