### Nuprl Lemma : member_null

`∀[T:Type]. ∀[L:T List]. ∀[x:T].  ¬↑null(L) supposing (x ∈ 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 assert_wf l_member_wf list_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :isect_memberFormation_alt,  introduction cut lambdaFormation thin hypothesis extract_by_obid sqequalHypSubstitution isectElimination hypothesisEquality independent_isectElimination equalityTransitivity equalitySymmetry independent_functionElimination voidElimination sqequalRule lambdaEquality dependent_functionElimination because_Cache Error :universeIsType,  isect_memberEquality universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[L:T  List].  \mforall{}[x:T].    \mneg{}\muparrow{}null(L)  supposing  (x  \mmember{}  L)

Date html generated: 2019_06_20-PM-01_20_12
Last ObjectModification: 2018_09_26-PM-05_20_48

Theory : list_1

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