Nuprl Lemma : ext2Cantor_eq
∀[s:𝔹 List]. ∀[d:𝔹]. (ext2Cantor(||s||;λx.s[x];d) = extl2Cantor(s;d) ∈ (ℕ ⟶ 𝔹))
Proof
Definitions occuring in Statement :
extl2Cantor: extl2Cantor(s;b),
ext2Cantor: ext2Cantor(n;f;d),
select: L[n],
length: ||as||,
list: T List,
nat: ℕ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
function: x:A ⟶ B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
extl2Cantor: extl2Cantor(s;b),
ext2Cantor: ext2Cantor(n;f;d),
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,
hypothesisEquality,
hypothesis,
lambdaFormation,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
because_Cache,
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{}[d:\mBbbB{}]. (ext2Cantor(||s||;\mlambda{}x.s[x];d) = extl2Cantor(s;d))
Date html generated:
2017_04_17-AM-09_58_05
Last ObjectModification:
2017_02_27-PM-05_51_37
Theory : continuity
Home
Index