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#include <iostream>
 
int main() {
    int number;
    std::cin >> number; //read from keyboard
    std::cout << number; //save to file
 
    std::ifstream in("newinput.txt");
    std::cin.rdbuf(in.rdbuf()); 
    std::ofstream out("newoutput.txt");
    std::cout.rdbuf(out.rdbuf());
 
    std::cin >> number; //read from newinput.txt
    std::cout << number; //write to newoutput.txt
}
 
int main() {
    int number;
    std::io >> number; //read from keyboard
    std::io << number; //save to file
 
    std::fstream in("newinput.txt", std::ios::in);
    std::io.rdbuf(in.rdbuf());  //what gets rebound?  in or out?
    std::fstream out("newoutput.txt", std::ios::in);
    std::io.rdbuf(out.rdbuf());  //what gets rebound?  in or out?
 
    //alright, so for your hypothetical example, we replace with `rdbufin` and `rdbufout`
    std::fstream in("newinput.txt", std::ios::in);
    std::io.rdbufin(in.rdbufin()); 
    std::fstream out("newoutput.txt", std::ios::in);
    std::io.rdbufout(out.rdbufout());
 
    std::ifstream in2("infile2.txt");
    in2.rdbufout(in2.rdbufout()); //What part of this makes sense?
    // ergo, std::io cannot be like a `std::ifstream`
}

prog.cpp: In function 'int main()':
prog.cpp:8:21: error: variable 'std::ifstream in' has initializer but incomplete type
prog.cpp:10:22: error: variable 'std::ofstream out' has initializer but incomplete type
prog.cpp: In function 'int main()':
prog.cpp:17:5: error: redefinition of 'int main()'
prog.cpp:3:5: error: 'int main()' previously defined here
prog.cpp:19:5: error: 'io' is not a member of 'std'
prog.cpp:20:5: error: 'io' is not a member of 'std'
prog.cpp:22:20: error: variable 'std::fstream in' has initializer but incomplete type
prog.cpp:23:5: error: 'io' is not a member of 'std'
prog.cpp:24:21: error: variable 'std::fstream out' has initializer but incomplete type
prog.cpp:25:5: error: 'io' is not a member of 'std'
prog.cpp:29:5: error: 'io' is not a member of 'std'
prog.cpp:31:5: error: 'io' is not a member of 'std'
prog.cpp:33:22: error: variable 'std::ifstream in2' has initializer but incomplete type

Standard output is empty