8.3. Lemma

Let the sets of states S1◎ … SN◎ with channels that are formed by keys k1, … , kM:
sij◎ ∈ Sij◎: sij◎ ⊵ kj, (i = 1..N, j = 1..M)
which have the multiple:
SS◎ = ∏(Si◎)k1, … ,kM, (i = 1..N)

If at the same time to be limited to any projections of the specified channels:
Sij◎ ⊵ Sij⚪, (i = 1..N, j = 1..M)
preserving, however, as part of their states, the original keys as projections

sij⚪ ∈ Sij⚪: sij⚪ ⊵ kj, (i = 1..N, j = 1..M)

that such their projections also have a multiple on the same channels:
SS⚪ = ∏(Sij⚪)k1, … ,kM, (i = 1..N)

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