Update De_Rham_Cohomology_of_smooth_manifolds.cpp

De_Rham_Cohomology_of_smooth_manifolds.cpp

@@ -45,5 +45,22 @@ int main (/* implementation-defined */)
     auto chart = let_M_be_a_manifold_of_dimension_n. And (U_is_element_of_M).
                  And (a_pair_U_psi_where_U_is_open). And (psi_maps_U_to_V_a_homeomorphism_to_some_open_V);
 
+    Suppose_literal (the_pair_U_phi_is_a_chart_M, chart. Value(/* truth value */));
+
+    // like the supposed literal a_topological_space_M, you may introduce a function for each literal below
+    Suppose_literal (p_is_element_of_the_pair_U_phi, true);
+    Suppose_literal (p_is_element_of_U, true);
+    Suppose_literal (for_all_p_for_some_chart, true);
+
+    auto remark_2_1 = the_pair_U_phi_is_a_chart_M. And (p_is_element_of_U).
+                           Implying (p_is_element_of_the_pair_U_phi);
+
+    auto third_condition_from_definition_2_1 = for_all_p_there_is_an_open_neighbourhood_U.
+                                               And (U_is_element_of_M). And (U_is_homeomorphic_to_an_open_subset_V).
+                                               And (V_is_subset_of_real_coordinate_space_of_dimension_n);
+
+    auto rewrite_third_condition_from_definition_2_1 = for_all_p_for_some_chart.
+                                                       Implying (third_condition_from_definition_2_1);
+                                                       
     return 0;
 }