Nuprl Lemma : is-infinitesmal_wf
∀[x:ℝ*]. (is-infinitesmal(x) ∈ ℙ)
Proof
Definitions occuring in Statement :
is-infinitesmal: is-infinitesmal(x),
real*: ℝ*,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
is-infinitesmal: is-infinitesmal(x),
so_lambda: λ2x.t[x],
nat_plus: ℕ+,
so_apply: x[s]
Lemmas referenced :
all_wf,
nat_plus_wf,
rless*_wf,
rmul*_wf,
rstar_wf,
int-to-real_wf,
rabs*_wf,
real*_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
setElimination,
rename,
hypothesisEquality,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[x:\mBbbR{}*]. (is-infinitesmal(x) \mmember{} \mBbbP{})
Date html generated:
2018_05_22-PM-09_28_52
Last ObjectModification:
2017_10_06-PM-03_48_02
Theory : reals_2
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