Nuprl Lemma : bst_leaf_wf
∀[E:Type]. ∀[value:E]. (bst_leaf(value) ∈ bs_tree(E))
Proof
Definitions occuring in Statement :
bst_leaf: bst_leaf(value)
,
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_leaf: bst_leaf(value)
,
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)
,
has-value: (a)↓
,
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]
,
so_lambda: λ2x.t[x]
,
so_apply: x[s]
,
uimplies: b supposing a
Lemmas referenced :
bs_treeco-ext,
ifthenelse_wf,
eq_atom_wf,
unit_wf2,
bs_treeco_wf,
false_wf,
le_wf,
nat_wf,
has-value_wf_base,
set_subtype_base,
int_subtype_base,
is-exception_wf,
equal_wf,
has-value_wf-partial,
set-value-type,
int-value-type,
bs_treeco_size_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,
hypothesisEquality,
instantiate,
universeEquality,
productEquality,
voidEquality,
applyEquality,
productElimination,
natural_numberEquality,
independent_pairFormation,
lambdaFormation,
divergentSqle,
sqleReflexivity,
intEquality,
lambdaEquality,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
cumulativity
Latex:
\mforall{}[E:Type]. \mforall{}[value:E]. (bst\_leaf(value) \mmember{} bs\_tree(E))
Date html generated:
2017_10_01-AM-08_30_49
Last ObjectModification:
2017_07_26-PM-04_24_45
Theory : tree_1
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