### Nuprl Lemma : l_contains-no_repeats-length

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

Proof

Definitions occuring in Statement :  l_contains: `A ⊆ B` no_repeats: `no_repeats(T;l)` length: `||as||` list: `T List` uimplies: `b 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: `b 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 ⊆r B` lelt: `i ≤ j < k` and: `P ∧ Q` ge: `i ≥ j ` guard: `{T}` all: `∀x:A. B[x]` prop: `ℙ` decidable: `Dec(P)` or: `P ∨ Q` nat: `ℕ` satisfiable_int_formula: `satisfiable_int_formula(fmla)` false: `False` implies: `P `` Q` not: `¬A` top: `Top` le: `A ≤ B` so_lambda: `λ2x.t[x]` cand: `A 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: `P `⇐⇒` Q` rev_implies: `P `` 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

Latex:
\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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