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
Lemmas :
infix_ap_wf,
int_seg_wf,
lg-size_wf,
nat_wf,
rel_plus_wf,
lg-edge_wf,
labeled-graph_wf,
rel_plus_trans
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:
2015_07_22-PM-00_29_10
Last ObjectModification:
2015_01_28-PM-11_32_56
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