Nuprl Lemma : rnonneg-int
∀[n:ℤ]. uiff(rnonneg(r(n));0 ≤ n)
Proof
Definitions occuring in Statement :
rnonneg: rnonneg(x),
int-to-real: r(n),
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
le: A ≤ B,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
int-to-real: r(n),
rnonneg: rnonneg(x),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
le: A ≤ B,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
so_lambda: λ2x.t[x],
nat_plus: ℕ+,
so_apply: x[s],
all: ∀x:A. B[x],
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
nat: ℕ,
subtype_rel: A ⊆r B,
guard: {T},
ge: i ≥ j
Lemmas referenced :
less_than'_wf,
all_wf,
nat_plus_wf,
le_wf,
less_than_wf,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
itermMultiply_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_term_value_mul_lemma,
int_formula_prop_wf,
mul_bounds_1a,
nat_plus_subtype_nat,
nat_wf,
nat_properties,
nat_plus_properties,
intformeq_wf,
int_formula_prop_eq_lemma,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairEquality,
lambdaEquality,
dependent_functionElimination,
hypothesisEquality,
because_Cache,
extract_by_obid,
isectElimination,
natural_numberEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
minusEquality,
multiplyEquality,
setElimination,
rename,
lambdaFormation,
voidElimination,
isect_memberEquality,
intEquality,
dependent_set_memberEquality,
imageMemberEquality,
baseClosed,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
voidEquality,
computeAll,
applyEquality,
applyLambdaEquality,
independent_functionElimination
Latex:
\mforall{}[n:\mBbbZ{}]. uiff(rnonneg(r(n));0 \mleq{} n)
Date html generated:
2017_10_03-AM-08_23_53
Last ObjectModification:
2017_07_28-AM-07_23_07
Theory : reals
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