Nuprl Lemma : baire2cantor_wf
∀[a:ℕ ⟶ ℕ]. (baire2cantor(a) ∈ ℕ ⟶ 𝔹)
Proof
Definitions occuring in Statement :
baire2cantor: baire2cantor(a),
nat: ℕ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
nat: ℕ,
subtype_rel: A ⊆r B,
baire2cantor: baire2cantor(a),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
btrue_wf,
bfalse_wf,
bool_wf,
nat-pred_wf,
nat_wf,
eq_int_wf,
ifthenelse_wf
Rules used in proof :
functionEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
because_Cache,
rename,
setElimination,
hypothesis,
hypothesisEquality,
functionExtensionality,
applyEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
lambdaEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[a:\mBbbN{} {}\mrightarrow{} \mBbbN{}]. (baire2cantor(a) \mmember{} \mBbbN{} {}\mrightarrow{} \mBbbB{})
Date html generated:
2017_04_21-AM-11_21_24
Last ObjectModification:
2017_04_20-PM-03_37_11
Theory : continuity
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