### Nuprl Lemma : permute_list_select

`∀[T:Type]. ∀[L:T List]. ∀[f:ℕ||L|| ⟶ ℕ||L||]. ∀[i:ℕ||L||].  ((L o f)[i] = L[f i] ∈ T)`

Proof

Definitions occuring in Statement :  permute_list: `(L o f)` select: `L[n]` length: `||as||` list: `T List` int_seg: `{i..j-}` uall: `∀[x:A]. B[x]` apply: `f a` function: `x:A ⟶ B[x]` natural_number: `\$n` universe: `Type` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` permute_list: `(L o f)` subtype_rel: `A ⊆r B` uimplies: `b supposing a` ge: `i ≥ j ` guard: `{T}` int_seg: `{i..j-}` lelt: `i ≤ j < k` and: `P ∧ Q` all: `∀x:A. B[x]` le: `A ≤ B` prop: `ℙ` decidable: `Dec(P)` or: `P ∨ Q` nat: `ℕ` not: `¬A` implies: `P `` Q` false: `False` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` top: `Top` true: `True` squash: `↓T` iff: `P `⇐⇒` Q` rev_implies: `P `` Q`
Lemmas referenced :  mklist_select length_wf_nat int_seg_wf length_wf select_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 decidable__lt intformless_wf int_formula_prop_less_lemma equal_wf squash_wf true_wf iff_weakening_equal
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality cumulativity hypothesis natural_numberEquality sqequalRule isect_memberEquality axiomEquality because_Cache functionEquality lambdaEquality applyEquality functionExtensionality independent_isectElimination setElimination rename productElimination dependent_functionElimination dependent_set_memberEquality independent_pairFormation unionElimination equalityTransitivity equalitySymmetry applyLambdaEquality independent_functionElimination voidElimination dependent_pairFormation int_eqEquality intEquality voidEquality computeAll imageElimination imageMemberEquality baseClosed universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[L:T  List].  \mforall{}[f:\mBbbN{}||L||  {}\mrightarrow{}  \mBbbN{}||L||].  \mforall{}[i:\mBbbN{}||L||].    ((L  o  f)[i]  =  L[f  i])

Date html generated: 2017_04_17-AM-08_09_34
Last ObjectModification: 2017_02_27-PM-04_37_52

Theory : list_1

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