Nuprl Lemma : l_contains-no_repeats-length

[T:Type]. ∀[as,bs:T List].  (||as|| ≤ ||bs||) supposing (as ⊆ bs and no_repeats(T;as))


Definitions occuring in Statement :  l_contains: A ⊆ B no_repeats: no_repeats(T;l) length: ||as|| list: List uimplies: supposing a uall: [x:A]. B[x] le: A ≤ B universe: Type
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a l_contains: A ⊆ B l_member: (x ∈ l) l_all: (∀x∈L.P[x]) exists: x:A. B[x] int_seg: {i..j-} subtype_rel: A ⊆B lelt: i ≤ j < k and: P ∧ Q ge: i ≥  guard: {T} all: x:A. B[x] prop: decidable: Dec(P) or: P ∨ Q nat: satisfiable_int_formula: satisfiable_int_formula(fmla) false: False implies:  Q not: ¬A top: Top le: A ≤ B so_lambda: λ2x.t[x] cand: c∧ B less_than: a < b squash: T so_apply: x[s] pi1: fst(t) inject: Inj(A;B;f) no_repeats: no_repeats(T;l) less_than': less_than'(a;b) true: True iff: ⇐⇒ Q rev_implies:  Q
Lemmas referenced :  injection_le length_wf_nat int_seg_wf length_wf non_neg_length int_seg_properties decidable__le lelt_wf nat_properties satisfiable-full-omega-tt intformand_wf intformle_wf itermConstant_wf itermVar_wf intformnot_wf int_formula_prop_and_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_not_lemma int_formula_prop_wf inject_wf less_than'_wf l_contains_wf no_repeats_wf list_wf exists_wf nat_wf less_than_wf equal_wf select_wf decidable__lt intformless_wf int_formula_prop_less_lemma all_wf decidable__equal_int_seg int_seg_subtype_nat false_wf intformeq_wf int_formula_prop_eq_lemma squash_wf true_wf iff_weakening_equal le_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalHypSubstitution sqequalRule hypothesis promote_hyp thin productElimination extract_by_obid isectElimination cumulativity hypothesisEquality independent_isectElimination dependent_pairFormation functionExtensionality dependent_set_memberEquality applyEquality natural_numberEquality because_Cache independent_pairFormation setElimination rename dependent_functionElimination unionElimination equalityTransitivity equalitySymmetry applyLambdaEquality lambdaEquality int_eqEquality intEquality isect_memberEquality voidElimination voidEquality computeAll independent_pairEquality axiomEquality universeEquality productEquality imageElimination lambdaFormation independent_functionElimination imageMemberEquality baseClosed

\mforall{}[T:Type].  \mforall{}[as,bs:T  List].    (||as||  \mleq{}  ||bs||)  supposing  (as  \msubseteq{}  bs  and  no\_repeats(T;as))

Date html generated: 2017_04_17-AM-07_29_44
Last ObjectModification: 2017_02_27-PM-04_07_44

Theory : list_1

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