= Finite interpolation by lattice operations
{title2=$h=\bigvee_i\bigwedge_jh_{ij}$}
Suppose $h_{ij}$ sends the $i$th and $j$th nodes of an increasing input tuple to the corresponding output nodes. At the $i$th input, every $h_{ij}$ agrees, so their pointwise <minimum> takes the required value. At every other input it is bounded above by the required value, using the corresponding $j$ term. The pointwise <maximum> over $i$ therefore interpolates the entire tuple. The construction uses closure under finite <join> and <meet>, without assuming arbitrary restrictions of group elements belong to the group.
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