Nuprl Lemma : NoBallRetraction_wf
∀[n:ℕ]. (NoBallRetraction(n) ∈ ℙ)
Proof
Definitions occuring in Statement :
NoBallRetraction: NoBallRetraction(n),
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
NoBallRetraction: NoBallRetraction(n),
prop: ℙ,
exists: ∃x:A. B[x],
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
real-unit-ball: B(n),
subtype_rel: A ⊆r B
Lemmas referenced :
not_wf,
real-unit-ball_wf,
req-vec_wf,
req_wf,
real-vec-norm_wf,
int-to-real_wf,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
productEquality,
functionEquality,
hypothesisEquality,
hypothesis,
setElimination,
rename,
applyEquality,
lambdaEquality_alt,
inhabitedIsType,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
because_Cache,
axiomEquality
Latex:
\mforall{}[n:\mBbbN{}]. (NoBallRetraction(n) \mmember{} \mBbbP{})
Date html generated:
2019_10_30-AM-11_29_41
Last ObjectModification:
2019_07_08-PM-09_28_43
Theory : real!vectors
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