Nuprl Lemma : baire_eq_from_wf
∀[a:ℕ ⟶ ℕ]. ∀[k:ℕ]. (baire_eq_from(a;k) ∈ ℕ ⟶ ℕ)
Proof
Definitions occuring in Statement :
baire_eq_from: baire_eq_from(a;k),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
nat: ℕ,
baire_eq_from: baire_eq_from(a;k),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
nat_wf,
lt_int_wf,
ifthenelse_wf
Rules used in proof :
functionEquality,
because_Cache,
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
functionExtensionality,
applyEquality,
hypothesis,
hypothesisEquality,
rename,
setElimination,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
lambdaEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[a:\mBbbN{} {}\mrightarrow{} \mBbbN{}]. \mforall{}[k:\mBbbN{}]. (baire\_eq\_from(a;k) \mmember{} \mBbbN{} {}\mrightarrow{} \mBbbN{})
Date html generated:
2017_04_21-AM-11_24_21
Last ObjectModification:
2017_04_20-PM-06_39_47
Theory : continuity
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