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Step * 1 1 of Lemma csm-univ-trans


1. G : CubicalSet{j}
2. T : {G.𝕀 ⊢ _:c𝕌}
3. H : CubicalSet{j}
4. s : H j⟶ G
5. (transprt-fun(G;decode(T);cop-to-cfun(compOp(T))))s
= transprt-fun(H;(decode(T))s+;(cop-to-cfun(compOp(T)))s+)
∈ {H ⊢ _:(((decode(T))s+)[0(𝕀)] ⟶ ((decode(T))s+)[1(𝕀)])}
⊢ decode((T)s+) ~ (decode(T))s+
BY
{ (RWO "csm-universe-decode" 0 THEN Auto) }

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Latex:

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Latex:

1.  G  :  CubicalSet\{j\}
2.  T  :  \{G.\mBbbI{}  \mvdash{}  \_:c\mBbbU{}\}
3.  H  :  CubicalSet\{j\}
4.  s  :  H  j{}\mrightarrow{}  G
5.  (transprt-fun(G;decode(T);cop-to-cfun(compOp(T))))s
=  transprt-fun(H;(decode(T))s+;(cop-to-cfun(compOp(T)))s+)
\mvdash{}  decode((T)s+)  \msim{}  (decode(T))s+


By

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Latex:
(RWO  "csm-universe-decode"  0  THEN  Auto)

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