{ 
[A,T:Type].
f:A 
T
[P:T 
]. g:LabeledGraph(A). (x
lg-map(f;g).P[x] 
xg.P[f x]) }
{ Proof }
Definitions occuring in Statement :
lg-all: xG.P[x],
lg-map: lg-map(f;g),
labeled-graph: LabeledGraph(T),
uall: [x:A]. B[x],
prop: ,
so_apply: x[s],
all: x:A. B[x],
iff: P Q,
apply: f a,
function: x:A B[x],
universe: Type
Definitions :
uall: [x:A]. B[x],
all: x:A. B[x],
prop: ,
iff: P Q,
lg-all: xG.P[x],
lg-map: lg-map(f;g),
so_apply: x[s],
and: P 
Q,
implies: P Q,
rev_implies: P Q,
int_seg: {i..j
},
lg-size: lg-size(g),
lg-label: lg-label(g;x),
spreadn: spread3,
top: Top,
member: t T,
pi1: fst(t),
lelt: i 
j < k,
le: A B,
not: 
A,
false: False,
so_lambda: 
x.t[x],
labeled-graph: LabeledGraph(T),
nat: 
,
uimplies: b supposing a,
guard: {T}
Lemmas :
length-map-sq,
select-map,
le_wf,
length_wf_nat,
nat_wf,
lg-size_wf,
select_wf,
int_seg_wf,
lg-all_wf,
lg-map_wf,
labeled-graph_wf
\mforall{}[A,T:Type]. \mforall{}f:A {}\mrightarrow{} T. \mforall{}[P:T {}\mrightarrow{} \mBbbP{}]. \mforall{}g:LabeledGraph(A). (\mforall{}x\mmember{}lg-map(f;g).P[x] \mLeftarrow{}{}\mRightarrow{} \mforall{}x\mmember{}g.P[f x])
Date html generated:
2011_08_16-PM-06_46_19
Last ObjectModification:
2011_06_18-AM-10_58_34
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