Many theorems have the form : Premise(es) implies Conclusion(s)
Example A of wrongness:
There are many examples in which a theorem is stated without mentioning that part of the premise is not necessary to reach the conclusion.
Usually it is simple (and much better) to add a remark stating that the result is not sharp (ideally providing an example of weaker premise holding with the solution).
But there is another type of bias :
Added Note: Below composition means the AND of two relations ( for classical composition the transitivity does not compose! ( thanks to HenrikRüping remark).
Example B of wrongness:
Theorem 1 : The composition of 2 equivalence relations is an equivalence relation.
Or in fewer words : Equivalence relations are stable under composition.
Actually there is a much finer version of B :
Theorem A: For relations each of the following properties are stable under composition : Reflexive , Transitive , Symmetric.
By conjunction of the above we obtain:
Corollary B: Equivalence relations are stable under composition
Note: The second form is not only more precise but it also makes the mention "left as an easy exercise" more acceptable.
The "WRONG" notion:
I called theorem 1 (or its statement) wrong as it induced the reader to think that the conjunction of the 3 properties plays a role in proving the conclusion.
Of course only true theorems may be qualified as wrong.
Taking an absolute stance you may call wrong any theorem that is not a tautology.
A less absolute stance would call wrong any theorem that is not a tautology and in which you forget to mention non-sharpness.
Question 1: is there a better / more adequate term than wrong ( the subtext is: do you think it is a good notion?) .
Question 2: Do you know examples that follow a pattern like B or some variation in lack of tautology?
ADDED TO BE MORE SPECIFIC:
Question 3: More specifically : Are there other types of patterns showing a distance between premise and conclusion. The types need to be common in the mathematical literature, not purely logical types ( of course those are more countable).