Nuprl Lemma : setmem_wf
∀[x,s:coSet{i:l}]. ((x ∈ s) ∈ ℙ)
Proof
Definitions occuring in Statement :
setmem: (x ∈ s),
coSet: coSet{i:l},
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
coSet: coSet{i:l},
so_apply: x[s],
so_lambda: λ2x.t[x],
setmem: (x ∈ s),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
coSet_wf,
coWmem_wf
Rules used in proof :
because_Cache,
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesis,
hypothesisEquality,
lambdaEquality,
universeEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[x,s:coSet\{i:l\}]. ((x \mmember{} s) \mmember{} \mBbbP{})
Date html generated:
2018_07_29-AM-09_49_59
Last ObjectModification:
2018_07_11-AM-11_21_35
Theory : constructive!set!theory
Home
Index