Nuprl Lemma : full-partition-non-dec
∀[I:Interval]. ∀[p:partition(I)]. frs-non-dec(full-partition(I;p)) supposing icompact(I)
Proof
Definitions occuring in Statement :
full-partition: full-partition(I;p),
partition: partition(I),
frs-non-dec: frs-non-dec(L),
icompact: icompact(I),
interval: Interval,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
full-partition: full-partition(I;p),
partition: partition(I),
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
all: ∀x:A. B[x],
cand: A c∧ B,
frs-non-dec: frs-non-dec(L),
rleq: x ≤ y,
rnonneg: rnonneg(x),
le: A ≤ B,
not: ¬A,
false: False,
int_seg: {i..j-},
nat_plus: ℕ+,
guard: {T},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
prop: ℙ,
less_than: a < b,
squash: ↓T,
subtype_rel: A ⊆r B,
icompact: icompact(I),
sq_stable: SqStable(P),
so_lambda: λ2x.t[x],
so_apply: x[s],
partitions: partitions(I;p),
rbetween: x≤y≤z
Lemmas referenced :
frs-non-dec-sorted-by,
cons_wf,
real_wf,
left-endpoint_wf,
append_wf,
right-endpoint_wf,
nil_wf,
sorted-by-cons,
rleq_wf,
less_than'_wf,
rsub_wf,
select_wf,
full-partition_wf,
nat_plus_properties,
int_seg_properties,
length_wf,
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,
nat_plus_wf,
le_wf,
int_seg_wf,
partition_wf,
icompact_wf,
interval_wf,
sorted-by-append,
sq_stable__frs-non-dec,
sorted-by-single,
l_member_wf,
l_all_single,
equal_wf,
l_all_iff,
l_all_wf2,
all_wf,
sq_stable__rleq,
i-member-compact,
partition-point-member,
i-member_wf,
partitions_wf,
l_all_append,
icompact-endpoints-rleq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
independent_isectElimination,
because_Cache,
setElimination,
rename,
productElimination,
independent_functionElimination,
lambdaEquality,
dependent_functionElimination,
independent_pairFormation,
sqequalRule,
independent_pairEquality,
applyEquality,
natural_numberEquality,
unionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
imageElimination,
minusEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
imageMemberEquality,
baseClosed,
lambdaFormation,
addLevel,
allFunctionality,
impliesFunctionality,
setEquality,
levelHypothesis,
allLevelFunctionality,
impliesLevelFunctionality,
functionEquality,
dependent_set_memberEquality,
andLevelFunctionality,
productEquality
Latex:
\mforall{}[I:Interval]. \mforall{}[p:partition(I)]. frs-non-dec(full-partition(I;p)) supposing icompact(I)
Date html generated:
2017_10_03-AM-09_40_27
Last ObjectModification:
2017_07_28-AM-07_55_55
Theory : reals
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