### Nuprl Lemma : no_repeats_append

`∀[T:Type]. ∀[l1,l2:T List].  l_disjoint(T;l1;l2) supposing no_repeats(T;l1 @ l2)`

Proof

Definitions occuring in Statement :  l_disjoint: `l_disjoint(T;l1;l2)` no_repeats: `no_repeats(T;l)` append: `as @ bs` list: `T List` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` universe: `Type`
Definitions unfolded in proof :  l_disjoint: `l_disjoint(T;l1;l2)` no_repeats: `no_repeats(T;l)` uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` all: `∀x:A. B[x]` not: `¬A` implies: `P `` Q` false: `False` l_member: `(x ∈ l)` and: `P ∧ Q` exists: `∃x:A. B[x]` cand: `A c∧ B` prop: `ℙ` so_lambda: `λ2x.t[x]` nat: `ℕ` top: `Top` ge: `i ≥ j ` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` so_apply: `x[s]` less_than: `a < b` squash: `↓T` guard: `{T}` int_seg: `{i..j-}` lelt: `i ≤ j < k` le: `A ≤ B` true: `True` subtype_rel: `A ⊆r B` iff: `P `⇐⇒` Q` rev_implies: `P `` Q`
Lemmas referenced :  l_member_wf uall_wf nat_wf isect_wf less_than_wf length_wf append_wf not_wf equal_wf select_wf length-append nat_properties decidable__le satisfiable-full-omega-tt intformand_wf intformnot_wf intformle_wf itermConstant_wf itermVar_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_wf list_wf itermAdd_wf intformless_wf int_term_value_add_lemma int_formula_prop_less_lemma le_wf decidable__lt intformeq_wf int_formula_prop_eq_lemma squash_wf true_wf select_append_front lelt_wf iff_weakening_equal select_append_back add-subtract-cancel
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut lambdaFormation thin sqequalHypSubstitution productElimination because_Cache hypothesis independent_functionElimination voidElimination productEquality extract_by_obid isectElimination cumulativity hypothesisEquality lambdaEquality dependent_functionElimination setElimination rename independent_isectElimination isect_memberEquality voidEquality natural_numberEquality unionElimination dependent_pairFormation int_eqEquality intEquality independent_pairFormation computeAll equalityTransitivity equalitySymmetry universeEquality dependent_set_memberEquality addEquality imageElimination applyLambdaEquality applyEquality imageMemberEquality baseClosed hyp_replacement

Latex:
\mforall{}[T:Type].  \mforall{}[l1,l2:T  List].    l\_disjoint(T;l1;l2)  supposing  no\_repeats(T;l1  @  l2)

Date html generated: 2017_04_17-AM-07_28_47
Last ObjectModification: 2017_02_27-PM-04_07_02

Theory : list_1

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