Nuprl Lemma : lg-all-append
∀[T:Type]. ∀[P:T ─→ ℙ]. ∀g1,g2:LabeledGraph(T). (∀x∈lg-append(g1;g2).P[x] ⇐⇒ ∀x∈g1.P[x] ∧ ∀x∈g2.P[x])
Proof
Definitions occuring in Statement :
lg-all: ∀x∈G.P[x],
lg-append: lg-append(g1;g2),
labeled-graph: LabeledGraph(T),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
function: x:A ─→ B[x],
universe: Type
Lemmas :
lg-size_wf,
length-append,
length-map-sq,
nat_wf,
labeled-graph_wf,
and_wf,
all_wf,
int_seg_wf,
lg-label_wf,
lg-append_wf,
lelt_wf,
lg-label-append,
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
less_than_wf,
add-associates,
minus-one-mul,
add-mul-special,
zero-mul,
add-zero,
int_subtype_base,
subtract_wf,
decidable__le,
false_wf,
not-le-2,
condition-implies-le,
minus-add,
zero-add,
minus-minus,
add-swap,
add-commutes,
minus-zero,
add_functionality_wrt_le,
le-add-cancel,
decidable__lt,
less-iff-le,
zero-le-nat,
le_wf
Latex:
\mforall{}[T:Type]. \mforall{}[P:T {}\mrightarrow{} \mBbbP{}].
\mforall{}g1,g2:LabeledGraph(T). (\mforall{}x\mmember{}lg-append(g1;g2).P[x] \mLeftarrow{}{}\mRightarrow{} \mforall{}x\mmember{}g1.P[x] \mwedge{} \mforall{}x\mmember{}g2.P[x])
Date html generated:
2015_07_23-AM-11_04_45
Last ObjectModification:
2015_01_28-PM-11_35_34
Home
Index