Students are allowed to write out the proof using another method and email it to their tutor for correction and feedback. This allows students the ability to execute proofs without using the Proof Environment. The options listed below outline ways advanced learners can accomplish this:

Option 1: See the handwritten proof example.

Option 2: A proof where each step is written out line by line, such as the one below, is also valid.

1. Let l be a fixed line and P be a point.

2. Let n be a line that goes through P and parallel to l.

3. Let m be a line that goes through P and parallel to l

4. By transitivity (and symmetry), n is parallel to m.

5. n is parallel to m and share point P, hence by definition of being parallel, n=m

6. Since the choice of l,n,m, and P were arbitrary, we can conclude for any l,n,m, P, if n is parallel to l and m is parallel to l, and l and m go through P, then l =P.

Keywords: proof environment, cd course, proof, example

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