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Step * 1 of Lemma free-dl-1-join-irreducible


1. T : Type@i'
2. eq : EqDecider(T)@i
3. x : Point(free-dist-lattice(T; eq))@i
4. y : Point(free-dist-lattice(T; eq))@i
5. x ∨ y = 1 ∈ Point(free-dist-lattice(T; eq))
⊢ (x = 1 ∈ Point(free-dist-lattice(T; eq))) ∨ (y = 1 ∈ Point(free-dist-lattice(T; eq)))
BY
{ (RWO "free-dl-1" (-1) THENA Auto) }

1
1. T : Type@i'
2. eq : EqDecider(T)@i
3. x : Point(free-dist-lattice(T; eq))@i
4. y : Point(free-dist-lattice(T; eq))@i
5. {} ∈ x ∨ y
⊢ (x = 1 ∈ Point(free-dist-lattice(T; eq))) ∨ (y = 1 ∈ Point(free-dist-lattice(T; eq)))

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Latex:

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Latex:

1.  T  :  Type@i'
2.  eq  :  EqDecider(T)@i
3.  x  :  Point(free-dist-lattice(T;  eq))@i
4.  y  :  Point(free-dist-lattice(T;  eq))@i
5.  x  \mvee{}  y  =  1
\mvdash{}  (x  =  1)  \mvee{}  (y  =  1)


By

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Latex:
(RWO  "free-dl-1"  (-1)  THENA  Auto)

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