### Nuprl Lemma : l_disjoint_nil_iff

`∀[A:Type]. ∀[L:A List].  (l_disjoint(A;L;[]) `⇐⇒` True)`

Proof

Definitions occuring in Statement :  l_disjoint: `l_disjoint(T;l1;l2)` nil: `[]` list: `T List` uall: `∀[x:A]. B[x]` iff: `P `⇐⇒` Q` true: `True` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` iff: `P `⇐⇒` Q` and: `P ∧ Q` implies: `P `` Q` true: `True` prop: `ℙ` rev_implies: `P `` Q` l_disjoint: `l_disjoint(T;l1;l2)` all: `∀x:A. B[x]` not: `¬A` false: `False`
Lemmas referenced :  l_disjoint_wf nil_wf l_disjoint_nil2 true_wf and_wf l_member_wf list_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut independent_pairFormation lambdaFormation natural_numberEquality lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis sqequalRule productElimination independent_pairEquality lambdaEquality dependent_functionElimination axiomEquality equalityTransitivity equalitySymmetry because_Cache isect_memberEquality voidElimination universeEquality

Latex:
\mforall{}[A:Type].  \mforall{}[L:A  List].    (l\_disjoint(A;L;[])  \mLeftarrow{}{}\mRightarrow{}  True)

Date html generated: 2016_05_14-AM-07_56_04
Last ObjectModification: 2015_12_26-PM-04_50_11

Theory : list_1

Home Index