let A, B be non empty transitive with_units AltCatStr ; :: thesis: for F1, F2 being covariant Functor of A,B st F1 is_naturally_transformable_to F2 holds
for t being natural_transformation of F1,F2 holds
( (idt F2) `*` t = t & t `*` (idt F1) = t )
let F1, F2 be covariant Functor of A,B; :: thesis: ( F1 is_naturally_transformable_to F2 implies for t being natural_transformation of F1,F2 holds
( (idt F2) `*` t = t & t `*` (idt F1) = t ) )
assume F1 is_naturally_transformable_to F2 ; :: thesis: for t being natural_transformation of F1,F2 holds
( (idt F2) `*` t = t & t `*` (idt F1) = t )
then A1: F1 is_transformable_to F2 by Def6;
let t be natural_transformation of F1,F2; :: thesis: ( (idt F2) `*` t = t & t `*` (idt F1) = t )
thus (idt F2) `*` t = t by A1, Th7; :: thesis: t `*` (idt F1) = t
thus t `*` (idt F1) = t by A1, Th7; :: thesis: verum