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Step * 1 1 of Lemma rel-path-between-cons


1. [T] : Type
2. [R] : T ⟶ T ⟶ ℙ
3. x : T
4. y : T
5. z : T
6. [] = [] ∈ (T List)
⊢ rel-path-between(T;R;x;y;[z])
⇐⇒ (x = z ∈ T) ∧ y = z ∈ T supposing True ∧ (x R hd([])) ∧ rel-path-between(T;R;hd([]);y;[]) supposing ¬True
BY
{ ((Unfold `rel-path-between` 0 THEN Reduce 0) THEN Auto THEN (D 0 THEN All Reduce) THEN Auto) }

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Latex:

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Latex:

1.  [T]  :  Type
2.  [R]  :  T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}
3.  x  :  T
4.  y  :  T
5.  z  :  T
6.  []  =  []
\mvdash{}  rel-path-between(T;R;x;y;[z])
\mLeftarrow{}{}\mRightarrow{}  (x  =  z)
        \mwedge{}  y  =  z  supposing  True
        \mwedge{}  (x  R  hd([]))  \mwedge{}  rel-path-between(T;R;hd([]);y;[])  supposing  \mneg{}True


By

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Latex:
((Unfold  `rel-path-between`  0  THEN  Reduce  0)  THEN  Auto  THEN  (D  0  THEN  All  Reduce)  THEN  Auto)

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