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Step * 1 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
⊢ (x = 1 ∈ Point(free-dist-lattice(T; eq))) ∨ (y = 1 ∈ Point(free-dist-lattice(T; eq)))
BY
{ (Assert ⌜{} ∈ x ∨ {} ∈ y⌝⋅ THENM (ParallelLast THEN BLemma `free-dl-1` THEN Auto)) }

1
.....assertion..... 
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 ∨ {} ∈ y

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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.  \{\}  \mmember{}  x  \mvee{}  y
\mvdash{}  (x  =  1)  \mvee{}  (y  =  1)


By

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Latex:
(Assert  \mkleeneopen{}\{\}  \mmember{}  x  \mvee{}  \{\}  \mmember{}  y\mkleeneclose{}\mcdot{}  THENM  (ParallelLast  THEN  BLemma  `free-dl-1`  THEN  Auto))

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