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Step * 1 1 1 2 of Lemma cosetTC-transitive


1. a : coSet{i:l}
2. t : {p:copath(T.T;a)| 0 < copath-length(p)} 
3. t1 : set-dom(copath-at(a;t))
⊢ seteq(set-item(copath-at(a;t);t1);copath-at(a;copath-extend(t;t1)))
BY
{ (BLemma `seteq_weakening` THEN Auto THEN Symmetry) }

1
1. a : coSet{i:l}
2. t : {p:copath(T.T;a)| 0 < copath-length(p)} 
3. t1 : set-dom(copath-at(a;t))
⊢ copath-at(a;copath-extend(t;t1)) = set-item(copath-at(a;t);t1) ∈ coSet{i:l}

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Latex:

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Latex:

1.  a  :  coSet\{i:l\}
2.  t  :  \{p:copath(T.T;a)|  0  <  copath-length(p)\} 
3.  t1  :  set-dom(copath-at(a;t))
\mvdash{}  seteq(set-item(copath-at(a;t);t1);copath-at(a;copath-extend(t;t1)))


By

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Latex:
(BLemma  `seteq\_weakening`  THEN  Auto  THEN  Symmetry)

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