### Nuprl Lemma : interleaving_sublist

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

Proof

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

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

Date html generated: 2017_10_01-AM-08_37_15
Last ObjectModification: 2017_07_26-PM-04_26_23

Theory : list!

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