### Nuprl Lemma : interleaving_occurence_wf

`∀[T:Type]. ∀[L1,L2,L:T List]. ∀[f1:ℕ||L1|| ⟶ ℕ||L||]. ∀[f2:ℕ||L2|| ⟶ ℕ||L||].`
`  (interleaving_occurence(T;L1;L2;L;f1;f2) ∈ ℙ)`

Proof

Definitions occuring in Statement :  interleaving_occurence: `interleaving_occurence(T;L1;L2;L;f1;f2)` length: `||as||` list: `T List` int_seg: `{i..j-}` uall: `∀[x:A]. B[x]` prop: `ℙ` member: `t ∈ T` function: `x:A ⟶ B[x]` natural_number: `\$n` universe: `Type`
Definitions unfolded in proof :  interleaving_occurence: `interleaving_occurence(T;L1;L2;L;f1;f2)` uall: `∀[x:A]. B[x]` member: `t ∈ T` prop: `ℙ` and: `P ∧ Q` nat: `ℕ` all: `∀x:A. B[x]` implies: `P `` Q` 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` subtype_rel: `A ⊆r B` int_seg: `{i..j-}` so_lambda: `λ2x.t[x]` lelt: `i ≤ j < k` less_than: `a < b` squash: `↓T` le: `A ≤ B` so_apply: `x[s]`
Lemmas referenced :  equal_wf nat_wf length_wf_nat length_wf add_nat_wf nat_properties decidable__le add-is-int-iff satisfiable-full-omega-tt intformand_wf intformnot_wf intformle_wf itermConstant_wf itermVar_wf itermAdd_wf intformeq_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_term_value_add_lemma int_formula_prop_eq_lemma int_formula_prop_wf false_wf le_wf increasing_wf int_seg_wf all_wf select_wf int_seg_properties decidable__lt intformless_wf int_formula_prop_less_lemma non_neg_length lelt_wf not_wf list_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut productEquality extract_by_obid sqequalHypSubstitution isectElimination thin hypothesis cumulativity hypothesisEquality dependent_set_memberEquality addEquality lambdaFormation equalityTransitivity equalitySymmetry applyLambdaEquality setElimination rename dependent_functionElimination natural_numberEquality unionElimination pointwiseFunctionality promote_hyp baseApply closedConclusion baseClosed productElimination independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll independent_functionElimination because_Cache functionExtensionality applyEquality imageElimination axiomEquality functionEquality universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[L1,L2,L:T  List].  \mforall{}[f1:\mBbbN{}||L1||  {}\mrightarrow{}  \mBbbN{}||L||].  \mforall{}[f2:\mBbbN{}||L2||  {}\mrightarrow{}  \mBbbN{}||L||].
(interleaving\_occurence(T;L1;L2;L;f1;f2)  \mmember{}  \mBbbP{})

Date html generated: 2017_10_01-AM-08_37_19
Last ObjectModification: 2017_07_26-PM-04_26_27

Theory : list!

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