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Step * of Lemma non-forking-wellfounded-linorder

∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ].
  (decidable-non-minimal(T;x,y.R[x;y])
  ⇒ WellFnd{i}(T;x,y.R[x;y])
  ⇒ (∀m:T. (unique-minimal(T;x,y.R[x;y];m) ⇒ non-forking(T;x,y.R[x;y]) ⇒ WeakLinorder(T;x,y.x (R^*) y))))
BY
{ (Auto
   THEN (InstLemma `unique-minimal-wellfounded-implies` [⌜T⌝;⌜R⌝;⌜m⌝]⋅ THENA Auto)
   THEN D 0
   THEN FLemma `rel_star_order` [4] 
   THEN Auto) }

1
1. [T] : Type
2. [R] : T ⟶ T ⟶ ℙ
3. decidable-non-minimal(T;x,y.R[x;y])
4. WellFnd{i}(T;x,y.R[x;y])
5. m : T
6. unique-minimal(T;x,y.R[x;y];m)
7. non-forking(T;x,y.R[x;y])
8. ∀y:T. (↓m ((λx,y. R[x;y])^*) y)
9. Order(T;x,y.x (R^*) y)
⊢ weak-connex(T; x,y.x (R^*) y)

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Latex:

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Latex:
\mforall{}[T:Type].  \mforall{}[R:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].
    (decidable-non-minimal(T;x,y.R[x;y])
    {}\mRightarrow{}  WellFnd\{i\}(T;x,y.R[x;y])
    {}\mRightarrow{}  (\mforall{}m:T
                (unique-minimal(T;x,y.R[x;y];m)
                {}\mRightarrow{}  non-forking(T;x,y.R[x;y])
                {}\mRightarrow{}  WeakLinorder(T;x,y.x  rel\_star(T;  R)  y))))


By

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Latex:
(Auto
  THEN  (InstLemma  `unique-minimal-wellfounded-implies`  [\mkleeneopen{}T\mkleeneclose{};\mkleeneopen{}R\mkleeneclose{};\mkleeneopen{}m\mkleeneclose{}]\mcdot{}  THENA  Auto)
  THEN  D  0
  THEN  FLemma  `rel\_star\_order`  [4] 
  THEN  Auto)

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