Nuprl Lemma : sublist_occurence_wf

`∀[T:Type]. ∀[L1,L2:T List]. ∀[f:ℕ||L1|| ⟶ ℕ||L2||].  (sublist_occurence(T;L1;L2;f) ∈ ℙ)`

Proof

Definitions occuring in Statement :  sublist_occurence: `sublist_occurence(T;L1;L2;f)` 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 :  sublist_occurence: `sublist_occurence(T;L1;L2;f)` uall: `∀[x:A]. B[x]` member: `t ∈ T` prop: `ℙ` and: `P ∧ Q` subtype_rel: `A ⊆r B` so_lambda: `λ2x.t[x]` so_apply: `x[s]` uimplies: `b supposing a` all: `∀x:A. B[x]` int_seg: `{i..j-}` guard: `{T}` lelt: `i ≤ j < k` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` implies: `P `` Q` not: `¬A` top: `Top` less_than: `a < b` squash: `↓T` ge: `i ≥ j ` nat: `ℕ`
Lemmas referenced :  list_wf le_wf nat_properties lelt_wf non_neg_length int_formula_prop_less_lemma intformless_wf decidable__lt int_formula_prop_wf int_term_value_var_lemma int_term_value_constant_lemma int_formula_prop_le_lemma int_formula_prop_not_lemma int_formula_prop_and_lemma itermVar_wf itermConstant_wf intformle_wf intformnot_wf intformand_wf satisfiable-full-omega-tt decidable__le int_seg_properties select_wf equal_wf all_wf length_wf int_seg_wf subtype_rel_dep_function length_wf_nat increasing_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut productEquality lemma_by_obid sqequalHypSubstitution isectElimination thin cumulativity hypothesisEquality hypothesis applyEquality natural_numberEquality lambdaEquality because_Cache intEquality independent_isectElimination lambdaFormation setElimination rename productElimination dependent_functionElimination unionElimination dependent_pairFormation int_eqEquality isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll imageElimination dependent_set_memberEquality equalityTransitivity equalitySymmetry setEquality axiomEquality functionEquality universeEquality

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

Date html generated: 2016_05_15-PM-01_57_25
Last ObjectModification: 2016_01_15-PM-11_30_41

Theory : list!

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