Nuprl Lemma : uniform-partition_wf
∀[I:Interval]. ∀[k:ℕ+]. (uniform-partition(I;k) ∈ partition(I)) supposing icompact(I)
Proof
Definitions occuring in Statement :
uniform-partition: uniform-partition(I;k),
partition: partition(I),
icompact: icompact(I),
interval: Interval,
nat_plus: ℕ+,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
uniform-partition: uniform-partition(I;k),
partition: partition(I),
nat: ℕ,
nat_plus: ℕ+,
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,
and: P ∧ Q,
prop: ℙ,
rneq: x ≠ y,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
int_seg: {i..j-},
lelt: i ≤ j < k,
partitions: partitions(I;p),
cand: A c∧ B,
subtype_rel: A ⊆r B,
icompact: icompact(I),
frs-non-dec: frs-non-dec(L),
rless: x < y,
sq_exists: ∃x:{A| B[x]},
sq_stable: SqStable(P),
squash: ↓T,
real: ℝ,
le: A ≤ B,
less_than: a < b,
true: True,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
ge: i ≥ j ,
rleq: x ≤ y,
rnonneg: rnonneg(x),
itermConstant: "const",
req_int_terms: t1 ≡ t2,
rdiv: (x/y),
less_than': less_than'(a;b),
rge: x ≥ y,
last: last(L)
Lemmas referenced :
mklist_wf,
subtract_wf,
nat_plus_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermSubtract_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_subtract_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
le_wf,
rdiv_wf,
radd_wf,
rmul_wf,
left-endpoint_wf,
right-endpoint_wf,
rless-int,
int_seg_properties,
decidable__lt,
rless_wf,
int-to-real_wf,
icompact-endpoints-rleq,
icompact-endpoints,
less_than_wf,
length_wf,
rsub_wf,
partitions_wf,
nat_plus_wf,
icompact_wf,
interval_wf,
mklist_length,
sq_stable__less_than,
real_wf,
int_seg_wf,
lelt_wf,
rleq_wf,
squash_wf,
true_wf,
mklist_select,
iff_weakening_equal,
req_wf,
req-int,
decidable__equal_int,
intformeq_wf,
itermAdd_wf,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
uiff_transitivity,
req_functionality,
rsub-int,
radd_functionality,
req_weakening,
radd-int,
rleq_functionality,
rdiv_functionality,
rmul_functionality,
equal_wf,
rmul-distrib2,
nat_wf,
rmul_preserves_rleq,
rinv_wf2,
rmul_preserves_rleq2,
rleq-int,
nat_properties,
less_than'_wf,
rleq-implies-rleq,
real_term_polynomial,
itermMultiply_wf,
real_term_value_const_lemma,
real_term_value_sub_lemma,
real_term_value_mul_lemma,
real_term_value_var_lemma,
real_term_value_add_lemma,
req-iff-rsub-is-0,
req_transitivity,
rmul-rinv3,
false_wf,
rminus_wf,
rleq_weakening,
itermMinus_wf,
real_term_value_minus_lemma,
rminus_functionality,
rleq_functionality_wrt_implies,
rleq_weakening_equal,
radd_functionality_wrt_rleq,
subtract-add-cancel,
trivial-int-eq1
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
dependent_set_memberEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
setElimination,
rename,
hypothesis,
natural_numberEquality,
hypothesisEquality,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
inrFormation,
productElimination,
independent_functionElimination,
lambdaFormation,
addEquality,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
imageMemberEquality,
baseClosed,
imageElimination,
universeEquality,
applyLambdaEquality,
independent_pairEquality,
minusEquality
Latex:
\mforall{}[I:Interval]. \mforall{}[k:\mBbbN{}\msupplus{}]. (uniform-partition(I;k) \mmember{} partition(I)) supposing icompact(I)
Date html generated:
2017_10_03-AM-09_43_42
Last ObjectModification:
2017_07_28-AM-07_57_56
Theory : reals
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