Nuprl Lemma : rat_termco_size_wf
∀[p:rat_termco()]. (rat_termco_size(p) ∈ partial(ℕ))
Proof
Definitions occuring in Statement :
rat_termco_size: rat_termco_size(p),
rat_termco: rat_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],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
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,
strong-type-continuous: Continuous+(T.F[T]),
type-continuous: Continuous(T.F[T]),
rat_termco: rat_termco(),
eq_atom: x =a y,
decidable: Dec(P),
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
prop: ℙ,
nequal: a ≠ b ∈ T ,
pi1: fst(t),
pi2: snd(t),
rat_termco_size: rat_termco_size(p)
Lemmas referenced :
fix_wf_corec-partial1,
nat_wf,
set-value-type,
le_wf,
istype-int,
int-value-type,
nat-mono,
ifthenelse_wf,
eq_atom_wf,
istype-universe,
subtype_rel_product,
istype-atom,
subtype_rel_ifthenelse,
istype-void,
subtype_rel_wf,
strong-continuous-depproduct,
eqtt_to_assert,
assert_of_eq_atom,
continuous-constant,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom,
strong-continuous-product,
continuous-id,
bool_wf,
subtype_rel_weakening,
istype-nat,
atom_subtype_base,
decidable__le,
full-omega-unsat,
intformnot_wf,
intformle_wf,
itermConstant_wf,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
istype-le,
inclusion-partial,
add-wf-partial-nat,
partial_wf,
rat_termco_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
independent_isectElimination,
sqequalRule,
intEquality,
lambdaEquality_alt,
natural_numberEquality,
hypothesisEquality,
productEquality,
atomEquality,
instantiate,
tokenEquality,
universeEquality,
voidEquality,
independent_pairFormation,
because_Cache,
lambdaFormation_alt,
voidElimination,
universeIsType,
axiomEquality,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
dependent_pairFormation_alt,
equalityIstype,
promote_hyp,
dependent_functionElimination,
independent_functionElimination,
cumulativity,
isectEquality,
applyEquality,
functionIsType,
dependent_set_memberEquality_alt,
approximateComputation,
productIsType
Latex:
\mforall{}[p:rat\_termco()]. (rat\_termco\_size(p) \mmember{} partial(\mBbbN{}))
Date html generated:
2019_10_29-AM-09_25_06
Last ObjectModification:
2019_03_31-PM-05_25_12
Theory : reals
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