Nuprl Lemma : null_member
∀[T:Type]. ∀[L:T List]. ∀[x:T]. ¬(x ∈ L) supposing ↑null(L)
Proof
Definitions occuring in Statement :
l_member: (x ∈ l),
null: null(as),
list: T List,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ
Lemmas referenced :
assert_elim,
null_wf,
member-implies-null-eq-bfalse,
btrue_neq_bfalse,
l_member_wf,
assert_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
voidElimination,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
because_Cache,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. \mforall{}[x:T]. \mneg{}(x \mmember{} L) supposing \muparrow{}null(L)
Date html generated:
2016_05_14-AM-07_39_34
Last ObjectModification:
2015_12_26-PM-02_13_21
Theory : list_1
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