Equivalence of Tidy Data and Third Normal Form
I believe it goes a like this, based on thinking about this myself:

Hadley's rule 1 &amp; 2 (call it TR1 &amp; TR2) is equivalent to 1NF with the exception that Hadley's rule 1 would permit repetition of columns. All we are saying in TR1 &amp; TR2 is that we have a single value in each cell of our table, although I think that is dependent on how you interpret observation. If an observation is an instance of a specific object then this is a stronger statement, although TR3 suggests that is not the case I think.

The combination of Hadley's rule 1, 2 and 3 is equivalent to 3NF. Using this link which also explains transitive dependence:

The table with UnitCode, UnitName, CourseCode, CourseName is in 2NF but violates TR3 since course and unit are different objects. The tables in 3NF where course and unit are separated and linked by foreign key comply with TR1, TR2 and TR3.

Let's say we want to prove implication and assume we have TR1, TR2 and TR3. Since those say nothing about repeating columns I think we have to either assume no repetition of columns or accept that these are not equivalent. Let's assume no repetition of columns. From the definitions TR1 &amp; TR2 => 1NF. If we have a table that is not in 2NF then TR3 is violated using the logic in the example above. Therefore we have 2NF. Similarly if we have a table that is not in 3NF then TR3 is violated, again using the logic above. Therefore TR1 &amp; TR2 &amp; TR3 => 3NF.

I think someone could probably do a more thorough proof with more time.

HTH