Nuprl Lemma : rset-member_wf
∀[A:Set(ℝ)]. ∀[x:ℝ]. (x ∈ A ∈ ℙ)
Proof
Definitions occuring in Statement :
rset-member: x ∈ A,
rset: Set(ℝ),
real: ℝ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
rset-member: x ∈ A,
rset: Set(ℝ),
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
so_apply: x[s],
all: ∀x:A. B[x]
Lemmas referenced :
real_wf,
set_wf,
all_wf,
req_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
applyEquality,
setElimination,
thin,
rename,
hypothesisEquality,
sqequalHypSubstitution,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
isect_memberEquality,
isectElimination,
because_Cache,
instantiate,
functionEquality,
cumulativity,
universeEquality,
lambdaEquality
Latex:
\mforall{}[A:Set(\mBbbR{})]. \mforall{}[x:\mBbbR{}]. (x \mmember{} A \mmember{} \mBbbP{})
Date html generated:
2016_05_18-AM-08_07_32
Last ObjectModification:
2015_12_28-AM-01_13_53
Theory : reals
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