Nuprl Lemma : union-sep_wf
∀[ss1,ss2:SeparationSpace]. ∀[p,q:Point(ss1) + Point(ss2)]. (union-sep(ss1;ss2;p;q) ∈ ℙ)
Proof
Definitions occuring in Statement :
union-sep: union-sep(ss1;ss2;p;q),
ss-point: Point(ss),
separation-space: SeparationSpace,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
union: left + right
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
union-sep: union-sep(ss1;ss2;p;q),
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
ss-sep_wf,
true_wf,
equal_wf,
ss-point_wf,
separation-space_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
thin,
because_Cache,
lambdaFormation,
unionElimination,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
unionEquality,
isect_memberEquality
Latex:
\mforall{}[ss1,ss2:SeparationSpace]. \mforall{}[p,q:Point(ss1) + Point(ss2)]. (union-sep(ss1;ss2;p;q) \mmember{} \mBbbP{})
Date html generated:
2019_10_31-AM-07_26_57
Last ObjectModification:
2019_03_19-PM-03_41_40
Theory : constructive!algebra
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