Nuprl Lemma : union-ss_wf
∀[ss1,ss2:SeparationSpace]. (ss1 + ss2 ∈ SeparationSpace)
Proof
Definitions occuring in Statement :
union-ss: ss1 + ss2,
separation-space: SeparationSpace,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
union-ss: ss1 + ss2,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
false: False,
union-sep: union-sep(ss1;ss2;p;q),
prop: ℙ,
subtype_rel: A ⊆r B,
or: P ∨ Q,
true: True,
separation-space: SeparationSpace,
record+: record+,
record-select: r.x,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
btrue: tt,
ss-sep: x # y,
ss-point: Point(ss),
uimplies: b supposing a
Lemmas referenced :
mk-ss_wf,
ss-point_wf,
union-sep_wf,
ss-sep-irrefl,
subtype_rel_self,
istype-void,
separation-space_wf,
istype-true,
ss-sep_wf,
not_wf,
subtype_rel_function
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
unionEquality,
hypothesisEquality,
hypothesis,
dependent_set_memberEquality_alt,
lambdaEquality_alt,
inhabitedIsType,
unionIsType,
universeIsType,
sqequalRule,
lambdaFormation_alt,
unionElimination,
independent_functionElimination,
voidElimination,
because_Cache,
functionIsType,
applyEquality,
instantiate,
universeEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality_alt,
isectIsTypeImplies,
inlEquality_alt,
closedConclusion,
natural_numberEquality,
inrEquality_alt,
dependentIntersectionElimination,
dependentIntersectionEqElimination,
tokenEquality,
setEquality,
functionEquality,
cumulativity,
functionExtensionality,
independent_isectElimination
Latex:
\mforall{}[ss1,ss2:SeparationSpace]. (ss1 + ss2 \mmember{} SeparationSpace)
Date html generated:
2019_10_31-AM-07_27_03
Last ObjectModification:
2019_09_19-PM-04_11_40
Theory : constructive!algebra
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