Nuprl Lemma : std-infinitesmal_wf
∈ ∈ ℝ*
Proof
Definitions occuring in Statement :
std-infinitesmal: ∈,
real*: ℝ*,
member: t ∈ T
Definitions unfolded in proof :
std-infinitesmal: ∈,
real*: ℝ*,
member: t ∈ T,
uall: ∀[x:A]. B[x],
nat: ℕ,
uimplies: b supposing a,
rneq: x ≠ y,
guard: {T},
or: P ∨ Q,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
ge: i ≥ j ,
decidable: Dec(P),
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
prop: ℙ
Lemmas referenced :
rdiv_wf,
int-to-real_wf,
rless-int,
nat_properties,
decidable__lt,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformless_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
rless_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaEquality,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesis,
addEquality,
setElimination,
rename,
because_Cache,
independent_isectElimination,
inrFormation,
dependent_functionElimination,
productElimination,
independent_functionElimination,
hypothesisEquality,
unionElimination,
approximateComputation,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation
Latex:
\mmember{} \mmember{} \mBbbR{}*
Date html generated:
2018_05_22-PM-09_29_06
Last ObjectModification:
2017_10_06-PM-04_13_45
Theory : reals_2
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