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Step * of Lemma wellfounded_functionality_wrt_iff

∀[T1,T2:Type]. ∀[r1:T1 ⟶ T1 ⟶ ℙ]. ∀[r2:T2 ⟶ T2 ⟶ ℙ].
  (∀x,y:T1.  (r1[x;y] ⇐⇒ r2[x;y])) ⇒ (WellFnd{i}(T1;x,y.r1[x;y]) ⇐⇒ WellFnd{i}(T2;x,y.r2[x;y])) 
  supposing T1 = T2 ∈ Type
BY
{ (UnivCD THENA Auto) }

1
1. [T1] : Type
2. [T2] : Type
3. [r1] : T1 ⟶ T1 ⟶ ℙ
4. [r2] : T2 ⟶ T2 ⟶ ℙ
5. T1 = T2 ∈ Type
6. ∀x,y:T1.  (r1[x;y] ⇐⇒ r2[x;y])
⊢ WellFnd{i}(T1;x,y.r1[x;y]) ⇐⇒ WellFnd{i}(T2;x,y.r2[x;y])

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Latex:

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Latex:
\mforall{}[T1,T2:Type].  \mforall{}[r1:T1  {}\mrightarrow{}  T1  {}\mrightarrow{}  \mBbbP{}].  \mforall{}[r2:T2  {}\mrightarrow{}  T2  {}\mrightarrow{}  \mBbbP{}].
    (\mforall{}x,y:T1.    (r1[x;y]  \mLeftarrow{}{}\mRightarrow{}  r2[x;y]))  {}\mRightarrow{}  (WellFnd\{i\}(T1;x,y.r1[x;y])  \mLeftarrow{}{}\mRightarrow{}  WellFnd\{i\}(T2;x,y.r2[x;y])) 
    supposing  T1  =  T2


By

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Latex:
(UnivCD  THENA  Auto)

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