reserve i,n for Nat;
reserve m for non zero Nat;
reserve p,q for Tuple of n, BOOLEAN;
reserve d,d1,d2 for Element of BOOLEAN;

theorem Th5:
  for i st i in Seg n & i = 1 holds (Bin1(n))/.i = TRUE
proof
  let i be Nat such that
A1: i in Seg n and
A2: i = 1;
  thus (Bin1(n))/.i = IFEQ(i,1,TRUE,FALSE) by A1,Def1
    .= TRUE by A2,FUNCOP_1:def 8;
end;
