### Nuprl Lemma : occurence_implies_interleaving

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

Proof

Definitions occuring in Statement :  interleaving_occurence: `interleaving_occurence(T;L1;L2;L;f1;f2)` interleaving: `interleaving(T;L1;L2;L)` length: `||as||` list: `T List` int_seg: `{i..j-}` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` function: `x:A ⟶ B[x]` natural_number: `\$n` universe: `Type`
Definitions unfolded in proof :  interleaving: `interleaving(T;L1;L2;L)` interleaving_occurence: `interleaving_occurence(T;L1;L2;L;f1;f2)` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` uimplies: `b supposing a` member: `t ∈ T` and: `P ∧ Q` increasing: `increasing(f;k)` int_seg: `{i..j-}` lelt: `i ≤ j < k` nat: `ℕ` guard: `{T}` ge: `i ≥ j ` decidable: `Dec(P)` or: `P ∨ Q` false: `False` uiff: `uiff(P;Q)` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` implies: `P `` Q` not: `¬A` top: `Top` prop: `ℙ` le: `A ≤ B` less_than: `a < b` subtype_rel: `A ⊆r B` subtract: `n - m` cand: `A c∧ B` so_lambda: `λ2x.t[x]` squash: `↓T` so_apply: `x[s]` disjoint_sublists: `disjoint_sublists(T;L1;L2;L)`
Lemmas referenced :  member-less_than int_seg_wf length_wf nat_properties decidable__lt add-is-int-iff satisfiable-full-omega-tt intformand_wf intformnot_wf intformless_wf itermVar_wf itermSubtract_wf itermConstant_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_less_lemma int_term_value_var_lemma int_term_value_subtract_lemma int_term_value_constant_lemma int_formula_prop_wf false_wf lelt_wf add-member-int_seg2 decidable__le subtract_wf intformle_wf int_formula_prop_le_lemma equal_wf nat_wf length_wf_nat add_nat_wf itermAdd_wf intformeq_wf int_term_value_add_lemma int_formula_prop_eq_lemma le_wf increasing_wf all_wf select_wf int_seg_properties non_neg_length not_wf list_wf exists_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation lambdaFormation cut introduction sqequalHypSubstitution productElimination thin independent_pairEquality axiomEquality hypothesis lambdaEquality dependent_functionElimination hypothesisEquality extract_by_obid isectElimination applyEquality functionExtensionality natural_numberEquality cumulativity setElimination rename dependent_set_memberEquality independent_pairFormation equalityTransitivity equalitySymmetry applyLambdaEquality unionElimination pointwiseFunctionality promote_hyp baseApply closedConclusion baseClosed independent_isectElimination dependent_pairFormation int_eqEquality intEquality isect_memberEquality voidElimination voidEquality computeAll because_Cache productEquality addEquality independent_functionElimination imageElimination 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(T;L1;L2;L)  supposing  interleaving\_occurence(T;L1;L2;L;f1;f2)

Date html generated: 2017_10_01-AM-08_37_43
Last ObjectModification: 2017_07_26-PM-04_26_37

Theory : list!

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