### 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

Home Index