let S be locally_directed OrderSortedSign; :: thesis: for U1, U2 being non-empty OSAlgebra of S
for F being ManySortedFunction of U1,U2 st F is_epimorphism U1,U2 & F is order-sorted holds
QuotOSAlg (U1,(OSCng F)),U2 are_isomorphic
let U1, U2 be non-empty OSAlgebra of S; :: thesis: for F being ManySortedFunction of U1,U2 st F is_epimorphism U1,U2 & F is order-sorted holds
QuotOSAlg (U1,(OSCng F)),U2 are_isomorphic
let F be ManySortedFunction of U1,U2; :: thesis: ( F is_epimorphism U1,U2 & F is order-sorted implies QuotOSAlg (U1,(OSCng F)),U2 are_isomorphic )
assume ( F is_epimorphism U1,U2 & F is order-sorted ) ; :: thesis: QuotOSAlg (U1,(OSCng F)),U2 are_isomorphic
then OSHomQuot F is_isomorphism QuotOSAlg (U1,(OSCng F)),U2 by Th18;
hence QuotOSAlg (U1,(OSCng F)),U2 are_isomorphic ; :: thesis: verum