Nuprl Lemma : MultiTreeco_size_wf
∀[T:Type]. ∀[p:MultiTreeco(T)]. (MultiTreeco_size(p) ∈ partial(ℕ))
Proof
Definitions occuring in Statement :
MultiTreeco_size: MultiTreeco_size(p),
MultiTreeco: MultiTreeco(T),
partial: partial(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
continuous-monotone: ContinuousMonotone(T.F[T]),
and: P ∧ Q,
type-monotone: Monotone(T.F[T]),
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
strong-type-continuous: Continuous+(T.F[T]),
type-continuous: Continuous(T.F[T]),
MultiTreeco: MultiTreeco(T),
eq_atom: x =a y,
pi1: fst(t),
pi2: snd(t),
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,
MultiTreeco_size: MultiTreeco_size(p)
Lemmas referenced :
MultiTreeco_wf,
partial_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,
length_wf_nat,
sum-partial-nat,
inclusion-partial,
false_wf,
add-wf-partial-nat,
atom_subtype_base,
subtype_rel_weakening,
continuous-constant,
continuous-id,
strong-continuous-function,
strong-continuous-depproduct,
subtype_rel_wf,
neg_assert_of_eq_atom,
assert-bnot,
bool_subtype_base,
subtype_base_sq,
bool_cases_sqequal,
equal_wf,
eqff_to_assert,
set_wf,
subtype_rel_dep_function,
assert_of_eq_atom,
eqtt_to_assert,
bool_wf,
subtype_rel_product,
l_member_wf,
length_wf,
less_than_wf,
list_wf,
eq_atom_wf,
ifthenelse_wf,
nat-mono,
int-value-type,
le_wf,
set-value-type,
nat_wf,
fix_wf_corec-partial1
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
independent_isectElimination,
sqequalRule,
intEquality,
lambdaEquality,
natural_numberEquality,
hypothesisEquality,
productEquality,
atomEquality,
instantiate,
tokenEquality,
universeEquality,
setEquality,
functionEquality,
setElimination,
rename,
voidEquality,
independent_pairFormation,
introduction,
because_Cache,
lambdaFormation,
unionElimination,
equalityElimination,
productElimination,
dependent_pairFormation,
equalityTransitivity,
equalitySymmetry,
promote_hyp,
dependent_functionElimination,
independent_functionElimination,
voidElimination,
cumulativity,
equalityEquality,
axiomEquality,
isect_memberEquality,
isectEquality,
applyEquality,
dependent_set_memberEquality,
int_eqEquality,
computeAll,
imageElimination
Latex:
\mforall{}[T:Type]. \mforall{}[p:MultiTreeco(T)]. (MultiTreeco\_size(p) \mmember{} partial(\mBbbN{}))
Date html generated:
2016_05_16-AM-08_52_27
Last ObjectModification:
2016_01_17-AM-09_42_22
Theory : C-semantics
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