Nuprl Lemma : setsubset_wf
∀[a,b:coSet{i:l}]. ((a ⊆ b) ∈ ℙ)
Proof
Definitions occuring in Statement :
setsubset: (a ⊆ b),
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],
setsubset: (a ⊆ b),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
coSet_wf,
setmem_wf,
allsetmem_wf
Rules used in proof :
because_Cache,
isect_memberEquality,
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{}[a,b:coSet\{i:l\}]. ((a \msubseteq{} b) \mmember{} \mBbbP{})
Date html generated:
2018_07_29-AM-10_01_11
Last ObjectModification:
2018_07_18-PM-01_27_16
Theory : constructive!set!theory
Home
Index