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  1. 'Marginally generalized theorems' refers to theorems that were generalized so marginally that they can still be taught, and understood by the students, in the same course.

Examples of theorems NOT marginally generalized:

  1. A skilled high-schooler can understand Puiseux series, Dirichlet's theorem on arithmetic progressions, and Lagrange's four-square theorem. But their generalizations are too cavernous.

Examples of theorems that can be marginally generalized:

  1. Spivak proves $\sqrt{2}$'s irrationality fully, but banishes $a^{\frac 1b}$'s to the exercises. Isn't proving (only) the latter more efficient?

  2. Most multivariate calculus textbooks devote 1 chapter to Green's Theorem. Why not introduce Stokes's first, and then state Green's as a corollary?

  3. Why not prove first Gauss's generalization of Wilson's Theorem:

$\forall \; p \; \text{odd prime}, \alpha \in \mathbb{N} : \quad \prod_{k = 1 \atop \gcd(k,m)=1}^{m} \!\!k \ \equiv \begin{cases} -1 \pmod{m} & \text{if } m=4,\;p^\alpha,\;2p^\alpha \\ \;\;\,1 \pmod{m} & \text{otherwise} \end{cases}?$

I refer not the further generalization requiring group theory.

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I don't have enough reputation to post this as a comment but a very standard proof of Stokes theorem in 3 dimensions is to reduce the problem and apply Green's theorem.

J.F
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