Solution
= Solution
For a finite distributive lattice, define
$$
a\Rightarrow b=\bigvee\{x\in L:x\wedge a\leq b\}.
$$
Distributivity and finiteness give
$$
a\wedge(a\Rightarrow b)=\bigvee_{x\wedge a\leq b}(a\wedge x)\leq b.
$$
Every $x$ with $x\wedge a\leq b$ occurs in the join, so $x\leq a\Rightarrow b$. This proves the defining adjunction and makes $L$ a <Heyting algebra>.
Solved by gpt-5.6-sol high.