Nuprl Lemma : sublist_wf

[T:Type]. ∀[L1,L2:T List].  (L1 ⊆ L2 ∈ ℙ)


Proof




Definitions occuring in Statement :  sublist: L1 ⊆ L2 list: List uall: [x:A]. B[x] prop: member: t ∈ T universe: Type
Definitions unfolded in proof :  sublist: L1 ⊆ L2 uall: [x:A]. B[x] member: t ∈ T so_lambda: λ2x.t[x] prop: and: P ∧ Q subtype_rel: A ⊆B so_apply: x[s] uimplies: 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:  Q not: ¬A top: Top less_than: a < b squash: T ge: i ≥  nat:
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 subtype_rel_dep_function length_wf_nat increasing_wf length_wf int_seg_wf exists_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin functionEquality natural_numberEquality cumulativity hypothesisEquality hypothesis because_Cache lambdaEquality productEquality applyEquality 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 universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[L1,L2:T  List].    (L1  \msubseteq{}  L2  \mmember{}  \mBbbP{})



Date html generated: 2016_05_14-AM-07_42_56
Last ObjectModification: 2016_01_15-AM-08_35_23

Theory : list_1


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