Nuprl Lemma : DegreeExists_wf
∀[n:ℕ]. (DegreeExists(n) ∈ ℙ)
Proof
Definitions occuring in Statement :
DegreeExists: DegreeExists(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,
DegreeExists: DegreeExists(n),
prop: ℙ,
exists: ∃x:A. B[x],
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
sphere-map: sphere-map(n),
subtype_rel: A ⊆r B
Lemmas referenced :
sphere-map_wf,
sphere-map-eq_wf,
equal-wf-base,
int_subtype_base,
real-unit-sphere_wf,
const-sphere-map_wf,
id-sphere-map_wf,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
productEquality,
functionEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
intEquality,
setElimination,
rename,
applyEquality,
baseClosed,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[n:\mBbbN{}]. (DegreeExists(n) \mmember{} \mBbbP{})
Date html generated:
2019_10_30-AM-11_30_11
Last ObjectModification:
2019_08_06-AM-11_41_55
Theory : real!vectors
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