Nuprl Lemma : transitive-set_wf
∀[s:coSet{i:l}]. (transitive-set(s) ∈ ℙ)
Proof
Definitions occuring in Statement :
transitive-set: transitive-set(s),
coSet: coSet{i:l},
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
prop: ℙ,
so_lambda: λ2x.t[x],
transitive-set: transitive-set(s),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
setmem_wf,
coSet_wf,
setsubset_wf,
allsetmem_wf
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
axiomEquality,
cumulativity,
setEquality,
hypothesis,
rename,
setElimination,
lambdaEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[s:coSet\{i:l\}]. (transitive-set(s) \mmember{} \mBbbP{})
Date html generated:
2018_07_29-AM-10_02_40
Last ObjectModification:
2018_07_18-PM-01_31_13
Theory : constructive!set!theory
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