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Step * of Lemma pcw-consistent-steps_wf

∀[P:Type]. ∀[A:P ⟶ Type]. ∀[B:p:P ⟶ A[p] ⟶ Type]. ∀[C:p:P ⟶ a:A[p] ⟶ B[p;a] ⟶ P].
∀[s1,s2:pcw-step(P;p.A[p];p,a.B[p;a];p,a,b.C[p;a;b])].
  (pcw-consistent-steps(P;p.A[p];p,a.B[p;a];p,a,b.C[p;a;b];s1;s2) ∈ ℙ)
BY
{ (InstLemma `param-co-W_wf` []
   THEN RepeatFor 4 (ParallelLast')
   THEN Auto
   THEN RepeatFor 2 (D (-2))
   THEN RepeatFor 2 (D (-1))
   THEN RepUR ``pcw-consistent-steps`` 0
   THEN Repeat (AndMemCD)
   THEN Try (pcoWEqD (-1)⋅)
   THEN Auto)⋅ }

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Latex:

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Latex:
\mforall{}[P:Type].  \mforall{}[A:P  {}\mrightarrow{}  Type].  \mforall{}[B:p:P  {}\mrightarrow{}  A[p]  {}\mrightarrow{}  Type].  \mforall{}[C:p:P  {}\mrightarrow{}  a:A[p]  {}\mrightarrow{}  B[p;a]  {}\mrightarrow{}  P].
\mforall{}[s1,s2:pcw-step(P;p.A[p];p,a.B[p;a];p,a,b.C[p;a;b])].
    (pcw-consistent-steps(P;p.A[p];p,a.B[p;a];p,a,b.C[p;a;b];s1;s2)  \mmember{}  \mBbbP{})


By

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Latex:
(InstLemma  `param-co-W\_wf`  []
  THEN  RepeatFor  4  (ParallelLast')
  THEN  Auto
  THEN  RepeatFor  2  (D  (-2))
  THEN  RepeatFor  2  (D  (-1))
  THEN  RepUR  ``pcw-consistent-steps``  0
  THEN  Repeat  (AndMemCD)
  THEN  Try  (pcoWEqD  (-1)\mcdot{})
  THEN  Auto)\mcdot{}

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