Nuprl Lemma : co-alt_wf
co-alt() ∈ colist(ℤ)
Proof
Definitions occuring in Statement :
co-alt: co-alt(),
colist: colist(T),
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
colist: colist(T),
corec: corec(T.F[T]),
member: t ∈ T,
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
subtype_rel: A ⊆r B,
le: A ≤ B,
less_than': less_than'(a;b),
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
co-alt: co-alt(),
b-union: A ⋃ B,
tunion: ⋃x:A.B[x],
ifthenelse: if b then t else f fi ,
bfalse: ff,
subtract: n - m,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
nequal: a ≠ b ∈ T ,
int_upper: {i...},
bnot: ¬bb,
assert: ↑b,
pi2: snd(t),
less_than: a < b
Lemmas referenced :
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,
int_seg_wf,
int_seg_properties,
decidable__le,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
decidable__equal_int,
int_seg_subtype,
false_wf,
intformeq_wf,
int_formula_prop_eq_lemma,
le_wf,
subtype_base_sq,
nat_wf,
set_subtype_base,
int_subtype_base,
primrec0_lemma,
primrec-unroll-1,
decidable__lt,
bfalse_wf,
lelt_wf,
bool_wf,
eqtt_to_assert,
int_upper_subtype_nat,
nequal-le-implies,
zero-add,
unit_wf2,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
primrec_wf,
int_upper_properties,
top_wf,
b-union_wf,
itermAdd_wf,
int_term_value_add_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberEquality,
cut,
thin,
lambdaFormation,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
sqequalRule,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
productElimination,
unionElimination,
applyEquality,
applyLambdaEquality,
hypothesis_subsumption,
dependent_set_memberEquality,
instantiate,
cumulativity,
imageMemberEquality,
dependent_pairEquality,
independent_pairEquality,
equalityElimination,
promote_hyp,
productEquality,
universeEquality,
baseClosed,
addEquality
Latex:
co-alt() \mmember{} colist(\mBbbZ{})
Date html generated:
2018_05_21-PM-10_20_27
Last ObjectModification:
2017_07_26-PM-06_37_28
Theory : eval!all
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