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
,
subtype_rel: A ⊆r B
,
ext-eq: A ≡ B
,
and: P ∧ Q
,
l_treeco_size: l_treeco_size(p)
,
l_tree_size: l_tree_size(p)
,
spreadn: spread3,
nat: ℕ
,
le: A ≤ B
,
less_than': less_than'(a;b)
,
false: False
,
not: ¬A
,
implies: P
⇒ Q
,
prop: ℙ
,
all: ∀x:A. B[x]
,
uimplies: b supposing a
,
so_lambda: λ2x.t[x]
,
so_apply: x[s]
Lemmas referenced :
l_treeco-ext,
l_treeco_wf,
ifthenelse_wf,
eq_atom_wf,
add_nat_wf,
false_wf,
le_wf,
l_tree_size_wf,
nat_wf,
value-type-has-value,
set-value-type,
int-value-type,
equal_wf,
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,
introduction,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
sqequalRule,
dependent_pairEquality,
tokenEquality,
setElimination,
rename,
productEquality,
instantiate,
universeEquality,
voidEquality,
applyEquality,
productElimination,
natural_numberEquality,
independent_pairFormation,
lambdaFormation,
cumulativity,
independent_isectElimination,
intEquality,
lambdaEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination
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:
2018_05_22-PM-09_38_43
Last ObjectModification:
2017_03_04-PM-07_25_21
Theory : labeled!trees
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