### Nuprl Lemma : swap_swap

`∀[T:Type]. ∀[L1:T List]. ∀[i,j:ℕ||L1||].  (swap(swap(L1;i;j);i;j) = L1 ∈ (T List))`

Proof

Definitions occuring in Statement :  swap: `swap(L;i;j)` length: `||as||` list: `T List` int_seg: `{i..j-}` uall: `∀[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` int_seg: `{i..j-}` lelt: `i ≤ j < k` and: `P ∧ Q` guard: `{T}` 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` prop: `ℙ` le: `A ≤ B` less_than: `a < b` nat: `ℕ` cand: `A c∧ B` subtype_rel: `A ⊆r B` ge: `i ≥ j ` true: `True` squash: `↓T` iff: `P `⇐⇒` Q` rev_implies: `P `` Q`
Lemmas referenced :  swap_length swap_wf int_seg_properties decidable__lt satisfiable-full-omega-tt intformand_wf intformnot_wf intformless_wf itermVar_wf intformeq_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_less_lemma int_term_value_var_lemma int_formula_prop_eq_lemma int_formula_prop_wf lelt_wf list_extensionality less_than_wf nat_wf int_seg_wf length_wf list_wf zero-le-nat nat_properties flip_wf length_wf_nat select_wf decidable__le intformle_wf itermConstant_wf int_formula_prop_le_lemma int_term_value_constant_lemma equal_wf squash_wf le_wf flip_twice iff_weakening_equal true_wf swap_select
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality because_Cache cumulativity hypothesis setElimination rename dependent_set_memberEquality productElimination independent_pairFormation natural_numberEquality equalityTransitivity equalitySymmetry dependent_functionElimination unionElimination independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality isect_memberEquality voidElimination voidEquality sqequalRule computeAll lambdaFormation axiomEquality universeEquality applyEquality imageElimination productEquality imageMemberEquality baseClosed independent_functionElimination

Latex:
\mforall{}[T:Type].  \mforall{}[L1:T  List].  \mforall{}[i,j:\mBbbN{}||L1||].    (swap(swap(L1;i;j);i;j)  =  L1)

Date html generated: 2017_10_01-AM-08_38_02
Last ObjectModification: 2017_07_26-PM-04_26_52

Theory : list!

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