theorem Th12: :: MSUALG_5:12

for S being non empty non void ManySortedSign
for A being non-empty MSAlgebra over S
for o being OperSymbol of S
for C1, C2 being MSCongruence of A
for x1, y1 being set
for a1, b1 being FinSequence st [x1,y1] in (C1 . ((the_arity_of o) /. ((len a1) + 1))) \/ (C2 . ((the_arity_of o) /. ((len a1) + 1))) holds
for x, y being Element of Args (o,A) st x = (a1 ^ <*x1*>) ^ b1 & y = (a1 ^ <*y1*>) ^ b1 holds
[((Den (o,A)) . x),((Den (o,A)) . y)] in (C1 . (the_result_sort_of o)) \/ (C2 . (the_result_sort_of o))