let C1 be non empty AltGraph ; :: thesis: for C2, C3 being non empty reflexive AltGraph
for F being feasible FunctorStr of C1,C2
for G being FunctorStr of 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 of C1,C2
for G being FunctorStr of 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 of C1,C2; :: thesis: for G being FunctorStr of C2,C3 st F is one-to-one & G is one-to-one holds
G * F is one-to-one
let G be FunctorStr of C2,C3; :: thesis: ( F is one-to-one & G is one-to-one implies G * F is one-to-one )
assume A1: ( F is one-to-one & G is one-to-one ) ; :: thesis: G * F is one-to-one
then A2: the ObjectMap of F is one-to-one by FUNCTOR0:def 7;
A3: the ObjectMap of G is one-to-one by A1, FUNCTOR0:def 7;
the ObjectMap of (G * F) = the ObjectMap of G * the ObjectMap of F by FUNCTOR0:def 37;
hence the ObjectMap of (G * F) is one-to-one by A2, A3; :: according to FUNCTOR0:def 7 :: thesis: verum