### Nuprl Lemma : no_repeats_member

`∀[T:Type]. ∀L:T List. ∀x:T.  (x ∈ L) `` (x ∈! L) supposing no_repeats(T;L)`

Proof

Definitions occuring in Statement :  l_member!: `(x ∈! l)` no_repeats: `no_repeats(T;l)` l_member: `(x ∈ l)` list: `T List` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` implies: `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]` uimplies: `b supposing a` prop: `ℙ` implies: `P `` Q` so_apply: `x[s]` not: `¬A` false: `False` iff: `P `⇐⇒` Q` and: `P ∧ Q` rev_implies: `P `` Q` uiff: `uiff(P;Q)` or: `P ∨ Q` cand: `A c∧ B` guard: `{T}`
Lemmas referenced :  list_induction all_wf isect_wf no_repeats_wf l_member_wf l_member!_wf list_wf no_repeats_witness nil_wf null_nil_lemma btrue_wf member-implies-null-eq-bfalse btrue_neq_bfalse cons_wf cons_member cons_member! no_repeats_cons not_wf equal_wf and_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation lambdaFormation cut thin introduction extract_by_obid sqequalHypSubstitution isectElimination hypothesisEquality sqequalRule lambdaEquality cumulativity hypothesis functionEquality independent_functionElimination because_Cache rename independent_isectElimination equalityTransitivity equalitySymmetry voidElimination dependent_functionElimination universeEquality productElimination unionElimination inlFormation independent_pairFormation productEquality inrFormation hyp_replacement dependent_set_memberEquality applyLambdaEquality setElimination

Latex:
\mforall{}[T:Type].  \mforall{}L:T  List.  \mforall{}x:T.    (x  \mmember{}  L)  {}\mRightarrow{}  (x  \mmember{}!  L)  supposing  no\_repeats(T;L)

Date html generated: 2017_04_17-AM-07_50_29
Last ObjectModification: 2017_02_27-PM-04_23_34

Theory : list_1

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