Step
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of Lemma
context-adjoin-subset
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∀[X,Y:j⊢]. ∀[A:{Y ⊢ _}].  sub_cubical_set{[i | j]:l}(X.A; Y.A) supposing sub_cubical_set{j:l}(X; Y)
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Latex:
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\mforall{}[X,Y:j\mvdash{}].  \mforall{}[A:\{Y  \mvdash{}  \_\}].    sub\_cubical\_set\{[i  |  j]:l\}(X.A;  Y.A)  supposing  sub\_cubical\_set\{j:l\}(X;  Y)
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