reserve S for non empty non void ManySortedSign;
reserve X for non-empty ManySortedSet of S;
reserve x,y,z for set, i,j for Nat;

theorem Th25:
  for A1,A2 being MSAlgebra over S
  st the MSAlgebra of A1 = the MSAlgebra of A2
  for B1 being MSSubset of A1, B2 being MSSubset of A2 st B1 = B2
  for o being OperSymbol of S st B1 is_closed_on o holds o/.B2 = o/.B1
  proof
    let A1,A2 be MSAlgebra over S;
    assume A1: the MSAlgebra of A1 = the MSAlgebra of A2;
    let B1 be MSSubset of A1;
    let B2 be MSSubset of A2;
    assume A2: B1 = B2;
    let o be OperSymbol of S;
    assume A3: B1 is_closed_on o;
    hence o/.B2 = (Den(o,A2)) | ((B2# * the Arity of S).o)
    by A1,A2,Th24,MSUALG_2:def 7
    .= (Den(o,A1)) | ((B1# * the Arity of S).o) by A1,A2
    .= o/.B1 by A3,MSUALG_2:def 7;
  end;
