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Step * 1 1 of Lemma one-dimensional-dM


1. i : ℕ
2. v : Point(dM({i}))
3. Point(dM({i})) ⊆r fset(fset(names({i}) + names({i})))
4. ∀x,y:Point(dM({i})).  (x = y ∈ Point(dM({i})) ⇐⇒ x = y ∈ fset(fset(names({i}) + names({i}))))
5. dM({i}) ∈ LatticeStructure
6. <i> ∈ Point(dM({i}))
7. <1-i> ∈ Point(dM({i}))
⊢ (v = 0 ∈ Point(dM({i})))
∨ (v = 1 ∈ Point(dM({i})))
∨ (v = <i> ∈ Point(dM({i})))
∨ (v = <1-i> ∈ Point(dM({i})))
∨ (v = <i> ∧ <1-i> ∈ Point(dM({i})))
∨ (v = <i> ∨ <1-i> ∈ Point(dM({i})))
BY
{ (RWO "-4" 0 THENA Auto) }

1
1. i : ℕ
2. v : Point(dM({i}))
3. Point(dM({i})) ⊆r fset(fset(names({i}) + names({i})))
4. ∀x,y:Point(dM({i})).  (x = y ∈ Point(dM({i})) ⇐⇒ x = y ∈ fset(fset(names({i}) + names({i}))))
5. dM({i}) ∈ LatticeStructure
6. <i> ∈ Point(dM({i}))
7. <1-i> ∈ Point(dM({i}))
⊢ (v = 0 ∈ fset(fset(names({i}) + names({i}))))
∨ (v = 1 ∈ fset(fset(names({i}) + names({i}))))
∨ (v = <i> ∈ fset(fset(names({i}) + names({i}))))
∨ (v = <1-i> ∈ fset(fset(names({i}) + names({i}))))
∨ (v = <i> ∧ <1-i> ∈ fset(fset(names({i}) + names({i}))))
∨ (v = <i> ∨ <1-i> ∈ fset(fset(names({i}) + names({i}))))

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Latex:

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Latex:

1.  i  :  \mBbbN{}
2.  v  :  Point(dM(\{i\}))
3.  Point(dM(\{i\}))  \msubseteq{}r  fset(fset(names(\{i\})  +  names(\{i\})))
4.  \mforall{}x,y:Point(dM(\{i\})).    (x  =  y  \mLeftarrow{}{}\mRightarrow{}  x  =  y)
5.  dM(\{i\})  \mmember{}  LatticeStructure
6.  <i>  \mmember{}  Point(dM(\{i\}))
7.  ə-i>  \mmember{}  Point(dM(\{i\}))
\mvdash{}  (v  =  0)  \mvee{}  (v  =  1)  \mvee{}  (v  =  <i>)  \mvee{}  (v  =  ə-i>)  \mvee{}  (v  =  <i>  \mwedge{}  ə-i>)  \mvee{}  (v  =  <i>  \mvee{}  ə-i>)


By

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Latex:
(RWO  "-4"  0  THENA  Auto)

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