Special case

In logic, especially as applied in mathematics, concept $A$ is a special case or specialization of concept $B$ precisely if every instance of $A$ is also an instance of $B$ but not vice versa, or equivalently, if $B$ is a generalization of $A$. A limiting case is a type of special case which is arrived at by taking some aspect of the concept to the extreme of what is permitted in the general case. If $B$ is true, one can immediately deduce that $A$ is true as well, and if $B$ is false, $A$ can also be immediately deduced to be false. A degenerate case is a special case which is in some way qualitatively different from almost all of the cases allowed.

Examples
Special case examples include the following:
 * All squares are rectangles (but not all rectangles are squares); therefore the square is a special case of the rectangle.
 * Fermat's Last Theorem, that $a^{n} + b^{n} = c^{n}$ has no solutions in positive integers with $n > 2$, is a special case of Beal's conjecture, that $a^{x} + b^{y} = c^{z}$ has no primitive solutions in positive integers with $x$, $y$, and $z$ all greater than 2, specifically, the case of $x = y = z$.
 * The unproven Riemann hypothesis is a special case of the generalized Riemann hypothesis, in the case that χ(n) = 1 for all n.
 * Fermat's little theorem, which states "if $p$ is a prime number, then for any integer a, then $$a^p \equiv a \pmod p$$" is a special case of Euler's theorem, which states "if n and a are coprime positive integers, and $$\phi(n)$$ is Euler's totient function, then $$a^{\varphi (n)} \equiv 1 \pmod{n}$$", in the case that $n$ is a prime number.
 * Euler's identity $$e^{i \pi} = -1$$ is a special case of Euler's formula which states "for any real number x: $$e^{ix} = \cos x + i\sin x$$", in the case that $x$ = $$\pi$$.