### Nuprl Lemma : round-robin-member

`∀[T:Type]. ∀L:T List. ∀n:ℕ. (round-robin(L) n ∈ L) supposing 0 < ||L||`

Proof

Definitions occuring in Statement :  round-robin: `round-robin(L)` l_member: `(x ∈ l)` length: `||as||` list: `T List` nat: `ℕ` less_than: `a < b` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` apply: `f a` natural_number: `\$n` universe: `Type`
Definitions unfolded in proof :  round-robin: `round-robin(L)` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` uimplies: `b supposing a` member: `t ∈ T` int_seg: `{i..j-}` int_nzero: `ℤ-o` nequal: `a ≠ b ∈ T ` nat: `ℕ` ge: `i ≥ j ` not: `¬A` implies: `P `` Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` top: `Top` and: `P ∧ Q` prop: `ℙ` subtype_rel: `A ⊆r B` so_lambda: `λ2x.t[x]` so_apply: `x[s]` lelt: `i ≤ j < k` nat_plus: `ℕ+` decidable: `Dec(P)` or: `P ∨ Q` less_than: `a < b` squash: `↓T`
Lemmas referenced :  member-less_than length_wf select_member remainder_wfa nat_properties full-omega-unsat intformand_wf intformeq_wf itermVar_wf itermConstant_wf intformless_wf istype-int int_formula_prop_and_lemma istype-void int_formula_prop_eq_lemma int_term_value_var_lemma int_term_value_constant_lemma int_formula_prop_less_lemma int_formula_prop_wf length_wf_nat set_subtype_base le_wf int_subtype_base nequal_wf rem_bounds_1 decidable__lt intformnot_wf int_formula_prop_not_lemma istype-less_than istype-le istype-nat list_wf istype-universe
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep Error :isect_memberFormation_alt,  Error :lambdaFormation_alt,  cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin natural_numberEquality hypothesisEquality hypothesis independent_isectElimination rename dependent_functionElimination Error :dependent_set_memberEquality_alt,  because_Cache setElimination equalityTransitivity equalitySymmetry approximateComputation independent_functionElimination Error :dependent_pairFormation_alt,  Error :lambdaEquality_alt,  int_eqEquality Error :isect_memberEquality_alt,  voidElimination independent_pairFormation Error :universeIsType,  Error :equalityIstype,  Error :inhabitedIsType,  applyEquality intEquality baseClosed sqequalBase unionElimination imageElimination productElimination Error :productIsType,  instantiate

Latex:
\mforall{}[T:Type].  \mforall{}L:T  List.  \mforall{}n:\mBbbN{}.  (round-robin(L)  n  \mmember{}  L)  supposing  0  <  ||L||

Date html generated: 2019_06_20-PM-01_56_44
Last ObjectModification: 2019_03_06-AM-10_52_15

Theory : decidable!equality

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