Nuprl Lemma : comem_wf
∀[s,x:coSet{i:l}]. (comem{i:l}(x;s) ∈ ℙ')
Proof
Definitions occuring in Statement :
comem: comem{i:l}(x;s),
coSet: coSet{i:l},
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
comem: comem{i:l}(x;s),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
set-item_wf,
coSet_wf,
equal_wf,
set-dom_wf,
exists_wf
Rules used in proof :
because_Cache,
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
lambdaEquality,
hypothesis,
hypothesisEquality,
cumulativity,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
instantiate,
thin,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[s,x:coSet\{i:l\}]. (comem\{i:l\}(x;s) \mmember{} \mBbbP{}')
Date html generated:
2018_07_29-AM-09_50_11
Last ObjectModification:
2018_07_11-PM-10_42_54
Theory : constructive!set!theory
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