let S be non empty non void ManySortedSign ; :: thesis: for A being non-empty MSAlgebra of S
for h being Endomorphism of A
for s1, s2 being SortSymbol of S st TranslationRel S reduces s1,s2 holds
for t being Translation of A,s1,s2 ex T being Translation of A,s1,s2 st T * (h . s1) = (h . s2) * t
let A be non-empty MSAlgebra of S; :: thesis: for h being Endomorphism of A
for s1, s2 being SortSymbol of S st TranslationRel S reduces s1,s2 holds
for t being Translation of A,s1,s2 ex T being Translation of A,s1,s2 st T * (h . s1) = (h . s2) * t
let h be Endomorphism of A; :: thesis: for s1, s2 being SortSymbol of S st TranslationRel S reduces s1,s2 holds
for t being Translation of A,s1,s2 ex T being Translation of A,s1,s2 st T * (h . s1) = (h . s2) * t
h is_homomorphism A,A by Def2;
hence for s1, s2 being SortSymbol of S st TranslationRel S reduces s1,s2 holds
for t being Translation of A,s1,s2 ex T being Translation of A,s1,s2 st T * (h . s1) = (h . s2) * t by Th25; :: thesis: verum