Nuprl Lemma : list-deq_wf
∀[A:Type]. ∀[eq:EqDecider(A)]. (list-deq(eq) ∈ EqDecider(A List))
Proof
Definitions occuring in Statement :
list-deq: list-deq(eq),
list: T List,
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
deq: EqDecider(T),
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
or: P ∨ Q,
assert: ↑b,
ifthenelse: if b then t else f fi ,
list-deq: list-deq(eq),
list_ind: list_ind,
nil: [],
it: ⋅,
null: null(as),
btrue: tt,
true: True,
cons: [a / b],
top: Top,
colength: colength(L),
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
not: ¬A,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
bfalse: ff,
le: A ≤ B,
less_than': less_than'(a;b),
less_than: a < b,
squash: ↓T,
sq_stable: SqStable(P),
subtract: n - m,
subtype_rel: A ⊆r B,
cand: A c∧ B,
decidable: Dec(P),
uiff: uiff(P;Q),
band: p ∧b q,
eqof: eqof(d)
Lemmas referenced :
list-deq_wf1,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
istype-less_than,
assert_witness,
list-cases,
nil_wf,
istype-assert,
product_subtype_list,
colength-cons-not-zero,
istype-void,
subtract-1-ge-0,
subtype_base_sq,
nat_wf,
set_subtype_base,
le_wf,
int_subtype_base,
spread_cons_lemma,
null_nil_lemma,
btrue_wf,
length_wf,
length_of_nil_lemma,
null_wf,
null_cons_lemma,
bfalse_wf,
btrue_neq_bfalse,
cons_wf,
list_ind_nil_lemma,
colength_wf_list,
le_weakening2,
istype-le,
istype-false,
sq_stable__le,
add-associates,
istype-int,
add-commutes,
add-swap,
zero-add,
length_of_cons_lemma,
list_ind_cons_lemma,
istype-nat,
deq_wf,
istype-universe,
reduce_hd_cons_lemma,
hd_wf,
cons_neq_nil,
length_wf_nat,
decidable__le,
not-ge-2,
condition-implies-le,
minus-add,
minus-one-mul,
minus-one-mul-top,
add_functionality_wrt_le,
add-zero,
le-add-cancel2,
assert_wf,
eqof_wf,
bool_cases,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
band_wf,
equal_wf,
safe-assert-deq,
iff_weakening_equal,
iff_transitivity,
iff_weakening_uiff,
assert_of_band,
reduce_tl_cons_lemma,
tl_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
Error :dependent_set_memberEquality_alt,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
setElimination,
rename,
because_Cache,
hypothesis,
Error :lambdaFormation_alt,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
independent_functionElimination,
voidElimination,
Error :universeIsType,
sqequalRule,
Error :lambdaEquality_alt,
dependent_functionElimination,
productElimination,
independent_pairEquality,
applyEquality,
Error :functionIsTypeImplies,
Error :inhabitedIsType,
axiomEquality,
unionElimination,
independent_pairFormation,
Error :equalityIstype,
baseClosed,
sqequalBase,
equalitySymmetry,
promote_hyp,
hypothesis_subsumption,
Error :isect_memberEquality_alt,
instantiate,
cumulativity,
intEquality,
closedConclusion,
equalityTransitivity,
Error :productIsType,
applyLambdaEquality,
imageElimination,
imageMemberEquality,
minusEquality,
baseApply,
Error :functionIsType,
Error :isectIsTypeImplies,
universeEquality,
addEquality,
productEquality,
hyp_replacement
Latex:
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. (list-deq(eq) \mmember{} EqDecider(A List))
Date html generated:
2019_06_20-PM-00_44_02
Last ObjectModification:
2018_11_26-AM-00_13_37
Theory : list_0
Home
Index