Nuprl Lemma : remove-repeats-l_contains-iff
∀[T:Type]. ∀eq:EqDecider(T). ∀as,bs:T List. (as ⊆ bs ⇐⇒ remove-repeats(eq;as) ⊆ remove-repeats(eq;bs))
Proof
Definitions occuring in Statement :
remove-repeats: remove-repeats(eq;L),
l_contains: A ⊆ B,
list: T List,
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
l_subset: l_subset(T;as;bs),
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
rev_implies: P ⇐ Q,
guard: {T}
Lemmas referenced :
l_member_wf,
all_wf,
member-remove-repeats,
remove-repeats_wf,
iff_wf,
l_subset-l_contains,
l_contains_wf,
l_subset_wf,
list_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
independent_pairFormation,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
lambdaEquality,
functionEquality,
because_Cache,
addLevel,
productElimination,
impliesFunctionality,
allFunctionality,
dependent_functionElimination,
independent_functionElimination,
allLevelFunctionality,
impliesLevelFunctionality,
universeEquality
Latex:
\mforall{}[T:Type]
\mforall{}eq:EqDecider(T). \mforall{}as,bs:T List. (as \msubseteq{} bs \mLeftarrow{}{}\mRightarrow{} remove-repeats(eq;as) \msubseteq{} remove-repeats(eq;bs))
Date html generated:
2016_05_14-PM-03_26_13
Last ObjectModification:
2015_12_26-PM-06_22_59
Theory : decidable!equality
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