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Step * of Lemma fset-minimals-singleton

∀[T:Type]
  ∀eq:EqDecider(T). ∀x:fset(T).  (fset-minimals(xs,ys.f-proper-subset-dec(eq;xs;ys); {x}) = {x} ∈ fset(fset(T)))
BY
{ (Auto
   THEN ((Using [`eq',⌜deq-fset(eq)⌝] (BLemma  `fset-extensionality`)⋅ THENM D 0) THENA Auto)
   THEN RWW "member-fset-minimals member-fset-singleton" 0
   THEN Auto) }

1
1. T : Type
2. eq : EqDecider(T)
3. x : fset(T)
4. a : fset(T)
5. a = x ∈ fset(T)
⊢ fset-all({x};ys.¬bf-proper-subset-dec(eq;ys;a))

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Latex:

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Latex:
\mforall{}[T:Type]
    \mforall{}eq:EqDecider(T).  \mforall{}x:fset(T).    (fset-minimals(xs,ys.f-proper-subset-dec(eq;xs;ys);  \{x\})  =  \{x\})


By

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Latex:
(Auto
  THEN  ((Using  [`eq',\mkleeneopen{}deq-fset(eq)\mkleeneclose{}]  (BLemma    `fset-extensionality`)\mcdot{}  THENM  D  0)  THENA  Auto)
  THEN  RWW  "member-fset-minimals  member-fset-singleton"  0
  THEN  Auto)

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