Nuprl Lemma : l_contains-append4

[T:Type]. ∀A,B,C:T List.  (A ⊆  A ⊆ C)


Proof




Definitions occuring in Statement :  l_contains: A ⊆ B append: as bs list: List uall: [x:A]. B[x] all: x:A. B[x] implies:  Q universe: Type
Definitions unfolded in proof :  l_contains: A ⊆ B l_all: (∀x∈L.P[x]) uall: [x:A]. B[x] all: x:A. B[x] implies:  Q guard: {T} or: P ∨ Q member: t ∈ T prop: int_seg: {i..j-} uimplies: supposing a lelt: i ≤ j < k and: P ∧ Q decidable: Dec(P) satisfiable_int_formula: satisfiable_int_formula(fmla) exists: x:A. B[x] false: False not: ¬A top: Top less_than: a < b squash: T so_lambda: λ2x.t[x] so_apply: x[s] iff: ⇐⇒ Q rev_implies:  Q subtype_rel: A ⊆B
Lemmas referenced :  or_wf uall_wf member_append list_wf all_wf int_seg_wf 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 length_wf int_seg_properties select_wf l_member_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep cut isect_memberFormation lambdaFormation hypothesis inrFormation lemma_by_obid sqequalHypSubstitution isectElimination thin cumulativity hypothesisEquality because_Cache setElimination rename independent_isectElimination natural_numberEquality productElimination dependent_functionElimination unionElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll imageElimination universeEquality addLevel uallFunctionality allFunctionality impliesFunctionality independent_functionElimination instantiate functionEquality introduction applyEquality

Latex:
\mforall{}[T:Type].  \mforall{}A,B,C:T  List.    (A  \msubseteq{}  C  {}\mRightarrow{}  A  \msubseteq{}  B  @  C)



Date html generated: 2016_05_14-AM-07_55_05
Last ObjectModification: 2016_01_15-AM-08_29_25

Theory : list_1


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