Nuprl Lemma : sorted-by-strict-no_repeats

[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. ∀[L:T List].  (no_repeats(T;L)) supposing (sorted-by(R;L) and (∀a:T. (R a))))


Definitions occuring in Statement :  sorted-by: sorted-by(R;L) no_repeats: no_repeats(T;l) list: List uimplies: supposing a uall: [x:A]. B[x] prop: all: x:A. B[x] not: ¬A apply: a function: x:A ⟶ B[x] universe: Type
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a no_repeats: no_repeats(T;l) not: ¬A implies:  Q false: False prop: nat: ge: i ≥  all: x:A. B[x] decidable: Dec(P) or: P ∨ Q satisfiable_int_formula: satisfiable_int_formula(fmla) exists: x:A. B[x] top: Top and: P ∧ Q subtype_rel: A ⊆B so_lambda: λ2x.t[x] so_apply: x[s] guard: {T} int_seg: {i..j-} lelt: i ≤ j < k le: A ≤ B sorted-by: sorted-by(R;L)
Lemmas referenced :  equal_wf select_wf 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 not_wf nat_wf less_than_wf length_wf no_repeats_witness sorted-by_wf subtype_rel_dep_function l_member_wf subtype_rel_self set_wf all_wf list_wf decidable__lt lelt_wf decidable__equal_int intformeq_wf intformless_wf int_formula_prop_eq_lemma int_formula_prop_less_lemma le_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lambdaFormation thin sqequalHypSubstitution independent_functionElimination voidElimination because_Cache hypothesis extract_by_obid isectElimination setElimination rename independent_isectElimination hypothesisEquality dependent_functionElimination natural_numberEquality unionElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality isect_memberEquality voidEquality sqequalRule independent_pairFormation computeAll equalityTransitivity equalitySymmetry cumulativity applyEquality instantiate functionEquality universeEquality setEquality functionExtensionality hyp_replacement applyLambdaEquality dependent_set_memberEquality productElimination

\mforall{}[T:Type].  \mforall{}[R:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].  \mforall{}[L:T  List].
    (no\_repeats(T;L))  supposing  (sorted-by(R;L)  and  (\mforall{}a:T.  (\mneg{}(R  a  a))))

Date html generated: 2017_04_17-AM-07_43_46
Last ObjectModification: 2017_02_27-PM-04_16_18

Theory : list_1

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