Nuprl Lemma : extl2Cantor_wf
∀[s:𝔹 List]. ∀[b:𝔹]. (extl2Cantor(s;b) ∈ ℕ ⟶ 𝔹)
Proof
Definitions occuring in Statement :
extl2Cantor: extl2Cantor(s;b)
,
list: T List
,
nat: ℕ
,
bool: 𝔹
,
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
extl2Cantor: extl2Cantor(s;b)
,
nat: ℕ
,
all: ∀x:A. B[x]
,
implies: P
⇒ Q
,
bool: 𝔹
,
unit: Unit
,
it: ⋅
,
btrue: tt
,
ifthenelse: if b then t else f fi
,
uiff: uiff(P;Q)
,
and: P ∧ Q
,
uimplies: b supposing a
,
ge: i ≥ j
,
decidable: Dec(P)
,
or: P ∨ Q
,
satisfiable_int_formula: satisfiable_int_formula(fmla)
,
exists: ∃x:A. B[x]
,
false: False
,
not: ¬A
,
top: Top
,
prop: ℙ
,
bfalse: ff
Lemmas referenced :
lt_int_wf,
length_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
select_wf,
nat_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
equal_wf,
nat_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
because_Cache,
hypothesis,
hypothesisEquality,
lambdaFormation,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
dependent_functionElimination,
natural_numberEquality,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
axiomEquality
Latex:
\mforall{}[s:\mBbbB{} List]. \mforall{}[b:\mBbbB{}]. (extl2Cantor(s;b) \mmember{} \mBbbN{} {}\mrightarrow{} \mBbbB{})
Date html generated:
2017_04_17-AM-09_58_03
Last ObjectModification:
2017_02_27-PM-05_51_02
Theory : continuity
Home
Index