### Nuprl Lemma : l_index_wf

`∀[T:Type]. ∀[dT:EqDecider(T)]. ∀[L:T List]. ∀[x:T].  index(L;x) ∈ ℕ||L|| supposing (x ∈ L)`

Proof

Definitions occuring in Statement :  l_index: `index(L;x)` l_member: `(x ∈ l)` length: `||as||` list: `T List` deq: `EqDecider(T)` int_seg: `{i..j-}` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` member: `t ∈ T` natural_number: `\$n` universe: `Type`
Definitions unfolded in proof :  l_index: `index(L;x)` uall: `∀[x:A]. B[x]` member: `t ∈ T` deq: `EqDecider(T)` int_seg: `{i..j-}` uimplies: `b supposing a` guard: `{T}` lelt: `i ≤ j < k` and: `P ∧ Q` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` implies: `P `` Q` not: `¬A` top: `Top` prop: `ℙ` less_than: `a < b` squash: `↓T` l_member: `(x ∈ l)` nat: `ℕ` le: `A ≤ B` cand: `A c∧ B` eqof: `eqof(d)` uiff: `uiff(P;Q)` rev_uimplies: `rev_uimplies(P;Q)` ge: `i ≥ j `
Lemmas referenced :  nat_properties assert_wf safe-assert-deq lelt_wf deq_wf list_wf l_member_wf int_seg_wf int_formula_prop_less_lemma intformless_wf decidable__lt int_formula_prop_wf int_term_value_var_lemma int_term_value_constant_lemma int_formula_prop_le_lemma int_formula_prop_not_lemma int_formula_prop_and_lemma itermVar_wf itermConstant_wf intformle_wf intformnot_wf intformand_wf satisfiable-full-omega-tt decidable__le length_wf int_seg_properties select_wf length_wf_nat mu-bound
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis lambdaEquality applyEquality setElimination rename cumulativity independent_isectElimination natural_numberEquality productElimination dependent_functionElimination unionElimination dependent_pairFormation int_eqEquality intEquality isect_memberEquality voidElimination voidEquality sqequalRule independent_pairFormation computeAll because_Cache imageElimination universeEquality isect_memberFormation introduction axiomEquality equalityTransitivity equalitySymmetry dependent_set_memberEquality

Latex:
\mforall{}[T:Type].  \mforall{}[dT:EqDecider(T)].  \mforall{}[L:T  List].  \mforall{}[x:T].    index(L;x)  \mmember{}  \mBbbN{}||L||  supposing  (x  \mmember{}  L)

Date html generated: 2016_05_14-PM-03_31_54
Last ObjectModification: 2016_01_14-PM-11_20_23

Theory : decidable!equality

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