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Step * 2 of Lemma valuation-exists


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)]
BY
{ (With ⌜prank(x) + 1⌝ (D (-1))⋅ THENA Auto') }

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

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Latex:

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Latex:

1.  x  :  formula()
2.  v0  :  \{a:formula()|  a  \msubseteq{}  x  \mwedge{}  (\muparrow{}pvar?(a))\}    {}\mrightarrow{}  \mBbbB{}
3.  \mforall{}[n:\mBbbN{}].  bdd-val(v0;x;n)
\mvdash{}  \mexists{}f:\{a:formula()|  a  \msubseteq{}  x\}    {}\mrightarrow{}  \mBbbB{}  [valuation(v0;x;f)]


By

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Latex:
(With  \mkleeneopen{}prank(x)  +  1\mkleeneclose{}  (D  (-1))\mcdot{}  THENA  Auto')

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