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Step * of Lemma ptuple-monotone

∀[P:Type]. ∀[a:Atom ⟶ P ⟶ ((P + P + Type) List)].  family-monotone{i:l}(P;λX.ptuple(lbl,p.a[lbl;p];X))
BY
{ (Auto
   THEN D 0
   THEN (Reduce 0 THEN Auto)
   THEN (D 0 THEN Auto)
   THEN RepUR ``ptuple`` 0
   THEN UseSubtypeRelLemmas
   THEN Auto
   THEN BLemma `tuple-type-monotone`
   THEN Auto
   THEN D 0
   THEN Reduce 0
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[P:Type].  \mforall{}[a:Atom  {}\mrightarrow{}  P  {}\mrightarrow{}  ((P  +  P  +  Type)  List)].
    family-monotone\{i:l\}(P;\mlambda{}X.ptuple(lbl,p.a[lbl;p];X))


By

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Latex:
(Auto
  THEN  D  0
  THEN  (Reduce  0  THEN  Auto)
  THEN  (D  0  THEN  Auto)
  THEN  RepUR  ``ptuple``  0
  THEN  UseSubtypeRelLemmas
  THEN  Auto
  THEN  BLemma  `tuple-type-monotone`
  THEN  Auto
  THEN  D  0
  THEN  Reduce  0
  THEN  Auto)

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