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Step * of Lemma valuation-exists

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∀x:formula(). ∀v0:{a:formula()| a ⊆ x ∧ (↑pvar?(a))}  ⟶ 𝔹.  (∃f:{a:formula()| a ⊆ x}  ⟶ 𝔹 [valuation(v0;x;f)])
BY
{ TACTIC:((D 0 THEN Auto) THEN Assert ⌜∀[n:ℕ]. bdd-val(v0;x;n)⌝⋅) }

1
.....assertion..... 
1. x : formula()
2. v0 : {a:formula()| a ⊆ x ∧ (↑pvar?(a))}  ⟶ 𝔹
⊢ ∀[n:ℕ]. bdd-val(v0;x;n)

2
1. x : formula()
2. v0 : {a:formula()| a ⊆ x ∧ (↑pvar?(a))}  ⟶ 𝔹
3. ∀[n:ℕ]. bdd-val(v0;x;n)
⊢ ∃f:{a:formula()| a ⊆ x}  ⟶ 𝔹 [valuation(v0;x;f)]

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Latex:

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Latex:
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\mforall{}x:formula().  \mforall{}v0:\{a:formula()|  a  \msubseteq{}  x  \mwedge{}  (\muparrow{}pvar?(a))\}    {}\mrightarrow{}  \mBbbB{}.
    (\mexists{}f:\{a:formula()|  a  \msubseteq{}  x\}    {}\mrightarrow{}  \mBbbB{}  [valuation(v0;x;f)])


By

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Latex:
TACTIC:((D  0  THEN  Auto)  THEN  Assert  \mkleeneopen{}\mforall{}[n:\mBbbN{}].  bdd-val(v0;x;n)\mkleeneclose{}\mcdot{})

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