Nuprl Lemma : std-is-infinitesmal
is-infinitesmal(∈)
Proof
Definitions occuring in Statement :
std-infinitesmal: ∈,
is-infinitesmal: is-infinitesmal(x)
Definitions unfolded in proof :
is-infinitesmal: is-infinitesmal(x),
all: ∀x:A. B[x],
rless*: x < y,
rrel*: R*(x,y),
exists: ∃x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
rstar: (x)*,
std-infinitesmal: ∈,
rabs*: |x|,
rfun*: f*(x),
uall: ∀[x:A]. B[x],
nat_plus: ℕ+,
prop: ℙ,
nat: ℕ,
so_lambda: λ2x.t[x],
real*: ℝ*,
uimplies: b supposing a,
rneq: x ≠ y,
guard: {T},
or: P ∨ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
int_upper: {i...},
ge: i ≥ j ,
decidable: Dec(P),
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
top: Top,
so_apply: x[s],
le: A ≤ B,
uiff: uiff(P;Q),
subtract: n - m,
less_than': less_than'(a;b),
true: True
Lemmas referenced :
nat_plus_subtype_nat,
int_upper_wf,
all_wf,
rless_wf,
rabs*_wf,
std-infinitesmal_wf,
real*_wf,
int_upper_subtype_nat,
rstar_wf,
rdiv_wf,
int-to-real_wf,
rless-int,
int_upper_properties,
nat_properties,
nat_plus_properties,
decidable__lt,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformless_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
nat_plus_wf,
rabs_wf,
itermAdd_wf,
intformle_wf,
int_term_value_add_lemma,
int_formula_prop_le_lemma,
rleq-int-fractions2,
false_wf,
not-lt-2,
less-iff-le,
condition-implies-le,
minus-add,
minus-one-mul,
zero-add,
minus-one-mul-top,
add-commutes,
add_functionality_wrt_le,
add-associates,
add-zero,
add-swap,
le-add-cancel,
less_than_wf,
decidable__le,
itermMultiply_wf,
int_term_value_mul_lemma,
rless-int-fractions,
rless_functionality,
rabs-of-nonneg,
req_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
dependent_pairFormation,
cut,
hypothesisEquality,
applyEquality,
introduction,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
sqequalRule,
isectElimination,
thin,
setElimination,
rename,
because_Cache,
lambdaEquality,
natural_numberEquality,
independent_isectElimination,
inrFormation,
dependent_functionElimination,
productElimination,
independent_functionElimination,
unionElimination,
approximateComputation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
addEquality,
dependent_set_memberEquality,
minusEquality,
multiplyEquality
Latex:
is-infinitesmal(\mmember{})
Date html generated:
2018_05_22-PM-09_29_12
Last ObjectModification:
2017_10_06-PM-04_17_09
Theory : reals_2
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