Nuprl Lemma : decidable__l_member
∀[A:Type]. ∀x:A. ((∀x,y:A. Dec(x = y ∈ A)) ⇒ (∀L:A List. Dec((x ∈ L))))
Proof
Definitions occuring in Statement :
l_member: (x ∈ l),
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 :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
prop: ℙ
Lemmas referenced :
list_induction,
decidable_wf,
l_member_wf,
list_wf,
decidable_functionality,
nil_wf,
false_wf,
nil_member,
decidable__false,
cons_wf,
or_wf,
equal_wf,
cons_member,
decidable__or,
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
thin,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
because_Cache,
sqequalRule,
lambdaEquality,
hypothesisEquality,
hypothesis,
independent_functionElimination,
dependent_functionElimination,
productElimination,
rename,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}x:A. ((\mforall{}x,y:A. Dec(x = y)) {}\mRightarrow{} (\mforall{}L:A List. Dec((x \mmember{} L))))
Date html generated:
2016_05_14-AM-06_43_14
Last ObjectModification:
2015_12_26-PM-00_28_44
Theory : list_0
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