Nuprl Lemma : member-closure_wf
∀[A:ℝ ⟶ ℙ]. ∀[y:ℝ]. (y ∈ closure(A) ∈ ℙ)
Proof
Definitions occuring in Statement :
member-closure: y ∈ closure(A),
real: ℝ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
member-closure: y ∈ closure(A),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ
Lemmas referenced :
exists_wf,
nat_wf,
real_wf,
and_wf,
converges-to_wf,
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
hypothesis,
lambdaEquality,
applyEquality,
hypothesisEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
cumulativity,
universeEquality
Latex:
\mforall{}[A:\mBbbR{} {}\mrightarrow{} \mBbbP{}]. \mforall{}[y:\mBbbR{}]. (y \mmember{} closure(A) \mmember{} \mBbbP{})
Date html generated:
2016_05_18-AM-08_10_54
Last ObjectModification:
2015_12_28-AM-01_16_26
Theory : reals
Home
Index