Nuprl Lemma : list-diff_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[as,bs:T List]. (as-bs ∈ T List)
Proof
Definitions occuring in Statement :
list-diff: as-bs,
list: T List,
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
list-diff: as-bs,
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
prop: ℙ
Lemmas referenced :
filter_wf5,
l_member_wf,
bnot_wf,
deq-member_wf,
list_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
lambdaEquality,
lambdaFormation,
hypothesis,
setElimination,
rename,
because_Cache,
setEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[as,bs:T List]. (as-bs \mmember{} T List)
Date html generated:
2016_05_14-PM-03_29_32
Last ObjectModification:
2015_12_26-PM-06_24_46
Theory : decidable!equality
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