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Step * 1 of Lemma pcw-path-coPath_wf

.....basecase..... 
1. A : 𝕌'
2. B : A ⟶ Type
3. w : coW(A;a.B[a])
4. p : Path
5. StepAgree(p 0;⋅;w)
6. n : ℤ
⊢ <Ax, λx.Ax> ∈ (pcw-path-coPath(0;p) ∈ copath(a.B[a];w))
  ∧ ((copath-length(pcw-path-coPath(0;p)) = 0 ∈ ℤ)
    ⇒ (copath-at(w;pcw-path-coPath(0;p)) = (fst(snd((p 0)))) ∈ coW(A;a.B[a])))
BY
{ ((Unfold `pcw-path-coPath` 0 THEN Reduce 0)
   THEN Auto
   THEN (MoveToConcl (-3) THEN (GenConclTerm ⌜p 0⌝⋅ THENA Auto))
   THEN RepeatFor 2 (D -2)
   THEN RepUR ``pcw-step-agree copath-at coPath-at`` 0
   THEN Fold `coW` 0
   THEN Auto) }

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Latex:

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Latex:
.....basecase..... 
1.  A  :  \mBbbU{}'
2.  B  :  A  {}\mrightarrow{}  Type
3.  w  :  coW(A;a.B[a])
4.  p  :  Path
5.  StepAgree(p  0;\mcdot{};w)
6.  n  :  \mBbbZ{}
\mvdash{}  <Ax,  \mlambda{}x.Ax>  \mmember{}  (pcw-path-coPath(0;p)  \mmember{}  copath(a.B[a];w))
    \mwedge{}  ((copath-length(pcw-path-coPath(0;p))  =  0)
        {}\mRightarrow{}  (copath-at(w;pcw-path-coPath(0;p))  =  (fst(snd((p  0))))))


By

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Latex:
((Unfold  `pcw-path-coPath`  0  THEN  Reduce  0)
  THEN  Auto
  THEN  (MoveToConcl  (-3)  THEN  (GenConclTerm  \mkleeneopen{}p  0\mkleeneclose{}\mcdot{}  THENA  Auto))
  THEN  RepeatFor  2  (D  -2)
  THEN  RepUR  ``pcw-step-agree  copath-at  coPath-at``  0
  THEN  Fold  `coW`  0
  THEN  Auto)

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