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Step * 2 of Lemma uorder_functionality_wrt_iff


1. [T] : Type
2. [R] : T ⟶ T ⟶ ℙ
3. [R'] : T ⟶ T ⟶ ℙ
4. ∀[x,y:T].  (R[x;y] ⇐⇒ R'[x;y])
5. UniformlyRefl(T;x,y.R'[x;y]) ∧ UniformlyTrans(T;x,y.R'[x;y]) ∧ UniformlyAntiSym(T;x,y.R'[x;y])
⊢ UniformlyRefl(T;x,y.R[x;y]) ∧ UniformlyTrans(T;x,y.R[x;y]) ∧ UniformlyAntiSym(T;x,y.R[x;y])
BY
{ (RWO "4" 0 THEN Auto) }

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Latex:

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Latex:

1.  [T]  :  Type
2.  [R]  :  T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}
3.  [R']  :  T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}
4.  \mforall{}[x,y:T].    (R[x;y]  \mLeftarrow{}{}\mRightarrow{}  R'[x;y])
5.  UniformlyRefl(T;x,y.R'[x;y])  \mwedge{}  UniformlyTrans(T;x,y.R'[x;y])  \mwedge{}  UniformlyAntiSym(T;x,y.R'[x;y])
\mvdash{}  UniformlyRefl(T;x,y.R[x;y])  \mwedge{}  UniformlyTrans(T;x,y.R[x;y])  \mwedge{}  UniformlyAntiSym(T;x,y.R[x;y])


By

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Latex:
(RWO  "4"  0  THEN  Auto)

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