Nuprl Lemma : l_tree_node-val_wf
∀[L,T:Type]. ∀[v:l_tree(L;T)]. l_tree_node-val(v) ∈ T supposing ↑l_tree_node?(v)
Proof
Definitions occuring in Statement :
l_tree_node-val: l_tree_node-val(v),
l_tree_node?: l_tree_node?(v),
l_tree: l_tree(L;T),
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
sq_type: SQType(T),
guard: {T},
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
l_tree_node?: l_tree_node?(v),
pi1: fst(t),
assert: ↑b,
bfalse: ff,
false: False,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
bnot: ¬bb,
l_tree_node-val: l_tree_node-val(v),
pi2: snd(t)
Lemmas referenced :
l_tree-ext,
eq_atom_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_atom,
subtype_base_sq,
atom_subtype_base,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom,
assert_wf,
l_tree_node?_wf,
l_tree_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
promote_hyp,
productElimination,
hypothesis_subsumption,
hypothesis,
applyEquality,
sqequalRule,
tokenEquality,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
instantiate,
cumulativity,
atomEquality,
dependent_functionElimination,
independent_functionElimination,
because_Cache,
voidElimination,
dependent_pairFormation,
universeEquality
Latex:
\mforall{}[L,T:Type]. \mforall{}[v:l\_tree(L;T)]. l\_tree\_node-val(v) \mmember{} T supposing \muparrow{}l\_tree\_node?(v)
Date html generated:
2018_05_22-PM-09_38_58
Last ObjectModification:
2017_03_04-PM-07_25_24
Theory : labeled!trees
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