Suppose I made a very complicated (not necessarily difficult) derivations in which it is very likely for anyone to make some silly mistakes, e.g., incorrect sign, overlooking a term, and so on.
I wonder if there is a software package that verifies every step of my work against this kind of mistakes.
Let me give you an over-simplified example of what I am looking for, or what I expect the software to do for me. Suppose I want to solve the linear equation:
$x+10=2x+1$
I want the software to kind of take this step as input, and verify that my next step is implied from the first step. For example:
For example, if I write $x+10 - 10 = 2x + 1 + 10$ as implication of the first step, the software should tell me it's wrong, regardless of why. However, if my step was a correct implication of the first step, the software should assure its correctness. It might also be very useful if there is a third alternative in which the software can not decide if the implication is correct or wrong (could this be logically possible?).
Aplusix is a software to do this kind of things in the context of education.