### Nuprl Lemma : select_l_interval

`∀[T:Type]. ∀[l:T List]. ∀[i:ℕ||l||]. ∀[j:ℕi + 1]. ∀[x:ℕi - j].  (l_interval(l;j;i)[x] = l[j + x] ∈ T)`

Proof

Definitions occuring in Statement :  l_interval: `l_interval(l;j;i)` select: `L[n]` length: `||as||` list: `T List` int_seg: `{i..j-}` uall: `∀[x:A]. B[x]` subtract: `n - m` add: `n + m` natural_number: `\$n` universe: `Type` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` l_interval: `l_interval(l;j;i)` squash: `↓T` prop: `ℙ` nat: `ℕ` int_seg: `{i..j-}` guard: `{T}` lelt: `i ≤ j < k` and: `P ∧ Q` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` uimplies: `b supposing a` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` implies: `P `` Q` not: `¬A` top: `Top` less_than: `a < b` true: `True` subtype_rel: `A ⊆r B` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` select: `L[n]`
Lemmas referenced :  equal_wf squash_wf true_wf mklist_select subtract_wf int_seg_properties length_wf decidable__le satisfiable-full-omega-tt intformand_wf intformnot_wf intformle_wf itermConstant_wf itermSubtract_wf itermVar_wf intformless_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_subtract_lemma int_term_value_var_lemma int_formula_prop_less_lemma int_formula_prop_wf le_wf select_wf itermAdd_wf int_term_value_add_lemma decidable__lt int_seg_wf iff_weakening_equal
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut applyEquality thin lambdaEquality sqequalHypSubstitution imageElimination extract_by_obid isectElimination hypothesisEquality equalityTransitivity hypothesis equalitySymmetry because_Cache dependent_set_memberEquality setElimination rename natural_numberEquality addEquality cumulativity productElimination dependent_functionElimination unionElimination independent_isectElimination dependent_pairFormation int_eqEquality intEquality isect_memberEquality voidElimination voidEquality sqequalRule independent_pairFormation computeAll imageMemberEquality baseClosed universeEquality independent_functionElimination axiomEquality

Latex:
\mforall{}[T:Type].  \mforall{}[l:T  List].  \mforall{}[i:\mBbbN{}||l||].  \mforall{}[j:\mBbbN{}i  +  1].  \mforall{}[x:\mBbbN{}i  -  j].    (l\_interval(l;j;i)[x]  =  l[j  +  x])

Date html generated: 2017_04_17-AM-07_42_40
Last ObjectModification: 2017_02_27-PM-04_15_14

Theory : list_1

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