Nuprl Lemma : reject_cons_tl

[T:Type]. ∀[a:T]. ∀[as:T List]. ∀[i:ℤ].
  ([a as]\[i] [a as\[i 1]] ∈ (T List)) 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 equal: t ∈ T
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a prop: 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 le: A ≤ B false: False guard: {T} bfalse: ff exists: x:A. B[x] or: P ∨ Q sq_type: SQType(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_wf length_wf less_than_wf list_wf le_int_wf bool_wf eqtt_to_assert assert_of_le_int reduce_tl_cons_lemma less_than_transitivity1 less_than_irreflexivity eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot not_functionality_wrt_uiff assert_wf list_ind_cons_lemma cons_wf reject_wf subtract_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :isect_memberFormation_alt,  introduction cut hypothesis Error :universeIsType,  extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality sqequalRule isect_memberEquality axiomEquality equalityTransitivity equalitySymmetry natural_numberEquality because_Cache intEquality universeEquality lambdaFormation unionElimination equalityElimination productElimination independent_isectElimination dependent_functionElimination voidElimination voidEquality independent_functionElimination dependent_pairFormation promote_hyp instantiate cumulativity

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

Date html generated: 2019_06_20-PM-00_40_17
Last ObjectModification: 2018_09_26-PM-02_47_36

Theory : list_0

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