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Step * of Lemma greatest-lower-bound-com

∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ].
  ∀[a,b,c,d:T].
    (c = d ∈ T) supposing (greatest-lower-bound(T;x,y.R[x;y];a;b;c) and greatest-lower-bound(T;x,y.R[x;y];b;a;d)) 
  supposing Order(T;x,y.R[x;y])
BY
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Latex:

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Latex:
\mforall{}[T:Type].  \mforall{}[R:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].
    \mforall{}[a,b,c,d:T].
        (c  =  d)  supposing 
              (greatest-lower-bound(T;x,y.R[x;y];a;b;c)  and 
              greatest-lower-bound(T;x,y.R[x;y];b;a;d)) 
    supposing  Order(T;x,y.R[x;y])


By

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Latex:
Auto

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