Nuprl Lemma : real-separation_wf
∀[A,B:ℝ ⟶ ℙ]. (real-separation(x.A[x];y.B[y]) ∈ ℙ)
Proof
Definitions occuring in Statement :
real-separation: real-separation(x.A[x];y.B[y]),
real: ℝ,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
real-separation: real-separation(x.A[x];y.B[y]),
prop: ℙ,
and: P ∧ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
exists: ∃x:A. B[x],
or: P ∨ Q,
all: ∀x:A. B[x]
Lemmas referenced :
real-disjoint_wf,
real_wf,
exists_wf,
all_wf,
or_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
productEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
lambdaEquality,
applyEquality,
functionExtensionality,
hypothesisEquality,
hypothesis,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
universeEquality,
isect_memberEquality
Latex:
\mforall{}[A,B:\mBbbR{} {}\mrightarrow{} \mBbbP{}]. (real-separation(x.A[x];y.B[y]) \mmember{} \mBbbP{})
Date html generated:
2017_10_03-AM-10_01_05
Last ObjectModification:
2017_06_30-AM-10_53_57
Theory : reals
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