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Step * of Lemma sub-presheaf-set-and

No Annotations
∀[C:SmallCategory]. ∀[X:ps_context{j:l}(C)]. ∀[P,Q:I:cat-ob(C) ⟶ X(I) ⟶ ℙ].
  X | I,rho.P[I;rho] | I,rho.Q[I;rho] ≡ X | I,rho.P[I;rho] ∧ Q[I;rho] 
  supposing psc-predicate(C; X; I,rho.P[I;rho]) ∧ psc-predicate(C; X; I,rho.Q[I;rho])
BY
{ (Auto
   THEN RepUR ``ext-eq-psc sub-presheaf-set`` 0
   THEN Unfold `ps_context` 2
   THEN Auto
   THEN Unfold `psc-predicate` -2
   THEN Unfold `psc-predicate` -1
   THEN Fold `presheaf` 2
   THEN BLemma `presheaf-subset-and`
   THEN Auto) }

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Latex:

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Latex:
No  Annotations
\mforall{}[C:SmallCategory].  \mforall{}[X:ps\_context\{j:l\}(C)].  \mforall{}[P,Q:I:cat-ob(C)  {}\mrightarrow{}  X(I)  {}\mrightarrow{}  \mBbbP{}].
    X  |  I,rho.P[I;rho]  |  I,rho.Q[I;rho]  \mequiv{}  X  |  I,rho.P[I;rho]  \mwedge{}  Q[I;rho] 
    supposing  psc-predicate(C;  X;  I,rho.P[I;rho])  \mwedge{}  psc-predicate(C;  X;  I,rho.Q[I;rho])


By

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Latex:
(Auto
  THEN  RepUR  ``ext-eq-psc  sub-presheaf-set``  0
  THEN  Unfold  `ps\_context`  2
  THEN  Auto
  THEN  Unfold  `psc-predicate`  -2
  THEN  Unfold  `psc-predicate`  -1
  THEN  Fold  `presheaf`  2
  THEN  BLemma  `presheaf-subset-and`
  THEN  Auto)

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