Nuprl Lemma : round-robin_wf
∀[T:Type]. ∀[L:T List]. round-robin(L) ∈ ℕ ⟶ T supposing 0 < ||L||
Proof
Definitions occuring in Statement :
round-robin: round-robin(L),
length: ||as||,
list: T List,
nat: ℕ,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
round-robin: round-robin(L),
nat: ℕ,
nequal: a ≠ b ∈ T ,
ge: i ≥ j ,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
all: ∀x:A. B[x],
top: Top,
and: P ∧ Q,
prop: ℙ,
nat_plus: ℕ+
Lemmas referenced :
list_wf,
nat_wf,
less_than_wf,
rem_bounds_1,
equal_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermConstant_wf,
itermVar_wf,
intformeq_wf,
intformand_wf,
satisfiable-full-omega-tt,
nat_properties,
length_wf,
select_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
remainderEquality,
setElimination,
rename,
hypothesis,
because_Cache,
lambdaFormation,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
dependent_set_memberEquality,
productElimination,
axiomEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. round-robin(L) \mmember{} \mBbbN{} {}\mrightarrow{} T supposing 0 < ||L||
Date html generated:
2016_05_14-PM-03_30_48
Last ObjectModification:
2016_01_14-PM-11_20_54
Theory : decidable!equality
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