Nuprl Lemma : permutation-rotate

`∀[A:Type]. ∀as,bs:A List.  permutation(A;as @ bs;bs @ as)`

Proof

Definitions occuring in Statement :  permutation: `permutation(T;L1;L2)` append: `as @ bs` list: `T List` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` universe: `Type`
Definitions unfolded in proof :  permutation: `permutation(T;L1;L2)` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` member: `t ∈ T` top: `Top` exists: `∃x:A. B[x]` int_seg: `{i..j-}` implies: `P `` Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` ifthenelse: `if b then t else f fi ` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` lelt: `i ≤ j < k` ge: `i ≥ j ` decidable: `Dec(P)` or: `P ∨ Q` le: `A ≤ B` satisfiable_int_formula: `satisfiable_int_formula(fmla)` false: `False` not: `¬A` prop: `ℙ` less_than: `a < b` squash: `↓T` bfalse: `ff` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` assert: `↑b` subtype_rel: `A ⊆r B` so_lambda: `λ2x.t[x]` so_apply: `x[s]` less_than': `less_than'(a;b)` true: `True` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` permute_list: `(L o f)` inject: `Inj(A;B;f)` nat: `ℕ`
Lemmas referenced :  list_wf lt_int_wf length_wf bool_wf eqtt_to_assert assert_of_lt_int add-member-int_seg2 non_neg_length decidable__le satisfiable-full-omega-tt intformand_wf intformnot_wf intformle_wf itermSubtract_wf itermConstant_wf itermVar_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_subtract_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_wf decidable__lt subtract_wf add-is-int-iff intformless_wf itermAdd_wf int_formula_prop_less_lemma int_term_value_add_lemma false_wf lelt_wf eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot less_than_wf int_seg_properties int_seg_wf inject_wf append_wf permute_list_wf subtype_rel_dep_function int_seg_subtype le_wf length_append subtype_rel_list top_wf iff_weakening_equal length-append equal-wf-T-base assert_wf decidable__equal_int intformeq_wf int_formula_prop_eq_lemma le_int_wf bnot_wf uiff_transitivity assert_functionality_wrt_uiff bnot_of_lt_int assert_of_le_int list_extensionality mklist_wf length_wf_nat select_wf add_nat_wf int_seg_subtype_nat nat_wf nat_properties mklist_length all_wf squash_wf true_wf mklist_select select_append_front select_append_back add-subtract-cancel
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation lambdaFormation cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin cumulativity hypothesisEquality hypothesis universeEquality isect_memberEquality voidElimination voidEquality because_Cache dependent_pairFormation lambdaEquality setElimination rename unionElimination equalityElimination productElimination independent_isectElimination natural_numberEquality addEquality dependent_set_memberEquality independent_pairFormation dependent_functionElimination int_eqEquality intEquality computeAll imageElimination pointwiseFunctionality equalityTransitivity equalitySymmetry promote_hyp baseApply closedConclusion baseClosed instantiate independent_functionElimination productEquality functionExtensionality applyEquality imageMemberEquality applyLambdaEquality functionEquality

Latex:
\mforall{}[A:Type].  \mforall{}as,bs:A  List.    permutation(A;as  @  bs;bs  @  as)

Date html generated: 2017_04_17-AM-08_10_46
Last ObjectModification: 2017_02_27-PM-04_38_43

Theory : list_1

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