Update De_Rham_Cohomology_of_smooth_manifolds.cpp

De_Rham_Cohomology_of_smooth_manifolds.cpp

@@ -1,45 +1,45 @@
-#include <satisfier>
-#include <string>
-
-bool is_topological_space(const std::string& M)
-{
-    bool is_topological_space = false;
-
-    // use M string to compute is_topological_space
-
-    return is_topological_space;
-}
-
-int main()
-{
-    // supposed A_topological_space_M, topological_space function
-    Suppose_literal (A_topological_space_M, is_topological_space("M string"));
-
-    // like above, you may create a function for each literal below
-    Suppose_literal (M_is_Hausdorff, true);
-    Suppose_literal (Points_can_be_seperated_by_open_sets, true);
-    Suppose_literal (M_is_second_countable, true);
-    Suppose_literal (M_has_a_countable_topological_base, true);
-    Suppose_literal (p_is_element_of_M, true);
-    Suppose_literal (U_is_proper_subset_of_M, true);
-    Suppose_literal (V_is_subset_of_real_coordinate_space_of_dimension_n, true);
-    Suppose_literal (For_all_p_there_is_an_open_neighbourhood_U, true);
-    Suppose_literal (U_is_homeomorphic_to_an_open_subset_V, true);
-
-    auto manifold_of_dimension_n = M_is_Hausdorff. And (Points_can_be_seperated_by_open_sets).
-    And (M_is_second_countable). And (M_has_a_countable_topological_base). And (p_is_element_of_M).
-    And (U_is_proper_subset_of_M). And (V_is_subset_of_real_coordinate_space_of_dimension_n).
-    And (For_all_p_there_is_an_open_neighbourhood_U). And (U_is_homeomorphic_to_an_open_subset_V).
-    Implying (A_topological_space_M);
-
-    // like above, you may create a function for each literal below
-    Suppose_literal (Let_M_be_a_manifold_of_dimension_n, manifold_of_dimension_n. Value());
-    Suppose_literal (A_pair_U_psi_where_U_is_element_of_M_is_open, true);
-    Suppose_literal (psi_maps_U_to_V_a_homeomorphism_to_some_open_V, true);
-
-    auto chart = Let_M_be_a_manifold_of_dimension_n. And (A_pair_U_psi_where_U_is_element_of_M_is_open).
-    And (psi_maps_U_to_V_a_homeomorphism_to_some_open_V);
-
-
-    return 0;
-}
+#include <satisfier>
+#include <string>
+
+bool is_topological_space(const std::string& M)
+{
+    bool is_topological_space = false;
+
+    // use M string to compute is_topological_space
+
+    return is_topological_space;
+}
+
+int main()
+{
+    // supposed A_topological_space_M, topological_space function
+    Suppose_literal (A_topological_space_M, is_topological_space("M string"));
+
+    // like above, you may create a function for each literal below
+    Suppose_literal (M_is_Hausdorff, true);
+    Suppose_literal (Points_can_be_seperated_by_open_sets, true);
+    Suppose_literal (M_is_second_countable, true);
+    Suppose_literal (M_has_a_countable_topological_base, true);
+    Suppose_literal (p_is_element_of_M, true);
+    Suppose_literal (U_is_proper_subset_of_M, true);
+    Suppose_literal (V_is_subset_of_real_coordinate_space_of_dimension_n, true);
+    Suppose_literal (For_all_p_there_is_an_open_neighbourhood_U, true);
+    Suppose_literal (U_is_homeomorphic_to_an_open_subset_V, true);
+
+    auto manifold_of_dimension_n = M_is_Hausdorff. And (Points_can_be_seperated_by_open_sets).
+    And (M_is_second_countable). And (M_has_a_countable_topological_base). And (p_is_element_of_M).
+    And (U_is_proper_subset_of_M). And (V_is_subset_of_real_coordinate_space_of_dimension_n).
+    And (For_all_p_there_is_an_open_neighbourhood_U). And (U_is_homeomorphic_to_an_open_subset_V).
+    Implying (A_topological_space_M);
+
+    Suppose_literal (Let_M_be_a_manifold_of_dimension_n, manifold_of_dimension_n. Value());
+    // like the supposed literal A_topological_space_M, you may create a function for each literal below
+    Suppose_literal (A_pair_U_psi_where_U_is_element_of_M_is_open, true);
+    Suppose_literal (psi_maps_U_to_V_a_homeomorphism_to_some_open_V, true);
+
+    auto chart = Let_M_be_a_manifold_of_dimension_n. And (A_pair_U_psi_where_U_is_element_of_M_is_open).
+    And (psi_maps_U_to_V_a_homeomorphism_to_some_open_V);
+
+
+    return 0;
+}