Nuprl Lemma : iroot-zero
∀[n:ℕ+]. (iroot(n;0) ~ 0)
Proof
Definitions occuring in Statement :
iroot: iroot(n;x),
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
iroot: iroot(n;x),
integer-nth-root-ext,
has-value: (a)↓,
nat_plus: ℕ+,
subtype_rel: A ⊆r B,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
and: P ∧ Q,
prop: ℙ,
genrec-ap: genrec-ap,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
false: False,
le: A ≤ B,
not: ¬A,
implies: P ⇒ Q,
sq_type: SQType(T),
guard: {T}
Lemmas referenced :
integer-nth-root-ext,
le_wf,
false_wf,
int_formula_prop_wf,
int_term_value_constant_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
itermConstant_wf,
intformeq_wf,
intformnot_wf,
satisfiable-full-omega-tt,
decidable__equal_int,
nat_plus_properties,
nat_plus_subtype_nat,
exp_wf_nat_plus,
int-value-type,
less_than_wf,
set-value-type,
nat_plus_wf,
value-type-has-value,
int_subtype_base,
set_subtype_base,
subtype_base_sq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
because_Cache,
independent_isectElimination,
sqequalRule,
hypothesis,
callbyvalueReduce,
intEquality,
lambdaEquality,
natural_numberEquality,
hypothesisEquality,
applyEquality,
dependent_set_memberEquality,
independent_pairFormation,
imageMemberEquality,
baseClosed,
setElimination,
rename,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
equalityTransitivity,
equalitySymmetry,
lambdaFormation,
independent_functionElimination,
axiomSqEquality
Latex:
\mforall{}[n:\mBbbN{}\msupplus{}]. (iroot(n;0) \msim{} 0)
Date html generated:
2019_06_20-PM-02_34_45
Last ObjectModification:
2019_03_19-AM-10_49_32
Theory : num_thy_1
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