Nuprl Lemma : closed-rset_wf
∀[A:ℝ ⟶ ℙ]. (closed-rset(A) ∈ ℙ)
Proof
Definitions occuring in Statement :
closed-rset: closed-rset(A),
real: ℝ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
closed-rset: closed-rset(A),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
all_wf,
real_wf,
member-closure_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
functionEquality,
hypothesisEquality,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
cumulativity,
universeEquality
Latex:
\mforall{}[A:\mBbbR{} {}\mrightarrow{} \mBbbP{}]. (closed-rset(A) \mmember{} \mBbbP{})
Date html generated:
2016_05_18-AM-08_11_08
Last ObjectModification:
2015_12_28-AM-01_16_41
Theory : reals
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