Nuprl Lemma : bst_node_wf
∀[E:Type]. ∀[left:bs_tree(E)]. ∀[value:E]. ∀[right:bs_tree(E)].  (bst_node(left;value;right) ∈ bs_tree(E))
Proof
Definitions occuring in Statement : 
bst_node: bst_node(left;value;right)
, 
bs_tree: bs_tree(E)
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
bs_tree: bs_tree(E)
, 
bst_node: bst_node(left;value;right)
, 
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
, 
bs_treeco_size: bs_treeco_size(p)
, 
bs_tree_size: bs_tree_size(p)
, 
pi1: fst(t)
, 
pi2: snd(t)
, 
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 : 
bs_treeco-ext, 
bs_treeco_wf, 
ifthenelse_wf, 
eq_atom_wf, 
unit_wf2, 
add_nat_wf, 
false_wf, 
le_wf, 
bs_tree_size_wf, 
nat_wf, 
value-type-has-value, 
set-value-type, 
int-value-type, 
equal_wf, 
has-value_wf-partial, 
bs_treeco_size_wf, 
bs_tree_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
cut, 
dependent_set_memberEquality, 
introduction, 
extract_by_obid, 
hypothesis, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
because_Cache, 
sqequalRule, 
dependent_pairEquality, 
tokenEquality, 
setElimination, 
rename, 
hypothesisEquality, 
productEquality, 
instantiate, 
universeEquality, 
voidEquality, 
applyEquality, 
productElimination, 
natural_numberEquality, 
independent_pairFormation, 
lambdaFormation, 
cumulativity, 
independent_isectElimination, 
intEquality, 
lambdaEquality, 
equalityTransitivity, 
equalitySymmetry, 
dependent_functionElimination, 
independent_functionElimination
Latex:
\mforall{}[E:Type].  \mforall{}[left:bs\_tree(E)].  \mforall{}[value:E].  \mforall{}[right:bs\_tree(E)].
    (bst\_node(left;value;right)  \mmember{}  bs\_tree(E))
Date html generated:
2017_10_01-AM-08_30_50
Last ObjectModification:
2017_07_26-PM-04_24_46
Theory : tree_1
Home
Index