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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