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Lemma 1

Given a tensor decomposition ⟨n×m×(p+1):r⟩, one can construct a tensor decomposition ⟨n×m×p:r-m⟩.
Given a tensor decomposition ⟨n×(m+1)×p:r⟩, one can construct a tensor decomposition ⟨n×m×p:r-n⟩.
Given a tensor decomposition ⟨(n+1)×m×p:r⟩, one can construct a tensor decomposition ⟨n×m×p:r-p⟩.