### Nuprl Lemma : interleaving_symmetry

`∀[T:Type]. ∀L,L1,L2:T List.  (interleaving(T;L1;L2;L) `⇐⇒` interleaving(T;L2;L1;L))`

Proof

Definitions occuring in Statement :  interleaving: `interleaving(T;L1;L2;L)` list: `T List` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` iff: `P `⇐⇒` Q` universe: `Type`
Definitions unfolded in proof :  interleaving: `interleaving(T;L1;L2;L)` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` iff: `P `⇐⇒` Q` and: `P ∧ Q` implies: `P `` Q` member: `t ∈ T` nat: `ℕ` guard: `{T}` ge: `i ≥ j ` decidable: `Dec(P)` or: `P ∨ Q` false: `False` uiff: `uiff(P;Q)` uimplies: `b supposing a` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` not: `¬A` top: `Top` prop: `ℙ` disjoint_sublists: `disjoint_sublists(T;L1;L2;L)` cand: `A c∧ B` int_seg: `{i..j-}` lelt: `i ≤ j < k` subtype_rel: `A ⊆r B` so_lambda: `λ2x.t[x]` less_than: `a < b` squash: `↓T` le: `A ≤ B` so_apply: `x[s]` rev_implies: `P `` Q`
Lemmas referenced :  nat_properties decidable__equal_int length_wf add-is-int-iff satisfiable-full-omega-tt intformand_wf intformnot_wf intformeq_wf itermVar_wf itermAdd_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_eq_lemma int_term_value_var_lemma int_term_value_add_lemma int_formula_prop_wf false_wf non_neg_length decidable__le intformle_wf itermConstant_wf int_formula_prop_le_lemma int_term_value_constant_lemma le_wf int_seg_properties equal_wf int_seg_wf increasing_wf length_wf_nat all_wf select_wf decidable__lt intformless_wf int_formula_prop_less_lemma lelt_wf not_wf exists_wf nat_wf add_nat_wf disjoint_sublists_wf list_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation lambdaFormation independent_pairFormation cut sqequalHypSubstitution productElimination thin introduction extract_by_obid isectElimination equalityTransitivity hypothesis equalitySymmetry applyLambdaEquality setElimination rename hypothesisEquality dependent_functionElimination addEquality cumulativity unionElimination pointwiseFunctionality promote_hyp baseApply closedConclusion baseClosed independent_isectElimination natural_numberEquality dependent_pairFormation lambdaEquality int_eqEquality intEquality isect_memberEquality voidElimination voidEquality computeAll dependent_set_memberEquality because_Cache applyEquality functionExtensionality independent_functionElimination productEquality imageElimination functionEquality universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}L,L1,L2:T  List.    (interleaving(T;L1;L2;L)  \mLeftarrow{}{}\mRightarrow{}  interleaving(T;L2;L1;L))

Date html generated: 2017_10_01-AM-08_36_15
Last ObjectModification: 2017_07_26-PM-04_26_10

Theory : list!

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