let C1 be non empty AltGraph ; :: thesis: for C2, C3 being non empty reflexive AltGraph
for F being feasible FunctorStr over C1,C2
for G being FunctorStr over C2,C3 st F is one-to-one & G is one-to-one holds
G * F is one-to-one
let C2, C3 be non empty reflexive AltGraph ; :: thesis: for F being feasible FunctorStr over C1,C2
for G being FunctorStr over C2,C3 st F is one-to-one & G is one-to-one holds
G * F is one-to-one
let F be feasible FunctorStr over C1,C2; :: thesis: for G being FunctorStr over C2,C3 st F is one-to-one & G is one-to-one holds
G * F is one-to-one
let G be FunctorStr over C2,C3; :: thesis: ( F is one-to-one & G is one-to-one implies G * F is one-to-one )
assume ( F is one-to-one & G is one-to-one ) ; :: thesis: G * F is one-to-one
then A1: ( the ObjectMap of F is one-to-one & the ObjectMap of G is one-to-one ) ;
the ObjectMap of (G * F) = the ObjectMap of G * the ObjectMap of F by FUNCTOR0:def 36;
hence the ObjectMap of (G * F) is one-to-one by A1; :: according to FUNCTOR0:def 6 :: thesis: verum