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Step * of Lemma sorted-by-eq-rels

∀T:Type. ∀R1,R2:T ⟶ T ⟶ ℙ. ∀L:T List.
  ((∀x∈L.(∀y∈L.R1[x;y] ⇐⇒ R2[x;y])) ⇒ sorted-by(λx,y. R1[x;y];L) ⇒ sorted-by(λx,y. R2[x;y];L))
BY
{ (Auto
   THEN (All(RWO "l-ordered-is-sorted-by<") THENA Auto)
   THEN InstLemma `l-ordered-eq-rels` [⌜T⌝;⌜R1⌝;⌜R2⌝;⌜L⌝]⋅
   THEN Auto) }

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Latex:

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Latex:
\mforall{}T:Type.  \mforall{}R1,R2:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}.  \mforall{}L:T  List.
    ((\mforall{}x\mmember{}L.(\mforall{}y\mmember{}L.R1[x;y]  \mLeftarrow{}{}\mRightarrow{}  R2[x;y]))  {}\mRightarrow{}  sorted-by(\mlambda{}x,y.  R1[x;y];L)  {}\mRightarrow{}  sorted-by(\mlambda{}x,y.  R2[x;y];L))


By

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Latex:
(Auto
  THEN  (All(RWO  "l-ordered-is-sorted-by<")  THENA  Auto)
  THEN  InstLemma  `l-ordered-eq-rels`  [\mkleeneopen{}T\mkleeneclose{};\mkleeneopen{}R1\mkleeneclose{};\mkleeneopen{}R2\mkleeneclose{};\mkleeneopen{}L\mkleeneclose{}]\mcdot{}
  THEN  Auto)

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