let S be non empty non void ManySortedSign ; :: thesis: for U1, U2 being non-empty MSAlgebra over S
for F being ManySortedFunction of U1,U2 st F is_epimorphism U1,U2 holds
QuotMSAlg (U1,(MSCng F)),U2 are_isomorphic
let U1, U2 be non-empty MSAlgebra over S; :: thesis: for F being ManySortedFunction of U1,U2 st F is_epimorphism U1,U2 holds
QuotMSAlg (U1,(MSCng F)),U2 are_isomorphic
let F be ManySortedFunction of U1,U2; :: thesis: ( F is_epimorphism U1,U2 implies QuotMSAlg (U1,(MSCng F)),U2 are_isomorphic )
assume F is_epimorphism U1,U2 ; :: thesis: QuotMSAlg (U1,(MSCng F)),U2 are_isomorphic
then MSHomQuot F is_isomorphism QuotMSAlg (U1,(MSCng F)),U2 by Th5;
hence QuotMSAlg (U1,(MSCng F)),U2 are_isomorphic ; :: thesis: verum