Nuprl Lemma : nearby-partitions_wf
∀[e:ℝ]. ∀[p,q:ℝ List]. (nearby-partitions(e;p;q) ∈ ℙ)
Proof
Definitions occuring in Statement :
nearby-partitions: nearby-partitions(e;p;q),
real: ℝ,
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nearby-partitions: nearby-partitions(e;p;q),
prop: ℙ,
and: P ∧ Q,
so_lambda: λ2x.t[x],
int_seg: {i..j-},
uimplies: b supposing a,
guard: {T},
lelt: i ≤ j < k,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
so_apply: x[s]
Lemmas referenced :
equal_wf,
length_wf,
real_wf,
all_wf,
int_seg_wf,
rleq_wf,
rabs_wf,
rsub_wf,
select_wf,
int_seg_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_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_formula_prop_wf,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
intformeq_wf,
int_formula_prop_eq_lemma,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
productEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
hypothesis,
hypothesisEquality,
because_Cache,
natural_numberEquality,
lambdaEquality,
setElimination,
rename,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
axiomEquality
Latex:
\mforall{}[e:\mBbbR{}]. \mforall{}[p,q:\mBbbR{} List]. (nearby-partitions(e;p;q) \mmember{} \mBbbP{})
Date html generated:
2017_10_03-AM-09_36_49
Last ObjectModification:
2017_07_28-AM-07_54_57
Theory : reals
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