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Step * of Lemma equiv_rel_per-quotient

∀[T:Type]. ∀[E1,E2:T ⟶ T ⟶ 𝔹].
  (EquivRel(T;x,y.↑E2[x;y])
  ⇒ EquivRel(T;x,y.↑E1[x;y])
  ⇒ (∀x,y:T.  ((↑E2[x;y]) ⇒ (↑E1[x;y])))
  ⇒ EquivRel(x,y:T/per/(↑E2[x;y]);x,y.↑E1[x;y]))
BY
{ ((Unfold `per-quotient` 0 THEN Fold `quotient` 0) THEN InstLemma `equiv_rel_quotient` [] THEN Trivial) }

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Latex:

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Latex:
\mforall{}[T:Type].  \mforall{}[E1,E2:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbB{}].
    (EquivRel(T;x,y.\muparrow{}E2[x;y])
    {}\mRightarrow{}  EquivRel(T;x,y.\muparrow{}E1[x;y])
    {}\mRightarrow{}  (\mforall{}x,y:T.    ((\muparrow{}E2[x;y])  {}\mRightarrow{}  (\muparrow{}E1[x;y])))
    {}\mRightarrow{}  EquivRel(x,y:T/per/(\muparrow{}E2[x;y]);x,y.\muparrow{}E1[x;y]))


By

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Latex:
((Unfold  `per-quotient`  0  THEN  Fold  `quotient`  0)
  THEN  InstLemma  `equiv\_rel\_quotient`  []
  THEN  Trivial)

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