Nuprl Lemma : values-for-distinct_wf
∀[A,V:Type]. ∀[eq:EqDecider(A)]. ∀[L:(A × V) List]. (values-for-distinct(eq;L) ∈ V List)
Proof
Definitions occuring in Statement :
values-for-distinct: values-for-distinct(eq;L),
list: T List,
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
values-for-distinct: values-for-distinct(eq;L),
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
outl: outl(x),
uimplies: b supposing a,
isl: isl(x),
and: P ∧ Q,
not: ¬A,
false: False,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
nat: ℕ,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
guard: {T},
or: P ∨ Q,
cons: [a / b],
colength: colength(L),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
decidable: Dec(P),
nil: [],
it: ⋅,
sq_type: SQType(T),
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
eqof: eqof(d),
deq: EqDecider(T),
bool: 𝔹,
unit: Unit,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
assert: ↑b,
true: True,
bfalse: ff,
bnot: ¬bb
Lemmas referenced :
list_wf,
deq_wf,
assert_wf,
isl_wf,
unit_wf2,
apply-alist_wf,
map_wf,
assert_elim,
bfalse_wf,
and_wf,
equal_wf,
btrue_neq_bfalse,
remove-repeats_wf,
strong-subtype-deq-subtype,
strong-subtype-set2,
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
less_than_wf,
equal-wf-T-base,
nat_wf,
colength_wf_list,
less_than_transitivity1,
less_than_irreflexivity,
list-cases,
map_nil_lemma,
product_subtype_list,
spread_cons_lemma,
intformeq_wf,
itermAdd_wf,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
decidable__le,
intformnot_wf,
int_formula_prop_not_lemma,
le_wf,
subtract_wf,
itermSubtract_wf,
int_term_value_subtract_lemma,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
decidable__equal_int,
apply_alist_cons_lemma,
map_cons_lemma,
nil_wf,
cons_wf,
ifthenelse_wf,
pi1_wf,
pi2_wf,
bool_wf,
eqtt_to_assert,
safe-assert-deq,
eqff_to_assert,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
subtype_rel_list_set
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
extract_by_obid,
isectElimination,
thin,
productEquality,
cumulativity,
hypothesisEquality,
isect_memberEquality,
because_Cache,
universeEquality,
setEquality,
lambdaFormation,
lambdaEquality,
setElimination,
rename,
unionEquality,
unionElimination,
addLevel,
independent_isectElimination,
levelHypothesis,
dependent_set_memberEquality,
independent_pairFormation,
applyLambdaEquality,
productElimination,
independent_functionElimination,
voidElimination,
dependent_functionElimination,
applyEquality,
intWeakElimination,
natural_numberEquality,
dependent_pairFormation,
int_eqEquality,
intEquality,
voidEquality,
computeAll,
promote_hyp,
hypothesis_subsumption,
addEquality,
baseClosed,
instantiate,
imageElimination,
independent_pairEquality,
inlEquality,
equalityElimination
Latex:
\mforall{}[A,V:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[L:(A \mtimes{} V) List]. (values-for-distinct(eq;L) \mmember{} V List)
Date html generated:
2017_04_17-AM-09_11_36
Last ObjectModification:
2017_02_27-PM-05_19_14
Theory : decidable!equality
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