Nuprl Lemma : member_append

[T:Type]. ∀x:T. ∀l1,l2:T List.  ((x ∈ l1 l2) ⇐⇒ (x ∈ l1) ∨ (x ∈ l2))


Proof




Definitions occuring in Statement :  l_member: (x ∈ l) append: as bs list: List uall: [x:A]. B[x] all: x:A. B[x] iff: ⇐⇒ Q or: P ∨ Q universe: Type
Definitions unfolded in proof :  uall: [x:A]. B[x] all: x:A. B[x] member: t ∈ T so_lambda: λ2x.t[x] so_apply: x[s] implies:  Q append: as bs so_lambda: so_lambda(x,y,z.t[x; y; z]) top: Top so_apply: x[s1;s2;s3] iff: ⇐⇒ Q and: P ∧ Q guard: {T} or: P ∨ Q prop: rev_implies:  Q false: False
Lemmas referenced :  list_induction all_wf list_wf iff_wf l_member_wf append_wf or_wf list_ind_nil_lemma false_wf nil_member nil_wf list_ind_cons_lemma equal_wf cons_member cons_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation lambdaFormation cut thin lemma_by_obid sqequalHypSubstitution isectElimination because_Cache sqequalRule lambdaEquality hypothesisEquality hypothesis independent_functionElimination dependent_functionElimination isect_memberEquality voidElimination voidEquality independent_pairFormation inrFormation unionElimination addLevel allFunctionality productElimination impliesFunctionality orFunctionality rename inlFormation universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}x:T.  \mforall{}l1,l2:T  List.    ((x  \mmember{}  l1  @  l2)  \mLeftarrow{}{}\mRightarrow{}  (x  \mmember{}  l1)  \mvee{}  (x  \mmember{}  l2))



Date html generated: 2016_05_14-AM-06_42_08
Last ObjectModification: 2015_12_26-PM-00_29_36

Theory : list_0


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