Nuprl Lemma : transmem_wf
∀[x,y:coSet{i:l}]. ((x ∈∈ y) ∈ ℙ')
Proof
Definitions occuring in Statement :
transmem: (x ∈∈ y),
coSet: coSet{i:l},
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
prop: ℙ,
infix_ap: x f y,
transmem: (x ∈∈ y),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
setmem_wf,
coSet_wf,
transitive-closure_wf
Rules used in proof :
because_Cache,
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesisEquality,
cumulativity,
lambdaEquality,
hypothesis,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
instantiate,
thin,
applyEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[x,y:coSet\{i:l\}]. ((x \mmember{}\mmember{} y) \mmember{} \mBbbP{}')
Date html generated:
2018_07_29-AM-10_03_21
Last ObjectModification:
2018_07_18-PM-11_36_14
Theory : constructive!set!theory
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