Nuprl Lemma : lg-edge-add
∀[T:Type]
∀g:LabeledGraph(T). ∀i,j,a,b:ℕlg-size(g).
(lg-edge(lg-add(g;i;j);a;b) ⇐⇒ lg-edge(g;a;b) ∨ ((a = i ∈ ℤ) ∧ (b = j ∈ ℤ)))
Proof
Definitions occuring in Statement :
lg-edge: lg-edge(g;a;b),
lg-add: lg-add(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,
or: P ∨ Q,
and: P ∧ Q,
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Lemmas :
int_seg_wf,
lg-size_wf,
nat_wf,
labeled-graph_wf,
select-mklist,
length_wf_nat,
top_wf,
dep-isect-subtype,
list_wf,
length_wf,
select_wf,
sq_stable__le,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
or_wf,
equal_wf,
l_member_wf,
subtype_rel_list,
decidable__equal_int,
false_wf,
not-equal-2,
le_antisymmetry_iff,
add_functionality_wrt_le,
add-associates,
add-commutes,
add-swap,
le-add-cancel,
cons_member,
cons_wf,
iff_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
int_subtype_base
Latex:
\mforall{}[T:Type]
\mforall{}g:LabeledGraph(T). \mforall{}i,j,a,b:\mBbbN{}lg-size(g).
(lg-edge(lg-add(g;i;j);a;b) \mLeftarrow{}{}\mRightarrow{} lg-edge(g;a;b) \mvee{} ((a = i) \mwedge{} (b = j)))
Date html generated:
2015_07_22-PM-00_28_54
Last ObjectModification:
2015_01_28-PM-11_33_54
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