Section set_lambda_fun1_def.
Variable c : C.
Definition S_lambda_fun2 (a : A) := f (Build_Sprod c a).
Definition S_lambda_fun1 := Build_Map S_lambda_map_law2.
End set_lambda_fun1_def.
Definition S_lambda1_fun := Build_Map S_lambda_map_law1.
End set_lambda_fun_def.

Lemma S_lambda_map_law : Map_law S_lambda1_fun.