Nuprl Lemma : intersectionset_wf
∀[s:coSet{i:l}]. (⋂(s) ∈ coSet{i:l})
Proof
Definitions occuring in Statement :
intersectionset: ⋂(s),
coSet: coSet{i:l},
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
prop: ℙ,
so_lambda: λ2x.t[x],
intersectionset: ⋂(s),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
coSet_wf,
setmem_wf,
allsetmem_wf,
unionset_wf,
sub-set_wf
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
axiomEquality,
cumulativity,
setEquality,
rename,
setElimination,
lambdaEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[s:coSet\{i:l\}]. (\mcap{}(s) \mmember{} coSet\{i:l\})
Date html generated:
2018_07_29-AM-10_00_57
Last ObjectModification:
2018_07_18-PM-02_47_40
Theory : constructive!set!theory
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