Nuprl Lemma : even-int-list_wf
∀[L:ℤ List]. (even-int-list(L) ∈ 𝔹)
Proof
Definitions occuring in Statement :
even-int-list: even-int-list(L),
list: T List,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
and: P ∧ Q,
ge: i ≥ j ,
le: A ≤ B,
cand: A c∧ B,
less_than: a < b,
squash: ↓T,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
not: ¬A,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
subtract: n - m,
top: Top,
less_than': less_than'(a;b),
true: True,
sq_type: SQType(T),
exists: ∃x:A. B[x],
sq_stable: SqStable(P),
cons: [a / b],
even-int-list: even-int-list(L),
bor: p ∨bq,
ifthenelse: if b then t else f fi ,
bfalse: ff,
bnot: ¬bb,
btrue: tt,
band: p ∧b q
Lemmas referenced :
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
istype-less_than,
int_seg_wf,
subtract-1-ge-0,
decidable__equal_int,
subtract_wf,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
decidable__le,
istype-false,
not-le-2,
less-iff-le,
le_antisymmetry_iff,
condition-implies-le,
minus-add,
istype-void,
minus-minus,
minus-one-mul,
add-swap,
minus-one-mul-top,
add-commutes,
zero-add,
add_functionality_wrt_le,
add-associates,
add-zero,
le-add-cancel,
decidable__lt,
not-lt-2,
le-add-cancel-alt,
istype-le,
subtype_rel_self,
int_seg_properties,
non_neg_length,
length_wf_nat,
istype-sqequal,
le_wf,
istype-int,
le_reflexive,
length_wf,
list_wf,
not-equal-2,
sq_stable__le,
add-mul-special,
zero-mul,
istype-nat,
list-cases,
product_subtype_list,
null_nil_lemma,
reduce_tl_nil_lemma,
testxxx_lemma,
btrue_wf,
null_cons_lemma,
reduce_tl_cons_lemma,
reduce_hd_cons_lemma,
bfalse_wf,
eq_int_wf,
bool_cases,
bool_subtype_base,
eqtt_to_assert,
band_wf,
assert_of_eq_int,
length_of_cons_lemma,
two-mul,
mul-distributes-right,
one-mul
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
thin,
Error :lambdaFormation_alt,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
sqequalRule,
intWeakElimination,
independent_pairFormation,
productElimination,
imageElimination,
natural_numberEquality,
independent_isectElimination,
independent_functionElimination,
voidElimination,
Error :universeIsType,
Error :lambdaEquality_alt,
dependent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :functionIsTypeImplies,
Error :inhabitedIsType,
because_Cache,
unionElimination,
applyEquality,
instantiate,
Error :dependent_set_memberEquality_alt,
addEquality,
minusEquality,
Error :isect_memberEquality_alt,
Error :productIsType,
hypothesis_subsumption,
intEquality,
Error :dependent_pairFormation_alt,
Error :equalityIstype,
promote_hyp,
imageMemberEquality,
baseClosed,
multiplyEquality,
cumulativity
Latex:
\mforall{}[L:\mBbbZ{} List]. (even-int-list(L) \mmember{} \mBbbB{})
Date html generated:
2019_06_20-PM-00_45_45
Last ObjectModification:
2019_04_08-PM-01_57_07
Theory : omega
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