Nuprl Lemma : deq-member_wf
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[L:A List]. ∀[x:A]. (x ∈b L ∈ 𝔹)
Proof
Definitions occuring in Statement :
deq-member: x ∈b L,
list: T List,
deq: EqDecider(T),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
deq-member: x ∈b L,
uall: ∀[x:A]. B[x],
member: t ∈ T,
deq: EqDecider(T)
Lemmas referenced :
reduce_wf,
bool_wf,
bor_wf,
bfalse_wf,
list_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
applyEquality,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[L:A List]. \mforall{}[x:A]. (x \mmember{}\msubb{} L \mmember{} \mBbbB{})
Date html generated:
2016_05_14-AM-06_30_19
Last ObjectModification:
2015_12_26-PM-00_39_30
Theory : list_0
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