Nuprl Lemma : rstar_wf
∀[x:ℝ]. ((x)* ∈ ℝ*)
Proof
Definitions occuring in Statement :
rstar: (x)*,
real*: ℝ*,
real: ℝ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rstar: (x)*,
subtype_rel: A ⊆r B,
real*: ℝ*,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
top: Top,
all: ∀x:A. B[x]
Lemmas referenced :
top_wf,
subtype_rel_dep_function,
real_wf,
nat_wf,
subtype_rel_self
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
hypothesisEquality,
extract_by_obid,
hypothesis,
applyEquality,
thin,
sqequalHypSubstitution,
isectElimination,
independent_isectElimination,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
lambdaFormation,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[x:\mBbbR{}]. ((x)* \mmember{} \mBbbR{}*)
Date html generated:
2018_05_22-PM-03_17_53
Last ObjectModification:
2017_10_06-PM-03_35_29
Theory : reals_2
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