Nuprl Lemma : enum-fin-seq_wf
∀[m:ℕ]. (enum-fin-seq(m) ∈ ℕ ⟶ 𝔹 List(2^m))
Proof
Definitions occuring in Statement :
enum-fin-seq: enum-fin-seq(m),
exp: i^n,
list_n: A List(n),
nat: ℕ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
list_n: A List(n),
prop: ℙ,
enum-fin-seq: enum-fin-seq(m),
nat: ℕ,
int_seg: {i..j-},
false: False,
implies: P ⇒ Q,
not: ¬A,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
all: ∀x:A. B[x],
top: Top,
and: P ∧ Q,
decidable: Dec(P),
or: P ∨ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
nat_plus: ℕ+,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
equal_wf,
length_wf,
nat_wf,
bool_wf,
exp_wf2,
primrec_wf,
list_wf,
cons_wf,
btrue_wf,
nil_wf,
append_wf,
map_wf,
bfalse_wf,
int_seg_wf,
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
less_than_wf,
exp0_lemma,
decidable__le,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
primrec0_lemma,
length_of_cons_lemma,
length_of_nil_lemma,
primrec-unroll,
eq_int_wf,
eqtt_to_assert,
assert_of_eq_int,
intformeq_wf,
int_formula_prop_eq_lemma,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
length-append,
map-length,
two-mul,
exp_step,
squash_wf,
true_wf,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
dependent_set_memberEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
functionEquality,
hypothesis,
hypothesisEquality,
natural_numberEquality,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
lambdaEquality,
int_eqEquality,
setElimination,
rename,
applyEquality,
functionExtensionality,
intWeakElimination,
lambdaFormation,
independent_isectElimination,
dependent_pairFormation,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
unionElimination,
equalityElimination,
productElimination,
promote_hyp,
instantiate,
cumulativity,
imageElimination,
universeEquality,
multiplyEquality,
imageMemberEquality,
baseClosed
Latex:
\mforall{}[m:\mBbbN{}]. (enum-fin-seq(m) \mmember{} \mBbbN{} {}\mrightarrow{} \mBbbB{} List(2\^{}m))
Date html generated:
2017_04_20-AM-07_22_34
Last ObjectModification:
2017_02_27-PM-05_58_24
Theory : continuity
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