Nuprl Lemma : fun2listCantor
∀n:ℕ. ∀f:ℕn ⟶ 𝔹. ∃l:𝔹 List. ((||l|| = n ∈ ℤ) ∧ (f = (λx.l[x]) ∈ (ℕn ⟶ 𝔹)))
Proof
Definitions occuring in Statement :
select: L[n],
length: ||as||,
list: T List,
int_seg: {i..j-},
nat: ℕ,
bool: 𝔹,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
and: P ∧ Q,
lambda: λx.A[x],
function: x:A ⟶ B[x],
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
prop: ℙ,
subtype_rel: A ⊆r B,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
decidable: Dec(P),
or: P ∨ Q,
ge: i ≥ j ,
select: L[n],
nil: [],
it: ⋅,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
cand: A c∧ B,
le: A ≤ B,
less_than': less_than'(a;b),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
subtract: n - m,
true: True,
label: ...$L... t,
squash: ↓T
Lemmas referenced :
int_seg_wf,
int_seg_properties,
full-omega-unsat,
intformand_wf,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
bool_wf,
subtract_wf,
list_wf,
length_wf_nat,
set_subtype_base,
le_wf,
int_subtype_base,
select_wf,
decidable__le,
intformnot_wf,
int_formula_prop_not_lemma,
decidable__lt,
itermSubtract_wf,
intformeq_wf,
int_term_value_subtract_lemma,
int_formula_prop_eq_lemma,
istype-less_than,
primrec-wf2,
all_wf,
exists_wf,
equal-wf-base,
equal_wf,
nat_properties,
istype-nat,
nil_wf,
length_of_nil_lemma,
stuck-spread,
istype-base,
subtype_rel_function,
int_seg_subtype,
istype-false,
not-le-2,
condition-implies-le,
add-associates,
minus-add,
minus-one-mul,
add-swap,
minus-one-mul-top,
add-mul-special,
zero-mul,
add-zero,
add-commutes,
le-add-cancel2,
subtype_rel_self,
append_wf,
cons_wf,
istype-le,
length-append,
length_of_cons_lemma,
decidable__equal_int,
itermAdd_wf,
int_term_value_add_lemma,
length_wf,
squash_wf,
true_wf,
istype-universe,
less_than_wf,
iff_weakening_equal,
select_append_back,
select-cons-hd,
select_append_front
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
cut,
thin,
Error :functionIsType,
Error :universeIsType,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
natural_numberEquality,
hypothesis,
hypothesisEquality,
setElimination,
rename,
productElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
Error :dependent_pairFormation_alt,
Error :lambdaEquality_alt,
int_eqEquality,
dependent_functionElimination,
Error :isect_memberEquality_alt,
voidElimination,
sqequalRule,
independent_pairFormation,
Error :productIsType,
Error :equalityIstype,
Error :inhabitedIsType,
applyEquality,
intEquality,
closedConclusion,
because_Cache,
baseApply,
baseClosed,
sqequalBase,
equalitySymmetry,
equalityTransitivity,
unionElimination,
Error :setIsType,
functionEquality,
productEquality,
Error :functionExtensionality_alt,
addEquality,
minusEquality,
multiplyEquality,
Error :dependent_set_memberEquality_alt,
functionExtensionality,
imageElimination,
instantiate,
universeEquality,
imageMemberEquality,
Error :equalityIsType1
Latex:
\mforall{}n:\mBbbN{}. \mforall{}f:\mBbbN{}n {}\mrightarrow{} \mBbbB{}. \mexists{}l:\mBbbB{} List. ((||l|| = n) \mwedge{} (f = (\mlambda{}x.l[x])))
Date html generated:
2019_06_20-PM-02_53_05
Last ObjectModification:
2018_11_22-AM-09_59_24
Theory : continuity
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