Nuprl Lemma : cantor-to-fb_wf
∀[b:ℕ ⟶ ℕ+]. ∀[g:ℕ ⟶ 𝔹]. ∀[n:ℕ]. (cantor-to-fb(b;g;n) ∈ ℕb n)
Proof
Definitions occuring in Statement :
cantor-to-fb: cantor-to-fb(b;g;n),
int_seg: {i..j-},
nat_plus: ℕ+,
nat: ℕ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
apply: f a,
function: x:A ⟶ B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
cantor-to-fb: cantor-to-fb(b;g;n),
has-value: (a)↓,
member: t ∈ T,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
nat_plus: ℕ+,
so_apply: x[s],
all: ∀x:A. B[x],
guard: {T},
int_seg: {i..j-},
ge: i ≥ j ,
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
iff: P ⇐⇒ Q,
uiff: uiff(P;Q),
rev_implies: P ⇐ Q
Lemmas referenced :
value-type-has-value,
int-value-type,
sum_wf,
nat_wf,
int_seg_subtype_nat,
false_wf,
nat_plus_wf,
int_seg_wf,
subtract_wf,
non_neg_sum,
le_weakening2,
int_seg_properties,
nat_properties,
decidable__lt,
le_wf,
nat_plus_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformless_wf,
itermConstant_wf,
itermVar_wf,
intformnot_wf,
int_formula_prop_and_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_not_lemma,
int_formula_prop_wf,
nat_plus_subtype_nat,
equal_wf,
bool_wf,
mu-property,
bor_wf,
lt_int_wf,
decidable__le,
intformle_wf,
itermAdd_wf,
intformeq_wf,
int_formula_prop_le_lemma,
int_term_value_add_lemma,
int_formula_prop_eq_lemma,
iff_transitivity,
assert_wf,
or_wf,
less_than_wf,
iff_weakening_uiff,
assert_of_bor,
assert_of_lt_int,
itermSubtract_wf,
int_term_value_subtract_lemma,
mu_wf,
lelt_wf,
uall_wf,
isect_wf,
not_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
sqequalRule,
callbyvalueReduce,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
independent_isectElimination,
hypothesis,
hypothesisEquality,
lambdaEquality,
applyEquality,
functionExtensionality,
natural_numberEquality,
setElimination,
rename,
independent_pairFormation,
lambdaFormation,
because_Cache,
dependent_set_memberEquality,
dependent_functionElimination,
productElimination,
unionElimination,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
independent_functionElimination,
voidElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidEquality,
computeAll,
functionEquality,
addEquality,
orFunctionality,
inlFormation,
promote_hyp
Latex:
\mforall{}[b:\mBbbN{} {}\mrightarrow{} \mBbbN{}\msupplus{}]. \mforall{}[g:\mBbbN{} {}\mrightarrow{} \mBbbB{}]. \mforall{}[n:\mBbbN{}]. (cantor-to-fb(b;g;n) \mmember{} \mBbbN{}b n)
Date html generated:
2018_05_21-PM-07_57_49
Last ObjectModification:
2017_07_26-PM-05_35_21
Theory : general
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