### Nuprl Lemma : map_permute_list

`∀[A,B:Type]. ∀[f:B ⟶ A]. ∀[x:B List]. ∀[g:ℕ||x|| ⟶ ℕ||x||].  (map(f;(x o g)) = (map(f;x) o g) ∈ (A List))`

Proof

Definitions occuring in Statement :  permute_list: `(L o f)` length: `||as||` map: `map(f;as)` list: `T List` int_seg: `{i..j-}` uall: `∀[x:A]. B[x]` 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` squash: `↓T` subtype_rel: `A ⊆r B` uimplies: `b supposing a` guard: `{T}` iff: `P `⇐⇒` Q` and: `P ∧ Q` rev_implies: `P `` Q` implies: `P `` Q` top: `Top` so_lambda: `λ2x.t[x]` so_apply: `x[s]` le: `A ≤ B` less_than': `less_than'(a;b)` false: `False` not: `¬A` prop: `ℙ` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` int_seg: `{i..j-}` lelt: `i ≤ j < k` nat: `ℕ` true: `True` ge: `i ≥ j `
Lemmas referenced :  equal_wf map_length permute_list_wf int_seg_wf length_wf iff_weakening_equal permute_list_length map_wf list_extensionality subtype_rel_dep_function int_seg_subtype false_wf decidable__le satisfiable-full-omega-tt intformand_wf intformnot_wf intformle_wf itermVar_wf intformeq_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_var_lemma int_formula_prop_eq_lemma int_formula_prop_wf int_seg_properties less_than_wf nat_wf list_wf map_length_nat lelt_wf decidable__lt intformless_wf int_formula_prop_less_lemma select_wf non_neg_length nat_properties length_wf_nat itermConstant_wf int_term_value_constant_lemma map_select permute_list_select
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut applyEquality thin lambdaEquality sqequalHypSubstitution imageElimination extract_by_obid isectElimination because_Cache hypothesis cumulativity hypothesisEquality functionExtensionality natural_numberEquality sqequalRule imageMemberEquality baseClosed equalityTransitivity equalitySymmetry independent_isectElimination productElimination independent_functionElimination isect_memberEquality voidElimination voidEquality independent_pairFormation lambdaFormation dependent_functionElimination unionElimination dependent_pairFormation int_eqEquality intEquality computeAll setElimination rename functionEquality axiomEquality universeEquality dependent_set_memberEquality applyLambdaEquality

Latex:
\mforall{}[A,B:Type].  \mforall{}[f:B  {}\mrightarrow{}  A].  \mforall{}[x:B  List].  \mforall{}[g:\mBbbN{}||x||  {}\mrightarrow{}  \mBbbN{}||x||].    (map(f;(x  o  g))  =  (map(f;x)  o  g))

Date html generated: 2017_10_01-AM-08_38_29
Last ObjectModification: 2017_07_26-PM-04_27_01

Theory : list!

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