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Step * of Lemma lifting-2-strict

∀[f:Top]. ∀[b:bag(Top)].  ((lifting-2(f) {} b ~ {}) ∧ (lifting-2(f) b {} ~ {}))
BY
{ (Auto
   THEN (InstLemma `lifting-gen-strict` [⌜2⌝;⌜f⌝]⋅ THENA Auto)
   THEN RepUR ``lifting-2 lifting2`` 0
   THEN RepUR ``lifting-gen`` -1
   THEN BHyp -1 
   THEN Auto
   THEN Reduce 0
   THEN Auto) }

1
1. f : Top
2. b : bag(Top)
3. ∀[a:k:ℕ2 ⟶ bag(Top)]. lifting-gen-rev(2;f;a) ~ {} supposing ∃k:ℕ2. (↑bag-null(a k))
⊢ ∃k:ℕ2. (↑bag-null([{}; b][k]))

2
1. f : Top
2. b : bag(Top)
3. lifting-2(f) {} b ~ {}
4. ∀[a:k:ℕ2 ⟶ bag(Top)]. lifting-gen-rev(2;f;a) ~ {} supposing ∃k:ℕ2. (↑bag-null(a k))
⊢ ∃k:ℕ2. (↑bag-null([b; {}][k]))

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Latex:

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Latex:
\mforall{}[f:Top].  \mforall{}[b:bag(Top)].    ((lifting-2(f)  \{\}  b  \msim{}  \{\})  \mwedge{}  (lifting-2(f)  b  \{\}  \msim{}  \{\}))


By

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Latex:
(Auto
  THEN  (InstLemma  `lifting-gen-strict`  [\mkleeneopen{}2\mkleeneclose{};\mkleeneopen{}f\mkleeneclose{}]\mcdot{}  THENA  Auto)
  THEN  RepUR  ``lifting-2  lifting2``  0
  THEN  RepUR  ``lifting-gen``  -1
  THEN  BHyp  -1 
  THEN  Auto
  THEN  Reduce  0
  THEN  Auto)

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