Nuprl Lemma : round-robin-onto
∀[T:Type]. ∀L:T List. (∀x∈L.∃b:ℕ. (x = (round-robin(L) b) ∈ T))
Proof
Definitions occuring in Statement :
round-robin: round-robin(L),
l_all: (∀x∈L.P[x]),
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
apply: f a,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
l_all: (∀x∈L.P[x]),
member: t ∈ T,
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
round-robin: round-robin(L),
squash: ↓T,
prop: ℙ,
int_seg: {i..j-},
nat_plus: ℕ+,
lelt: i ≤ j < k,
less_than: a < b,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
cand: A c∧ B,
nat: ℕ,
ge: i ≥ j
Lemmas referenced :
int_seg_wf,
length_wf,
list_wf,
istype-universe,
int_seg_subtype_nat,
istype-false,
select_wf,
squash_wf,
le_wf,
less_than_wf,
istype-int,
equal_wf,
true_wf,
rem_base_case,
int_seg_properties,
decidable__lt,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformless_wf,
itermConstant_wf,
itermVar_wf,
intformle_wf,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
istype-less_than,
subtype_rel_self,
iff_weakening_equal,
decidable__le,
nat_properties,
round-robin_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
Error :lambdaFormation_alt,
Error :universeIsType,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesisEquality,
hypothesis,
instantiate,
universeEquality,
Error :dependent_pairFormation_alt,
applyEquality,
independent_isectElimination,
sqequalRule,
independent_pairFormation,
Error :lambdaEquality_alt,
imageElimination,
productElimination,
equalityTransitivity,
equalitySymmetry,
productEquality,
Error :inhabitedIsType,
because_Cache,
intEquality,
setElimination,
rename,
Error :dependent_set_memberEquality_alt,
dependent_functionElimination,
unionElimination,
approximateComputation,
independent_functionElimination,
int_eqEquality,
Error :isect_memberEquality_alt,
voidElimination,
imageMemberEquality,
baseClosed,
Error :equalityIstype
Latex:
\mforall{}[T:Type]. \mforall{}L:T List. (\mforall{}x\mmember{}L.\mexists{}b:\mBbbN{}. (x = (round-robin(L) b)))
Date html generated:
2019_06_20-PM-01_56_49
Last ObjectModification:
2019_03_06-AM-10_52_42
Theory : decidable!equality
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