Nuprl Lemma : decidable__l_contains
∀[T:Type]. ((∀x,y:T. Dec(x = y ∈ T)) ⇒ (∀A,B:T List. Dec(A ⊆ B)))
Proof
Definitions occuring in Statement :
l_contains: A ⊆ B,
list: T List,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
l_contains: A ⊆ B,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
all: ∀x:A. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
decidable__l_all,
l_member_wf,
decidable__l_member,
set_wf,
list_wf,
all_wf,
decidable_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
lambdaEquality,
setElimination,
rename,
hypothesis,
setEquality,
independent_functionElimination,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. ((\mforall{}x,y:T. Dec(x = y)) {}\mRightarrow{} (\mforall{}A,B:T List. Dec(A \msubseteq{} B)))
Date html generated:
2016_05_14-AM-07_54_11
Last ObjectModification:
2015_12_26-PM-04_48_22
Theory : list_1
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