Nuprl Lemma : eq_ext2Cantor
∀n:ℕ. ∀s:ℕn ⟶ 𝔹. ∀d1,d2:𝔹. (ext2Cantor(n;s;d1) = ext2Cantor(n;s;d2) ∈ (ℕn ⟶ 𝔹))
Proof
Definitions occuring in Statement :
ext2Cantor: ext2Cantor(n;f;d),
int_seg: {i..j-},
nat: ℕ,
bool: 𝔹,
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
ext2Cantor: ext2Cantor(n;f;d),
uall: ∀[x:A]. B[x],
int_seg: {i..j-},
nat: ℕ,
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
ge: i ≥ j ,
lelt: i ≤ j < k,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top
Lemmas referenced :
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
int_seg_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
less_than_wf,
int_seg_properties,
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformless_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_formula_prop_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
because_Cache,
lambdaEquality,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
sqequalRule,
applyEquality,
functionExtensionality,
natural_numberEquality,
dependent_pairFormation,
equalityTransitivity,
equalitySymmetry,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
voidElimination,
int_eqEquality,
intEquality,
isect_memberEquality,
voidEquality,
independent_pairFormation,
computeAll
Latex:
\mforall{}n:\mBbbN{}. \mforall{}s:\mBbbN{}n {}\mrightarrow{} \mBbbB{}. \mforall{}d1,d2:\mBbbB{}. (ext2Cantor(n;s;d1) = ext2Cantor(n;s;d2))
Date html generated:
2017_04_17-AM-09_57_45
Last ObjectModification:
2017_02_27-PM-05_51_05
Theory : continuity
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