https://proofwiki.org/wiki/Mean_Value_Theorem
This isn't a question about the Mean Value Theorem per se, but about something in the first proof. There is this line towards the beginning of the proof: F(x) = f(x) + hx, which the previous line says is a construction. This I can understand. But my intuition tells me that the line in question could equally well have been introduced as 'Let F(x) = f(x) + hx'. The problem starts here. I find the 'Let F(x) = f(x) + hx' more natural than "we may construct the real function F(x) = f(x) + hx". But 'Let X...' in any other situation seems to indicate that X is the hypothesis/antecedent of a conditional statement whose consequent/conditional we have to find out. So, my question is, why does, in 'Let F(x) = f(x) + hx' ( F(x) not previously defined) 'F(x) = f(x) + hx' not the hypothesis/antecedent of a conditional whose conclusion/consequent we must find?
(I am a self-learner, so, please be understanding.)
