### Nuprl Lemma : decidable__no_repeats

`∀[T:Type]. ((∀x,y:T.  Dec(x = y ∈ T)) `` (∀L:T List. Dec(no_repeats(T;L))))`

Proof

Definitions occuring in Statement :  no_repeats: `no_repeats(T;l)` list: `T List` decidable: `Dec(P)` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` implies: `P `` Q` universe: `Type` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` implies: `P `` Q` all: `∀x:A. B[x]` no_repeats: `no_repeats(T;l)` member: `t ∈ T` so_lambda: `λ2x.t[x]` prop: `ℙ` subtype_rel: `A ⊆r B` uimplies: `b supposing a` le: `A ≤ B` and: `P ∧ Q` less_than': `less_than'(a;b)` false: `False` not: `¬A` int_seg: `{i..j-}` guard: `{T}` lelt: `i ≤ j < k` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` top: `Top` less_than: `a < b` squash: `↓T` so_apply: `x[s]` nat: `ℕ` ge: `i ≥ j `
Lemmas referenced :  decidable__all_int_seg length_wf all_wf int_seg_wf not_wf equal_wf nat_wf int_seg_subtype_nat false_wf select_wf int_seg_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 decidable__lt intformless_wf int_formula_prop_less_lemma decidable__implies decidable__not decidable__equal_nat list_wf decidable_wf uall_wf isect_wf less_than_wf nat_properties lelt_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation lambdaFormation cut thin instantiate introduction extract_by_obid sqequalHypSubstitution dependent_functionElimination natural_numberEquality isectElimination cumulativity hypothesisEquality hypothesis sqequalRule lambdaEquality functionEquality applyEquality independent_isectElimination independent_pairFormation because_Cache setElimination rename productElimination unionElimination dependent_pairFormation int_eqEquality intEquality isect_memberEquality voidElimination voidEquality computeAll imageElimination independent_functionElimination universeEquality inlFormation inrFormation equalityTransitivity equalitySymmetry dependent_set_memberEquality

Latex:
\mforall{}[T:Type].  ((\mforall{}x,y:T.    Dec(x  =  y))  {}\mRightarrow{}  (\mforall{}L:T  List.  Dec(no\_repeats(T;L))))

Date html generated: 2018_05_21-PM-06_40_13
Last ObjectModification: 2017_07_26-PM-04_53_41

Theory : general

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