reserve x,y,z for set;

theorem Th37:
  for S being non void non empty ManySortedSign for A being
  MSAlgebra over S for B being MSSubAlgebra of A for o being OperSymbol of S
  holds Args(o,B) c= Args(o,A)
proof
  let S be non void non empty ManySortedSign;
  let A be MSAlgebra over S;
  let B be MSSubAlgebra of A;
  reconsider SB = the Sorts of B as MSSubset of A by MSUALG_2:def 9;
  let o be OperSymbol of S;
  reconsider SA = the Sorts of A as MSSubset of A by PBOOLE:def 18;
A1: Args(o,B) = (SB# * the Arity of S).o by MSUALG_1:def 4;
  SB c= SA & Args(o,A) = (SA# * the Arity of S).o by MSUALG_1:def 4
,PBOOLE:def 18;
  hence thesis by A1,MSUALG_2:2;
end;
