Nuprl Lemma : l_tree_node_wf
∀[L,T:Type]. ∀[val:T]. ∀[left_subtree,right_subtree:l_tree(L;T)].
  (l_tree_node(val;left_subtree;right_subtree) ∈ l_tree(L;T))
Proof
Definitions occuring in Statement : 
l_tree_node: l_tree_node(val;left_subtree;right_subtree)
, 
l_tree: l_tree(L;T)
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
l_tree: l_tree(L;T)
, 
l_tree_node: l_tree_node(val;left_subtree;right_subtree)
, 
eq_atom: x =a y
, 
ifthenelse: if b then t else f fi 
, 
bfalse: ff
, 
btrue: tt
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
bool: 𝔹
, 
unit: Unit
, 
it: ⋅
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
, 
uimplies: b supposing a
, 
exists: ∃x:A. B[x]
, 
prop: ℙ
, 
or: P ∨ Q
, 
sq_type: SQType(T)
, 
guard: {T}
, 
bnot: ¬bb
, 
assert: ↑b
, 
false: False
, 
subtype_rel: A ⊆r B
, 
ext-eq: A ≡ B
, 
l_treeco_size: l_treeco_size(p)
, 
spreadn: spread3, 
l_tree_size: l_tree_size(p)
, 
nat: ℕ
, 
le: A ≤ B
, 
less_than': less_than'(a;b)
, 
not: ¬A
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
Lemmas referenced : 
l_treeco-ext, 
l_treeco_wf, 
eq_atom_wf, 
bool_wf, 
eqff_to_assert, 
equal_wf, 
bool_cases_sqequal, 
subtype_base_sq, 
bool_subtype_base, 
assert-bnot, 
neg_assert_of_eq_atom, 
eqtt_to_assert, 
assert_of_eq_atom, 
add_nat_wf, 
false_wf, 
le_wf, 
l_tree_size_wf, 
nat_wf, 
value-type-has-value, 
set-value-type, 
int-value-type, 
has-value_wf-partial, 
l_treeco_size_wf, 
l_tree_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
cut, 
dependent_set_memberEquality, 
lemma_by_obid, 
hypothesis, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
because_Cache, 
sqequalRule, 
dependent_pairEquality, 
tokenEquality, 
setElimination, 
rename, 
cumulativity, 
productEquality, 
lambdaFormation, 
unionElimination, 
equalityElimination, 
productElimination, 
independent_isectElimination, 
equalityTransitivity, 
equalitySymmetry, 
dependent_pairFormation, 
promote_hyp, 
dependent_functionElimination, 
instantiate, 
independent_functionElimination, 
voidElimination, 
voidEquality, 
equalityEquality, 
applyEquality, 
natural_numberEquality, 
independent_pairFormation, 
intEquality, 
lambdaEquality, 
universeEquality
Latex:
\mforall{}[L,T:Type].  \mforall{}[val:T].  \mforall{}[left$_{subtree}$,right$_{subtree}$:\000Cl\_tree(L;T)].
    (l\_tree\_node(val;left$_{subtree}$;right$_{subtree}$)  \mmember{}  l\_t\000Cree(L;T))
Date html generated:
2016_05_16-AM-08_43_13
Last ObjectModification:
2015_12_28-PM-06_41_52
Theory : labeled!trees
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