Nuprl Lemma : decidable__no_repeats
∀[T:Type]. ((∀x,y:T. Dec(x = y ∈ T)) ⇒ (∀L:T List. Dec(no_repeats(T;L))))
Proof
Definitions occuring in Statement :
no_repeats: no_repeats(T;l),
list: T List,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
all: ∀x:A. B[x],
no_repeats: no_repeats(T;l),
member: t ∈ T,
so_lambda: λ2x.t[x],
prop: ℙ,
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,
int_seg: {i..j-},
guard: {T},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
less_than: a < b,
squash: ↓T,
so_apply: x[s],
nat: ℕ,
ge: i ≥ j
Lemmas referenced :
decidable__all_int_seg,
length_wf,
all_wf,
int_seg_wf,
not_wf,
equal_wf,
nat_wf,
int_seg_subtype_nat,
false_wf,
select_wf,
int_seg_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
decidable__implies,
decidable__not,
decidable__equal_nat,
list_wf,
decidable_wf,
uall_wf,
isect_wf,
less_than_wf,
nat_properties,
lelt_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
natural_numberEquality,
isectElimination,
cumulativity,
hypothesisEquality,
hypothesis,
sqequalRule,
lambdaEquality,
functionEquality,
applyEquality,
independent_isectElimination,
independent_pairFormation,
because_Cache,
setElimination,
rename,
productElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
imageElimination,
independent_functionElimination,
universeEquality,
inlFormation,
inrFormation,
equalityTransitivity,
equalitySymmetry,
dependent_set_memberEquality
Latex:
\mforall{}[T:Type]. ((\mforall{}x,y:T. Dec(x = y)) {}\mRightarrow{} (\mforall{}L:T List. Dec(no\_repeats(T;L))))
Date html generated:
2018_05_21-PM-06_40_13
Last ObjectModification:
2017_07_26-PM-04_53_41
Theory : general
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