Nuprl Lemma : intersectionset_wf2
∀[s:Set{i:l}]. (⋂(s) ∈ Set{i:l})
Proof
Definitions occuring in Statement :
intersectionset: ⋂(s),
Set: Set{i:l},
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uimplies: b supposing a,
so_apply: x[s],
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
intersectionset: ⋂(s),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
unionset_wf,
coSet_wf,
Set_wf,
subtype_rel_set,
setmem_wf,
set-subtype-coSet,
allsetmem_wf,
unionset_wf2,
sub-set_wf2
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
axiomEquality,
setEquality,
rename,
setElimination,
independent_isectElimination,
because_Cache,
cumulativity,
instantiate,
applyEquality,
lambdaEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[s:Set\{i:l\}]. (\mcap{}(s) \mmember{} Set\{i:l\})
Date html generated:
2018_07_29-AM-10_01_00
Last ObjectModification:
2018_07_18-PM-02_47_49
Theory : constructive!set!theory
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