Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 120 / 1 / b

For a finite distributive lattice, defineDistributivity and finiteness giveEvery $x$ with $x\wedge a\le b$ occurs in the join, so $x\le a\Rightarrow b$. This proves the defining adjunction and makes $L$ a Heyting algebra.

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