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[F] A4 P2.3.a Change wording

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Hykilpikonna
2021-11-08 21:11:14 -05:00
parent f060eee57e
commit 9c1bed84b1
1 changed files with 2 additions and 2 deletions
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assignments/a4/a4.tex
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@@ -105,7 +105,7 @@ Prove that each loop invariant holds.
\begin{proof} : \\
Variables: In this proof, $N$ is the abbreviation for the list \texttt{nums\_so\_far}. \\
\\
Assumption 1: The loop invariant 1 is true for the last iteration. \\
Assumption 1: The loop invariant 1 is true for the previous iteration. \\
That is $\forall k_2 \in N, gcd(k_2, 2) = 1 \land gcd(k_2, 3) = 1$ \\
\\
Assumption 2: The statement proven in Part 1.1: \\
@@ -115,7 +115,7 @@ We need to prove: $\forall k \in N \cup \{ N[-2] + 6 \}, gcd(k, 2) = 1 \land gcd
Which is equivalent to: $\forall k \in N, gcd(k, 2) = 1 \land gcd(k, 3) = 1$ and \\
$gcd(N[-2] + 6, 2) = 1 \land gcd(N[-2] + 6, 3) = 1$ \\
\\
Since the first part is the same as the last iteration, it is true. \\
Since the first part is the same as the previous iteration, it is true. \\
What we need to prove becomes:
$gcd(N[-2] + 6, 2) = 1 \land gcd(N[-2] + 6, 3) = 1$ \\
\\