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Step * of Lemma utrans_functionality_wrt_iff

∀[T:Type]. ∀[R,R':T ⟶ T ⟶ ℙ].
  ((∀[x,y:T].  (R[x;y] ⇐⇒ R'[x;y])) ⇒ (UniformlyTrans(T;y,x.R[x;y]) ⇐⇒ UniformlyTrans(T;y,x.R'[x;y])))
BY
{ (Unfold `utrans` 0 THEN Auto THEN (InstHyp [⌜a⌝;⌜b⌝;⌜c⌝] 5⋅ THEN Auto THEN HypBackchain THEN Auto)⋅) }

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Latex:

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Latex:
\mforall{}[T:Type].  \mforall{}[R,R':T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].
    ((\mforall{}[x,y:T].    (R[x;y]  \mLeftarrow{}{}\mRightarrow{}  R'[x;y]))
    {}\mRightarrow{}  (UniformlyTrans(T;y,x.R[x;y])  \mLeftarrow{}{}\mRightarrow{}  UniformlyTrans(T;y,x.R'[x;y])))


By

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Latex:
(Unfold  `utrans`  0  THEN  Auto  THEN  (InstHyp  [\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{}]  5\mcdot{}  THEN  Auto  THEN  HypBackchain  THEN  Auto)\mcdot{})

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