Nuprl Lemma : nearby-partitions_functionality
∀p,q:ℝ List. ∀e1,e2:ℝ. ((e1 ≤ e2) ⇒ {nearby-partitions(e1;p;q) ⇒ nearby-partitions(e2;p;q)})
Proof
Definitions occuring in Statement :
nearby-partitions: nearby-partitions(e;p;q),
rleq: x ≤ y,
real: ℝ,
list: T List,
guard: {T},
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
nearby-partitions: nearby-partitions(e;p;q),
and: P ∧ Q,
int_seg: {i..j-},
uimplies: b supposing a,
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top
Lemmas referenced :
nearby-partitions_wf,
rleq_wf,
real_wf,
list_wf,
rleq_transitivity,
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,
int_seg_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_pairFormation,
productElimination,
promote_hyp,
dependent_functionElimination,
setElimination,
rename,
because_Cache,
independent_isectElimination,
natural_numberEquality,
equalityTransitivity,
equalitySymmetry,
unionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
computeAll
Latex:
\mforall{}p,q:\mBbbR{} List. \mforall{}e1,e2:\mBbbR{}. ((e1 \mleq{} e2) {}\mRightarrow{} \{nearby-partitions(e1;p;q) {}\mRightarrow{} nearby-partitions(e2;p;q)\})
Date html generated:
2016_10_26-AM-09_34_23
Last ObjectModification:
2016_08_16-AM-11_45_49
Theory : reals
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