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Step * 1 1 of Lemma unique-poset-functor

.....assertion..... 
1. C : SmallCategory@i'
2. I : Cname List@i
3. L : name-morph(I;[]) ⟶ cat-ob(C)@i
4. E : i:nameset(I) ⟶ c:{c:name-morph(I;[])| (c i) = 0 ∈ ℕ2}  ⟶ (cat-arrow(C) (L c) (L flip(c;i)))@i
5. edge-arrows-commute(C;I;L;E)@i
⊢ <L, λc1,c2,p. poset_functor_extend(C;I;L;E;c1;c2)> ∈ Functor(poset-cat(I);C)
BY
{ (InstLemma `poset_functor_extend-is-functor` [⌜C⌝;⌜I⌝;⌜L⌝;⌜E⌝]⋅ THEN Auto) }

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Latex:

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Latex:
.....assertion..... 
1.  C  :  SmallCategory@i'
2.  I  :  Cname  List@i
3.  L  :  name-morph(I;[])  {}\mrightarrow{}  cat-ob(C)@i
4.  E  :  i:nameset(I)  {}\mrightarrow{}  c:\{c:name-morph(I;[])|  (c  i)  =  0\}    {}\mrightarrow{}  (cat-arrow(C)  (L  c)  (L  flip(c;i)))@i
5.  edge-arrows-commute(C;I;L;E)@i
\mvdash{}  <L,  \mlambda{}c1,c2,p.  poset\_functor\_extend(C;I;L;E;c1;c2)>  \mmember{}  Functor(poset-cat(I);C)


By

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Latex:
(InstLemma  `poset\_functor\_extend-is-functor`  [\mkleeneopen{}C\mkleeneclose{};\mkleeneopen{}I\mkleeneclose{};\mkleeneopen{}L\mkleeneclose{};\mkleeneopen{}E\mkleeneclose{}]\mcdot{}  THEN  Auto)

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