Nuprl Lemma : reject_wf
∀[A:Type]. ∀[l:A List]. ∀[n:ℤ]. (l\[n] ∈ A List)
Proof
Definitions occuring in Statement :
reject: as\[i],
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
reject: as\[i],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
subtract: n - m,
subtype_rel: A ⊆r B,
top: Top,
le: A ≤ B,
less_than': less_than'(a;b),
true: True,
so_apply: x[s1;s2;s3],
nat: ℕ,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
ge: i ≥ j ,
le_int: i ≤z j,
lt_int: i <z j
Lemmas referenced :
decidable__lt,
list_wf,
le_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_le_int,
tl_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
le_wf,
list_ind_wf,
nil_wf,
cons_wf,
not-le-2,
condition-implies-le,
minus-add,
minus-zero,
add-zero,
add-commutes,
zero-add,
less-iff-le,
add_functionality_wrt_le,
add-associates,
le-add-cancel2,
nat_wf,
decidable__le,
false_wf,
not-lt-2,
minus-one-mul,
minus-one-mul-top,
le-add-cancel,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
not_wf,
subtract_wf,
not-ge-2,
minus-minus,
add-swap,
decidable__int_equal,
int_subtype_base,
not-equal-2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
natural_numberEquality,
hypothesis,
unionElimination,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
intEquality,
isect_memberEquality,
isectElimination,
because_Cache,
cumulativity,
universeEquality,
lambdaFormation,
equalityElimination,
productElimination,
independent_isectElimination,
dependent_pairFormation,
promote_hyp,
instantiate,
independent_functionElimination,
voidElimination,
lambdaEquality,
addEquality,
applyEquality,
voidEquality,
minusEquality,
hypothesis_subsumption,
setElimination,
rename,
dependent_set_memberEquality,
independent_pairFormation,
intWeakElimination
Latex:
\mforall{}[A:Type]. \mforall{}[l:A List]. \mforall{}[n:\mBbbZ{}]. (l\mbackslash{}[n] \mmember{} A List)
Date html generated:
2017_04_14-AM-08_34_29
Last ObjectModification:
2017_02_27-PM-03_22_16
Theory : list_0
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