A form of proof in which the premise is proved true by assuming that it's true. Proof by Assertion is actually a logical fallacy, or a method in an unproof. It is an extreme case of Begging the Question.

An example: "It's true because it's true".

To prove the use of Proof by Assertion, prove that the conclusion is one of the premises.

This should not be confused with the use of assertions in proofs, particularly proofs of algorithms. In these cases, the assertion is used to introduce as a premise what has been proven up to this point. For example, a proof of a simple sorting algorithm gone a little overboard with assertions:
void sort(int [a], int length){
    int i, k;

    for(i=0; i<length; i++){
          /* ASSERT: a[0..i] is sorted */
          /* ASSERT: all elements in a[0..i] are <= all elements
             in a[i..length] */
        k=indexOfSmallest(a, i, length);
          /* ASSERT: k has the index of the smallest element in the
             unsorted portion of a */
        swap(a, i, k);
          /* ASSERT: a[0..i] <= a[i] <= a[i+1..length] */
          /* Because a[0..i] is sorted and a[0..i] <= a[i],
             a[0..i+1] is sorted */
      /* because i==length and a[0..i] is sorted, a is sorted. */

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