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Step * of Lemma strong-subtype-set3

∀[A,B:Type]. ∀[P:A ⟶ ℙ].  strong-subtype({x:A| P[x]} ;B) supposing strong-subtype(A;B)
BY
{ (((Auto THEN (InstLemma `strong-subtype-set` [⌜A⌝; ⌜B⌝; ⌜P⌝; ⌜λx.True⌝])⋅) THENA Auto)
   THEN ReduceSOAps 0
   THEN Auto
   THEN (InstLemma `strong-subtype-set2` [⌜B⌝; ⌜λx.True⌝])⋅
   THEN Auto) }

1
1. A : Type
2. B : Type
3. P : A ⟶ ℙ
4. strong-subtype(A;B)
5. strong-subtype({x:A| P[x]} ;{x:B| λx.True[x]} )
6. strong-subtype({x:B| λx.True[x]} ;B)
⊢ strong-subtype({x:A| P x} ;B)

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Latex:

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Latex:
\mforall{}[A,B:Type].  \mforall{}[P:A  {}\mrightarrow{}  \mBbbP{}].    strong-subtype(\{x:A|  P[x]\}  ;B)  supposing  strong-subtype(A;B)


By

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Latex:
(((Auto  THEN  (InstLemma  `strong-subtype-set`  [\mkleeneopen{}A\mkleeneclose{};  \mkleeneopen{}B\mkleeneclose{};  \mkleeneopen{}P\mkleeneclose{};  \mkleeneopen{}\mlambda{}x.True\mkleeneclose{}])\mcdot{})  THENA  Auto)
  THEN  ReduceSOAps  0
  THEN  Auto
  THEN  (InstLemma  `strong-subtype-set2`  [\mkleeneopen{}B\mkleeneclose{};  \mkleeneopen{}\mlambda{}x.True\mkleeneclose{}])\mcdot{}
  THEN  Auto)

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