Nuprl Lemma : ext2Cantor_wf
∀[n:ℕ]. ∀[f:ℕn ⟶ 𝔹]. ∀[d:𝔹]. (ext2Cantor(n;f;d) ∈ ℕ ⟶ 𝔹)
Proof
Definitions occuring in Statement :
ext2Cantor: ext2Cantor(n;f;d),
int_seg: {i..j-},
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,
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,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
prop: ℙ,
bfalse: ff
Lemmas referenced :
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
int_seg_wf,
lelt_wf,
equal_wf,
nat_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,
lambdaFormation,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
applyEquality,
functionExtensionality,
hypothesisEquality,
natural_numberEquality,
dependent_set_memberEquality,
independent_pairFormation,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
isect_memberEquality,
functionEquality
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[f:\mBbbN{}n {}\mrightarrow{} \mBbbB{}]. \mforall{}[d:\mBbbB{}]. (ext2Cantor(n;f;d) \mmember{} \mBbbN{} {}\mrightarrow{} \mBbbB{})
Date html generated:
2017_04_17-AM-09_57_41
Last ObjectModification:
2017_02_27-PM-05_50_53
Theory : continuity
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