lemma_flatten_cardinality_under_disjointness_same_length

Function lemma_flatten_cardinality_under_disjointness_same_length 

Source
pub proof fn lemma_flatten_cardinality_under_disjointness_same_length<A>(
    parts: Set<Set<A>>,
    c: nat,
)
Expand description
requires
parts.finite(),
pairwise_disjoint(parts),
parts.all(|p: Set<A>| p.finite() && p.len() == c),
ensures
parts.flatten().len() == parts.len() * c,
parts.flatten().finite(),

If parts is a finite set of finite, pairwise-disjoint sets, and each set has the same length c, then the cardinality of the union is the product of the number of sets and c.