Nuprl Lemma : sq_stable__fset-member
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[a:T]. ∀[s:fset(T)]. SqStable(a ∈ s)
Proof
Definitions occuring in Statement :
fset-member: a ∈ s,
fset: fset(T),
deq: EqDecider(T),
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T,
prop: ℙ
Lemmas referenced :
squash_wf,
fset-member_wf,
fset-member_witness,
fset_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalHypSubstitution,
imageElimination,
hypothesis,
extract_by_obid,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
independent_functionElimination,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[a:T]. \mforall{}[s:fset(T)]. SqStable(a \mmember{} s)
Date html generated:
2017_02_20-AM-10_48_40
Last ObjectModification:
2017_02_02-PM-07_20_04
Theory : finite!sets
Home
Index