Nuprl Lemma : general-iroot_wf
∀[n:ℕ+]. ∀[x:ℤ]. (general-iroot(n;x) ∈ ℤ)
Proof
Definitions occuring in Statement :
general-iroot: general-iroot(n;x),
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
general-iroot: general-iroot(n;x),
has-value: (a)↓,
uimplies: b supposing a,
nat_plus: ℕ+,
so_lambda: λ2x.t[x],
so_apply: x[s],
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
int_seg: {i..j-},
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
top: Top,
not: ¬A,
false: False,
int_lower: {...i},
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
nat: ℕ,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
assert: ↑b,
nequal: a ≠ b ∈ T
Lemmas referenced :
value-type-has-value,
nat_plus_wf,
set-value-type,
less_than_wf,
int-value-type,
eq_int_wf,
modulus_wf_int_mod,
subtype_rel_set,
int_mod_wf,
int-subtype-int_mod,
int_seg_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
integer-nth-root2,
nat_plus_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermVar_wf,
itermConstant_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
le_wf,
iroot_wf,
nat_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
callbyvalueReduce,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
independent_isectElimination,
intEquality,
lambdaEquality,
natural_numberEquality,
hypothesisEquality,
dependent_set_memberEquality,
independent_pairFormation,
imageMemberEquality,
baseClosed,
applyEquality,
setElimination,
rename,
lambdaFormation,
unionElimination,
equalityElimination,
because_Cache,
productElimination,
int_eqReduceTrueSq,
lessCases,
equalityTransitivity,
equalitySymmetry,
axiomSqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
imageElimination,
independent_functionElimination,
instantiate,
dependent_functionElimination,
approximateComputation,
dependent_pairFormation,
int_eqEquality,
promote_hyp,
cumulativity,
int_eqReduceFalseSq,
axiomEquality
Latex:
\mforall{}[n:\mBbbN{}\msupplus{}]. \mforall{}[x:\mBbbZ{}]. (general-iroot(n;x) \mmember{} \mBbbZ{})
Date html generated:
2019_06_20-PM-02_35_02
Last ObjectModification:
2019_03_19-AM-10_49_45
Theory : num_thy_1
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