Nuprl Lemma : greatest-p-zero_wf
∀[a:ℕ+ ⟶ ℤ]. ∀[n:ℕ]. (greatest-p-zero(n;a) ∈ ℕ)
Proof
Definitions occuring in Statement :
greatest-p-zero: greatest-p-zero(n;a),
nat_plus: ℕ+,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
greatest-p-zero: greatest-p-zero(n;a),
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
nat_plus: ℕ+,
int_seg: {i..j-},
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
uimplies: b supposing a,
lelt: i ≤ j < k,
subtract: n - m,
subtype_rel: A ⊆r B,
top: Top,
true: True,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
guard: {T},
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
bfalse: ff
Lemmas referenced :
primrec_wf,
nat_wf,
false_wf,
le_wf,
eq_int_wf,
nat_plus_wf,
decidable__lt,
not-lt-2,
condition-implies-le,
minus-add,
minus-one-mul,
zero-add,
minus-one-mul-top,
add-commutes,
add_functionality_wrt_le,
add-associates,
add-zero,
le-add-cancel,
less_than_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
nat_properties,
int_seg_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
equal_wf,
int_seg_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
lambdaFormation,
lambdaEquality,
applyEquality,
functionExtensionality,
addEquality,
setElimination,
rename,
productElimination,
dependent_functionElimination,
unionElimination,
voidElimination,
independent_functionElimination,
independent_isectElimination,
isect_memberEquality,
voidEquality,
intEquality,
because_Cache,
minusEquality,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
approximateComputation,
dependent_pairFormation,
int_eqEquality,
axiomEquality,
functionEquality
Latex:
\mforall{}[a:\mBbbN{}\msupplus{} {}\mrightarrow{} \mBbbZ{}]. \mforall{}[n:\mBbbN{}]. (greatest-p-zero(n;a) \mmember{} \mBbbN{})
Date html generated:
2018_05_21-PM-03_22_04
Last ObjectModification:
2018_05_19-AM-08_19_00
Theory : rings_1
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