### Nuprl Lemma : list-diff-disjoint

`∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[as,bs:T List].  as-bs = as ∈ (T List) supposing l_disjoint(T;as;bs)`

Proof

Definitions occuring in Statement :  list-diff: `as-bs` l_disjoint: `l_disjoint(T;l1;l2)` list: `T List` deq: `EqDecider(T)` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` universe: `Type` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` so_lambda: `λ2x.t[x]` uimplies: `b supposing a` prop: `ℙ` so_apply: `x[s]` implies: `P `` Q` list-diff: `as-bs` all: `∀x:A. B[x]` top: `Top` l_disjoint: `l_disjoint(T;l1;l2)` not: `¬A` and: `P ∧ Q` cand: `A c∧ B` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` guard: `{T}` or: `P ∨ Q` false: `False` squash: `↓T` true: `True` subtype_rel: `A ⊆r B` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` ifthenelse: `if b then t else f fi ` bfalse: `ff` exists: `∃x:A. B[x]` sq_type: `SQType(T)` bnot: `¬bb` assert: `↑b`
Lemmas referenced :  list_induction uall_wf list_wf isect_wf l_disjoint_wf equal_wf list-diff_wf filter_nil_lemma nil_wf cons_wf deq_wf cons_member l_member_wf squash_wf true_wf list-diff-cons iff_weakening_equal deq-member_wf bool_wf eqtt_to_assert assert-deq-member eqff_to_assert bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut thin extract_by_obid sqequalHypSubstitution isectElimination hypothesisEquality sqequalRule lambdaEquality cumulativity hypothesis independent_functionElimination dependent_functionElimination isect_memberEquality voidElimination voidEquality axiomEquality equalityTransitivity equalitySymmetry because_Cache lambdaFormation rename independent_isectElimination universeEquality productElimination inrFormation independent_pairFormation productEquality applyEquality imageElimination natural_numberEquality imageMemberEquality baseClosed unionElimination equalityElimination dependent_pairFormation promote_hyp instantiate inlFormation

Latex:
\mforall{}[T:Type].  \mforall{}[eq:EqDecider(T)].  \mforall{}[as,bs:T  List].    as-bs  =  as  supposing  l\_disjoint(T;as;bs)

Date html generated: 2017_04_17-AM-09_13_17
Last ObjectModification: 2017_02_27-PM-05_20_31

Theory : decidable!equality

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