Nuprl Lemma : lg-edge-map
∀[T,S:Type]. ∀f:T ─→ S. ∀g:LabeledGraph(T). ∀a,b:ℕlg-size(g). (lg-edge(lg-map(f;g);a;b) ⇐⇒ lg-edge(g;a;b))
Proof
Definitions occuring in Statement :
lg-map: lg-map(f;g),
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],
iff: P ⇐⇒ Q,
function: x:A ─→ B[x],
natural_number: $n,
universe: Type
Lemmas :
select-map,
dep-isect-subtype,
list_wf,
top_wf,
int_seg_wf,
length_wf,
length_wf_nat,
select_wf,
sq_stable__le,
l_member_wf,
lg-size_wf,
nat_wf,
labeled-graph_wf
Latex:
\mforall{}[T,S:Type].
\mforall{}f:T {}\mrightarrow{} S. \mforall{}g:LabeledGraph(T). \mforall{}a,b:\mBbbN{}lg-size(g). (lg-edge(lg-map(f;g);a;b) \mLeftarrow{}{}\mRightarrow{} lg-edge(g;a;b))
Date html generated:
2015_07_23-AM-11_03_27
Last ObjectModification:
2015_01_28-PM-11_34_43
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