Nuprl Lemma : fset-intersection_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[a,b:fset(T)]. (a ⋂ b ∈ fset(T))
Proof
Definitions occuring in Statement :
fset-intersection: a ⋂ b,
fset: fset(T),
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
fset-intersection: a ⋂ b,
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
fset-filter_wf,
deq-fset-member_wf,
fset_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[a,b:fset(T)]. (a \mcap{} b \mmember{} fset(T))
Date html generated:
2016_05_14-PM-03_40_02
Last ObjectModification:
2015_12_26-PM-06_41_19
Theory : finite!sets
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