Nuprl Lemma : lg-edge-lg-connected
∀[T:Type]. ∀g:LabeledGraph(T). ∀a,b:ℕlg-size(g).  (lg-edge(g;a;b) 
⇒ lg-connected(g;a;b))
Proof
Definitions occuring in Statement : 
lg-connected: lg-connected(g;a;b)
, 
lg-edge: lg-edge(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 : 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
lg-connected: lg-connected(g;a;b)
, 
member: t ∈ T
, 
prop: ℙ
, 
subtype_rel: A ⊆r B
, 
nat: ℕ
, 
and: P ∧ Q
, 
cand: A c∧ B
, 
uimplies: b supposing a
, 
infix_ap: x f y
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
, 
exists: ∃x:A. B[x]
Latex:
\mforall{}[T:Type].  \mforall{}g:LabeledGraph(T).  \mforall{}a,b:\mBbbN{}lg-size(g).    (lg-edge(g;a;b)  {}\mRightarrow{}  lg-connected(g;a;b))
Date html generated:
2016_05_17-AM-10_10_05
Last ObjectModification:
2015_12_29-PM-05_32_43
Theory : process-model
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