### Nuprl Lemma : permutation-contains

`∀[A:Type]. ∀L1,L2:A List.  (permutation(A;L1;L2) `` L2 ⊆ L1)`

Proof

Definitions occuring in Statement :  permutation: `permutation(T;L1;L2)` l_contains: `A ⊆ B` list: `T List` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` implies: `P `` Q` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` implies: `P `` Q` member: `t ∈ T` uimplies: `b supposing a` permutation: `permutation(T;L1;L2)` exists: `∃x:A. B[x]` l_contains: `A ⊆ B` l_all: `(∀x∈L.P[x])` and: `P ∧ Q` prop: `ℙ` squash: `↓T` int_seg: `{i..j-}` lelt: `i ≤ j < k` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` false: `False` not: `¬A` top: `Top` true: `True` subtype_rel: `A ⊆r B` guard: `{T}` iff: `P `⇐⇒` Q` rev_implies: `P `` Q`
Lemmas referenced :  permutation-length equal_wf list_wf l_member_wf permute_list_select 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 iff_weakening_equal select_member int_seg_wf select_wf int_seg_properties decidable__le intformle_wf itermConstant_wf int_formula_prop_le_lemma int_term_value_constant_lemma permute_list_length less_than_wf length_wf permutation_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation lambdaFormation cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality independent_isectElimination hypothesis productElimination dependent_set_memberEquality because_Cache cumulativity equalityTransitivity equalitySymmetry applyEquality lambdaEquality imageElimination setElimination rename independent_pairFormation dependent_functionElimination unionElimination natural_numberEquality dependent_pairFormation int_eqEquality intEquality isect_memberEquality voidElimination voidEquality sqequalRule computeAll imageMemberEquality baseClosed independent_functionElimination functionExtensionality hyp_replacement Error :applyLambdaEquality,  universeEquality

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

Date html generated: 2016_10_21-AM-10_17_29
Last ObjectModification: 2016_07_12-AM-05_32_58

Theory : list_1

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