### Nuprl Lemma : remove-repeats-length-no-repeats

`∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[L:T List].  ||remove-repeats(eq;L)|| = ||L|| ∈ ℤ supposing no_repeats(T;L)`

Proof

Definitions occuring in Statement :  remove-repeats: `remove-repeats(eq;L)` no_repeats: `no_repeats(T;l)` length: `||as||` list: `T List` deq: `EqDecider(T)` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` int: `ℤ` universe: `Type` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` so_lambda: `λ2x.t[x]` implies: `P `` Q` prop: `ℙ` so_apply: `x[s]` all: `∀x:A. B[x]` uimplies: `b supposing a` top: `Top` uiff: `uiff(P;Q)` and: `P ∧ Q` append: `as @ bs` so_lambda: `so_lambda(x,y,z.t[x; y; z])` so_apply: `x[s1;s2;s3]` squash: `↓T` true: `True` subtype_rel: `A ⊆r B` guard: `{T}` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` or: `P ∨ Q` not: `¬A` false: `False` decidable: `Dec(P)` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]`
Lemmas referenced :  list_induction no_repeats_wf equal_wf length_wf remove-repeats_wf list_wf deq_wf remove_repeats_nil_lemma length_of_nil_lemma nil_wf no_repeats_cons list_ind_cons_lemma list_ind_nil_lemma squash_wf true_wf remove-repeats-append cons_wf append_wf iff_weakening_equal remove-repeats-append-one-member length-append length_of_cons_lemma decidable__equal_int satisfiable-full-omega-tt intformand_wf intformnot_wf intformeq_wf itermVar_wf itermAdd_wf itermConstant_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_eq_lemma int_term_value_var_lemma int_term_value_add_lemma int_term_value_constant_lemma int_formula_prop_wf
Rules used in proof :  cut thin introduction extract_by_obid sqequalHypSubstitution sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isectElimination hypothesisEquality sqequalRule lambdaEquality functionEquality cumulativity hypothesis intEquality independent_functionElimination lambdaFormation rename because_Cache dependent_functionElimination universeEquality isect_memberFormation isect_memberEquality axiomEquality equalityTransitivity equalitySymmetry voidElimination voidEquality natural_numberEquality productElimination independent_isectElimination applyEquality imageElimination equalityUniverse levelHypothesis imageMemberEquality baseClosed unionElimination dependent_pairFormation int_eqEquality independent_pairFormation computeAll

Latex:
\mforall{}[T:Type].  \mforall{}[eq:EqDecider(T)].  \mforall{}[L:T  List].
||remove-repeats(eq;L)||  =  ||L||  supposing  no\_repeats(T;L)

Date html generated: 2017_04_17-AM-09_12_42
Last ObjectModification: 2017_02_27-PM-05_19_39

Theory : decidable!equality

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