Nuprl Lemma : power-type-subtype-list

T:Type. ∀k:ℕ.  ((T^k) ⊆(T List))


Proof




Definitions occuring in Statement :  power-type: (T^k) list: List nat: subtype_rel: A ⊆B all: x:A. B[x] universe: Type
Definitions unfolded in proof :  all: x:A. B[x] uall: [x:A]. B[x] member: t ∈ T nat: implies:  Q false: False ge: i ≥  uimplies: supposing a satisfiable_int_formula: satisfiable_int_formula(fmla) exists: x:A. B[x] not: ¬A top: Top and: P ∧ Q prop: subtype_rel: A ⊆B power-type: (T^k) eq_int: (i =z j) subtract: m ifthenelse: if then else fi  btrue: tt decidable: Dec(P) or: P ∨ Q bool: 𝔹 unit: Unit it: uiff: uiff(P;Q) bfalse: ff sq_type: SQType(T) guard: {T} bnot: ¬bb assert: b cons: [a b] nequal: a ≠ b ∈ 
Lemmas referenced :  nat_properties satisfiable-full-omega-tt intformand_wf intformle_wf itermConstant_wf itermVar_wf intformless_wf int_formula_prop_and_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_less_lemma int_formula_prop_wf ge_wf less_than_wf unit_subtype_list decidable__le subtract_wf intformnot_wf itermSubtract_wf int_formula_prop_not_lemma int_term_value_subtract_lemma eq_int_wf bool_wf eqtt_to_assert assert_of_eq_int eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot neg_assert_of_eq_int nat_wf cons_wf power-type_wf le_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis setElimination rename intWeakElimination natural_numberEquality independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality dependent_functionElimination isect_memberEquality voidElimination voidEquality sqequalRule independent_pairFormation computeAll independent_functionElimination axiomEquality unionElimination equalityElimination equalityTransitivity equalitySymmetry productElimination because_Cache promote_hyp instantiate universeEquality cumulativity applyEquality productEquality dependent_set_memberEquality

Latex:
\mforall{}T:Type.  \mforall{}k:\mBbbN{}.    ((T\^{}k)  \msubseteq{}r  (T  List))



Date html generated: 2018_05_21-PM-08_13_54
Last ObjectModification: 2017_07_26-PM-05_48_50

Theory : general


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