theory prime_def imports Main begin
consts prime :: "nat ⇒ bool"
text‹
\begin{warn}
A common mistake when writing definitions is to introduce extra free
variables on the right-hand side. Consider the following, flawed definition
(where @{text"dvd"} means ``divides''):
@{term[display,quotes]"prime(p) ≡ 1 < p ∧ (m dvd p ⟶ (m=1 ∨ m=p))"}
\par\noindent\hangindent=0pt
Isabelle rejects this ``definition'' because of the extra @{term"m"} on the
right-hand side, which would introduce an inconsistency (why?).
The correct version is
@{term[display,quotes]"prime(p) ≡ 1 < p ∧ (∀m. m dvd p ⟶ (m=1 ∨ m=p))"}
\end{warn}
›
end