Nuprl Lemma : list-diff-subset
∀[T:Type]. ∀eq:EqDecider(T). ∀as,bs:T List. l_subset(T;as-bs;as)
Proof
Definitions occuring in Statement :
list-diff: as-bs,
l_subset: l_subset(T;as;bs),
list: T List,
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
l_subset: l_subset(T;as;bs),
implies: P ⇒ Q,
list-diff: as-bs,
member: t ∈ T,
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q
Lemmas referenced :
member_filter_2,
l_member_wf,
bnot_wf,
deq-member_wf,
list-diff_wf,
list_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
cut,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
lambdaEquality,
hypothesis,
setElimination,
rename,
cumulativity,
setEquality,
because_Cache,
productElimination,
independent_functionElimination,
sqequalRule,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}eq:EqDecider(T). \mforall{}as,bs:T List. l\_subset(T;as-bs;as)
Date html generated:
2016_05_14-PM-03_29_50
Last ObjectModification:
2015_12_26-PM-06_02_59
Theory : decidable!equality
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