Sample Proof

To illustrate the use of Igloo, we compare a human-written proof, to one in Igloo. The selected theorem A.1 is taken from Isabelle/Isar examples:
http://isabelle.in.tum.de/library/HOL/Isar_examples/.

$$2 \cdot \sum_{i=0}^{n} i = n (n + 1)$$ (1)