### Nuprl Lemma : permutation-map

`∀[A:Type]. ∀L1,L2:A List.  (permutation(A;L1;L2) `` (∀[B:Type]. ∀f:A ⟶ B. permutation(B;map(f;L1);map(f;L2))))`

Proof

Definitions occuring in Statement :  permutation: `permutation(T;L1;L2)` map: `map(f;as)` list: `T List` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` implies: `P `` Q` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` implies: `P `` Q` permutation: `permutation(T;L1;L2)` exists: `∃x:A. B[x]` member: `t ∈ T` and: `P ∧ Q` 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` prop: `ℙ` squash: `↓T` true: `True` guard: `{T}` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` top: `Top` nat: `ℕ` cand: `A c∧ B` int_seg: `{i..j-}` lelt: `i ≤ j < k` ge: `i ≥ j `
Lemmas referenced :  subtype_rel_dep_function int_seg_wf length_wf map_wf int_seg_subtype false_wf le_wf map_length_nat iff_weakening_equal 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 list_extensionality permute_list_wf map-length less_than_wf nat_wf equal_wf list_wf inject_wf permutation_wf permute_list_length lelt_wf select_wf non_neg_length nat_properties length_wf_nat int_seg_properties intformand_wf itermConstant_wf int_formula_prop_and_lemma int_term_value_constant_lemma decidable__lt intformless_wf int_formula_prop_less_lemma length-map map_select permute_list_select
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation lambdaFormation sqequalHypSubstitution productElimination thin dependent_pairFormation cut hypothesisEquality applyEquality introduction extract_by_obid isectElimination natural_numberEquality cumulativity hypothesis sqequalRule lambdaEquality functionExtensionality independent_isectElimination because_Cache independent_pairFormation imageElimination imageMemberEquality baseClosed equalityTransitivity equalitySymmetry independent_functionElimination dependent_functionElimination unionElimination int_eqEquality intEquality isect_memberEquality voidElimination voidEquality computeAll promote_hyp setElimination rename hyp_replacement applyLambdaEquality productEquality functionEquality universeEquality dependent_set_memberEquality

Latex:
\mforall{}[A:Type]
\mforall{}L1,L2:A  List.
(permutation(A;L1;L2)  {}\mRightarrow{}  (\mforall{}[B:Type].  \mforall{}f:A  {}\mrightarrow{}  B.  permutation(B;map(f;L1);map(f;L2))))

Date html generated: 2017_04_17-AM-08_24_31
Last ObjectModification: 2017_02_27-PM-04_47_19

Theory : list_1

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