Nuprl Lemma : lg-connected_transitivity
∀[T:Type]. ∀g:LabeledGraph(T). ∀a,b,c:ℕlg-size(g).  (lg-connected(g;a;b) 
⇒ lg-connected(g;b;c) 
⇒ lg-connected(g;a;c))
Proof
Definitions occuring in Statement : 
lg-connected: lg-connected(g;a;b)
, 
lg-size: lg-size(g)
, 
labeled-graph: LabeledGraph(T)
, 
int_seg: {i..j-}
, 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
natural_number: $n
, 
universe: Type
Definitions unfolded in proof : 
lg-connected: lg-connected(g;a;b)
, 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
member: t ∈ T
, 
infix_ap: x f y
, 
subtype_rel: A ⊆r B
, 
nat: ℕ
, 
prop: ℙ
, 
trans: Trans(T;x,y.E[x; y])
Latex:
\mforall{}[T:Type]
    \mforall{}g:LabeledGraph(T).  \mforall{}a,b,c:\mBbbN{}lg-size(g).
        (lg-connected(g;a;b)  {}\mRightarrow{}  lg-connected(g;b;c)  {}\mRightarrow{}  lg-connected(g;a;c))
Date html generated:
2016_05_17-AM-10_10_17
Last ObjectModification:
2015_12_29-PM-05_32_38
Theory : process-model
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