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Step * of Lemma cond_safety_and

∀[A:Type]. ∀[P,Q:(A List) ⟶ ℙ].
  (safety(A;x.P[x]) ⇒ (∀tr1,tr2:A List.  (tr1 ≤ tr2 ⇒ P[tr2] ⇒ Q[tr2] ⇒ Q[tr1])) ⇒ safety(A;x.P[x] ∧ Q[x]))
BY
{ (Unfold `safety` 0 THEN Auto) }

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Latex:

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Latex:
\mforall{}[A:Type].  \mforall{}[P,Q:(A  List)  {}\mrightarrow{}  \mBbbP{}].
    (safety(A;x.P[x])
    {}\mRightarrow{}  (\mforall{}tr1,tr2:A  List.    (tr1  \mleq{}  tr2  {}\mRightarrow{}  P[tr2]  {}\mRightarrow{}  Q[tr2]  {}\mRightarrow{}  Q[tr1]))
    {}\mRightarrow{}  safety(A;x.P[x]  \mwedge{}  Q[x]))


By

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Latex:
(Unfold  `safety`  0  THEN  Auto)

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