[FMFP] Mostly summarized formal reasoning

semester4/fmfp/parts/01_formal-reasoning/01_natural-deduction.tex

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+\subsection{Natural deduction}
+The rules from above here are used to construct derivations under assumptions, e.g.
+$A_1, \ldots, A_n \vdash A$, which is read as ``$A$ follows from $A_1, \ldots, A_n$''.
+
+The derivations are always represented as derivation trees and a \bi{proof} is a derivation whose root has no assumptions.
+
+Since we have to prove a statement, we have to draw the derivation trees from the bottom up, with the goal of reaching an axiom or a rule that is an assumption
+using the other rules of the rule set.