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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