Nuprl Lemma : MTree_Node_wf
∀[T:Type]. ∀[labels:{L:Atom List| 0 < ||L||} ]. ∀[children:{a:Atom| (a ∈ labels)} ⟶ MultiTree(T)].
(MTree_Node(labels;children) ∈ MultiTree(T))
Proof
Definitions occuring in Statement :
MTree_Node: MTree_Node(labels;children),
MultiTree: MultiTree(T),
l_member: (x ∈ l),
length: ||as||,
list: T List,
less_than: a < b,
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
natural_number: $n,
atom: Atom,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
MultiTree: MultiTree(T),
MTree_Node: MTree_Node(labels;children),
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
btrue: tt,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
and: P ∧ Q,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
ext-eq: A ≡ B,
MultiTreeco_size: MultiTreeco_size(p),
pi1: fst(t),
pi2: snd(t),
MultiTree_size: MultiTree_size(p),
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
not: ¬A,
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
less_than: a < b,
squash: ↓T
Lemmas referenced :
MultiTreeco_size_wf,
has-value_wf-partial,
int-value-type,
set-value-type,
value-type-has-value,
nat_wf,
int_seg_wf,
int_formula_prop_less_lemma,
intformless_wf,
decidable__lt,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
int_seg_properties,
list-subtype,
select_wf,
MultiTree_size_wf,
length_wf_nat,
sum-nat,
le_wf,
false_wf,
add_nat_wf,
neg_assert_of_eq_atom,
assert-bnot,
bool_subtype_base,
subtype_base_sq,
bool_cases_sqequal,
equal_wf,
eqff_to_assert,
assert_of_eq_atom,
eqtt_to_assert,
bool_wf,
eq_atom_wf,
list_wf,
set_wf,
MultiTreeco_wf,
MultiTree_wf,
l_member_wf,
subtype_rel_dep_function,
length_wf,
less_than_wf,
MultiTreeco-ext
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
dependent_set_memberEquality,
lemma_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
setElimination,
rename,
sqequalRule,
dependent_pairEquality,
tokenEquality,
natural_numberEquality,
atomEquality,
applyEquality,
setEquality,
lambdaEquality,
because_Cache,
independent_isectElimination,
lambdaFormation,
functionEquality,
cumulativity,
unionElimination,
equalityElimination,
productElimination,
productEquality,
equalityTransitivity,
equalitySymmetry,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
independent_functionElimination,
voidElimination,
voidEquality,
equalityEquality,
independent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
computeAll,
imageElimination,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[labels:\{L:Atom List| 0 < ||L||\} ]. \mforall{}[children:\{a:Atom| (a \mmember{} labels)\} {}\mrightarrow{} MultiTree(T)].
(MTree\_Node(labels;children) \mmember{} MultiTree(T))
Date html generated:
2016_05_16-AM-08_52_50
Last ObjectModification:
2016_01_17-AM-09_42_08
Theory : C-semantics
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