### Nuprl Lemma : permutation_inversion

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

Proof

Definitions occuring in Statement :  permutation: `permutation(T;L1;L2)` list: `T List` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` implies: `P `` Q` universe: `Type`
Definitions unfolded in proof :  permutation: `permutation(T;L1;L2)` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` implies: `P `` Q` exists: `∃x:A. B[x]` and: `P ∧ Q` member: `t ∈ T` top: `Top` prop: `ℙ` squash: `↓T` subtype_rel: `A ⊆r B` so_lambda: `λ2x.t[x]` so_apply: `x[s]` uimplies: `b supposing a` le: `A ≤ B` less_than': `less_than'(a;b)` false: `False` not: `¬A` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` true: `True` guard: `{T}` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` surject: `Surj(A;B;f)` int_seg: `{i..j-}` pi1: `fst(t)` cand: `A c∧ B` inject: `Inj(A;B;f)` lelt: `i ≤ j < k` nat: `ℕ` ge: `i ≥ j ` compose: `f o g`
Lemmas referenced :  permute_list_length equal_wf length_wf squash_wf true_wf permute_permute_list subtype_rel_dep_function int_seg_wf permute_list_wf int_seg_subtype false_wf decidable__le satisfiable-full-omega-tt intformnot_wf intformle_wf itermVar_wf int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_var_lemma int_formula_prop_wf iff_weakening_equal inject_wf exists_wf compose_wf subtype_rel_self list_wf injection-is-surjection length_wf_nat all_wf int_seg_properties intformand_wf itermConstant_wf intformeq_wf int_formula_prop_and_lemma int_term_value_constant_lemma int_formula_prop_eq_lemma decidable__lt intformless_wf int_formula_prop_less_lemma lelt_wf list_extensionality less_than_wf nat_wf select_wf nat_properties permute_list_select
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation lambdaFormation sqequalHypSubstitution productElimination thin cut hypothesis introduction extract_by_obid isectElimination hypothesisEquality isect_memberEquality voidElimination voidEquality because_Cache hyp_replacement equalitySymmetry applyLambdaEquality intEquality cumulativity addLevel existsFunctionality independent_pairFormation applyEquality lambdaEquality imageElimination equalityTransitivity equalityUniverse levelHypothesis natural_numberEquality functionExtensionality independent_isectElimination dependent_functionElimination unionElimination dependent_pairFormation int_eqEquality computeAll imageMemberEquality baseClosed universeEquality independent_functionElimination productEquality functionEquality promote_hyp setElimination rename dependent_set_memberEquality instantiate

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

Date html generated: 2017_04_17-AM-08_11_25
Last ObjectModification: 2017_02_27-PM-04_38_09

Theory : list_1

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