begin
begin
definition
let S be non
empty non
void ManySortedSign ;
let MSA be
non-empty MSAlgebra over
S;
existence
ex b1 being ManySortedFunction of (FreeEnv MSA),MSA st
( b1 is_homomorphism FreeEnv MSA,MSA & ( for s being SortSymbol of S
for x, y being set st y in FreeSort ( the Sorts of MSA,s) & y = root-tree [x,s] & x in the Sorts of MSA . s holds
(b1 . s) . y = x ) )
uniqueness
for b1, b2 being ManySortedFunction of (FreeEnv MSA),MSA st b1 is_homomorphism FreeEnv MSA,MSA & ( for s being SortSymbol of S
for x, y being set st y in FreeSort ( the Sorts of MSA,s) & y = root-tree [x,s] & x in the Sorts of MSA . s holds
(b1 . s) . y = x ) & b2 is_homomorphism FreeEnv MSA,MSA & ( for s being SortSymbol of S
for x, y being set st y in FreeSort ( the Sorts of MSA,s) & y = root-tree [x,s] & x in the Sorts of MSA . s holds
(b2 . s) . y = x ) holds
b1 = b2
end;
:: Many Sorted Signatures
::---------------------------------------------------------------------------