Nuprl Lemma : l_before_antisymmetry

[T:Type]. ∀[l:T List]. ∀[x,y:T].  before x ∈ l) supposing (x before y ∈ and no_repeats(T;l))


Definitions occuring in Statement :  l_before: before y ∈ l no_repeats: no_repeats(T;l) list: List uimplies: supposing a uall: [x:A]. B[x] not: ¬A universe: Type
Definitions unfolded in proof :  l_before: before y ∈ l uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a not: ¬A implies:  Q false: False prop: all: x:A. B[x] or: P ∨ Q and: P ∧ Q cand: c∧ B guard: {T} iff: ⇐⇒ Q rev_implies:  Q append: as bs so_lambda: so_lambda(x,y,z.t[x; y; z]) top: Top so_apply: x[s1;s2;s3] uiff: uiff(P;Q)
Lemmas referenced :  sublist_wf cons_wf nil_wf no_repeats_wf list_wf sublist_transitivity sublist_nil equal_wf or_wf member_wf cons_sublist_cons append_overlapping_sublists list_ind_cons_lemma list_ind_nil_lemma no_repeats_iff
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep Error :isect_memberFormation_alt,  introduction cut lambdaFormation thin because_Cache hypothesis sqequalHypSubstitution independent_functionElimination voidElimination extract_by_obid isectElimination hypothesisEquality lambdaEquality dependent_functionElimination Error :universeIsType,  isect_memberEquality equalityTransitivity equalitySymmetry Error :inhabitedIsType,  universeEquality inlFormation independent_pairFormation inrFormation productElimination productEquality cumulativity unionElimination promote_hyp independent_isectElimination voidEquality

\mforall{}[T:Type].  \mforall{}[l:T  List].  \mforall{}[x,y:T].    (\mneg{}y  before  x  \mmember{}  l)  supposing  (x  before  y  \mmember{}  l  and  no\_repeats(T;l))

Date html generated: 2019_06_20-PM-01_24_17
Last ObjectModification: 2018_09_26-PM-05_27_58

Theory : list_1

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