Nuprl Lemma : reject_cons_tl_sq

[T:Type]. ∀[a:T]. ∀[as:T List]. ∀[i:ℤ].  ([a as]\[i] [a as\[i 1]]) supposing ((i ≤ ||as||) and 0 < i)


Definitions occuring in Statement :  length: ||as|| reject: as\[i] cons: [a b] list: List less_than: a < b uimplies: supposing a uall: [x:A]. B[x] le: A ≤ B subtract: m natural_number: $n int: universe: Type sqequal: t
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a reject: as\[i] all: x:A. B[x] implies:  Q bool: 𝔹 unit: Unit it: btrue: tt uiff: uiff(P;Q) and: P ∧ Q ifthenelse: if then else fi  top: Top satisfiable_int_formula: satisfiable_int_formula(fmla) exists: x:A. B[x] false: False not: ¬A prop: bfalse: ff or: P ∨ Q sq_type: SQType(T) guard: {T} bnot: ¬bb assert: b so_lambda: so_lambda(x,y,z.t[x; y; z]) so_apply: x[s1;s2;s3]
Lemmas referenced :  le_int_wf bool_wf eqtt_to_assert assert_of_le_int reduce_tl_cons_lemma satisfiable-full-omega-tt intformand_wf intformle_wf itermVar_wf itermConstant_wf intformless_wf int_formula_prop_and_lemma int_formula_prop_le_lemma int_term_value_var_lemma int_term_value_constant_lemma int_formula_prop_less_lemma int_formula_prop_wf eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot le_wf list_ind_cons_lemma length_wf less_than_wf list_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality natural_numberEquality hypothesis lambdaFormation unionElimination equalityElimination equalityTransitivity equalitySymmetry productElimination independent_isectElimination dependent_functionElimination isect_memberEquality voidElimination voidEquality dependent_pairFormation lambdaEquality int_eqEquality intEquality independent_pairFormation computeAll promote_hyp instantiate cumulativity independent_functionElimination because_Cache sqequalAxiom universeEquality

\mforall{}[T:Type].  \mforall{}[a:T].  \mforall{}[as:T  List].  \mforall{}[i:\mBbbZ{}].
    ([a  /  as]\mbackslash{}[i]  \msim{}  [a  /  as\mbackslash{}[i  -  1]])  supposing  ((i  \mleq{}  ||as||)  and  0  <  i)

Date html generated: 2017_04_17-AM-08_48_39
Last ObjectModification: 2017_02_27-PM-05_05_59

Theory : list_1

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