Nuprl Lemma : int_termco_size_wf
∀[p:int_termco()]. (int_termco_size(p) ∈ partial(ℕ))
Proof
Definitions occuring in Statement : 
int_termco_size: int_termco_size(p)
, 
int_termco: int_termco()
, 
partial: partial(T)
, 
nat: ℕ
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
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]
, 
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]
, 
prop: ℙ
, 
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])
, 
int_termco: int_termco()
, 
eq_atom: x =a y
, 
le: A ≤ B
, 
less_than': less_than'(a;b)
, 
not: ¬A
, 
pi1: fst(t)
, 
pi2: snd(t)
, 
int_termco_size: int_termco_size(p)
Lemmas referenced : 
fix_wf_corec-partial1, 
nat_wf, 
set-value-type, 
le_wf, 
int-value-type, 
nat-mono, 
ifthenelse_wf, 
eq_atom_wf, 
subtype_rel_product, 
bool_wf, 
eqtt_to_assert, 
assert_of_eq_atom, 
subtype_rel_self, 
eqff_to_assert, 
equal_wf, 
bool_cases_sqequal, 
subtype_base_sq, 
bool_subtype_base, 
assert-bnot, 
neg_assert_of_eq_atom, 
subtype_rel_wf, 
strong-continuous-depproduct, 
continuous-constant, 
strong-continuous-product, 
continuous-id, 
subtype_rel_weakening, 
atom_subtype_base, 
false_wf, 
inclusion-partial, 
add-wf-partial-nat, 
partial_wf, 
int_termco_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
cut, 
introduction, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesis, 
independent_isectElimination, 
sqequalRule, 
intEquality, 
lambdaEquality, 
natural_numberEquality, 
hypothesisEquality, 
productEquality, 
atomEquality, 
instantiate, 
tokenEquality, 
universeEquality, 
cumulativity, 
voidEquality, 
independent_pairFormation, 
because_Cache, 
lambdaFormation, 
unionElimination, 
equalityElimination, 
productElimination, 
dependent_pairFormation, 
equalityTransitivity, 
equalitySymmetry, 
promote_hyp, 
dependent_functionElimination, 
independent_functionElimination, 
voidElimination, 
axiomEquality, 
isect_memberEquality, 
isectEquality, 
applyEquality, 
functionExtensionality, 
functionEquality, 
dependent_set_memberEquality
Latex:
\mforall{}[p:int\_termco()].  (int\_termco\_size(p)  \mmember{}  partial(\mBbbN{}))
Date html generated:
2017_04_14-AM-08_56_25
Last ObjectModification:
2017_02_27-PM-03_40_58
Theory : omega
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