Nuprl Lemma : trivial-partition_wf
∀[I:Interval]. trivial-partition(I) ∈ partition(I) supposing i-finite(I)
Proof
Definitions occuring in Statement :
trivial-partition: trivial-partition(I),
partition: partition(I),
i-finite: i-finite(I),
interval: Interval,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
bfalse: ff,
cons: [a / b],
btrue: tt,
ifthenelse: if b then t else f fi ,
assert: ↑b,
le: A ≤ B,
so_apply: x[s],
or: P ∨ Q,
decidable: Dec(P),
so_lambda: λ2x.t[x],
less_than': less_than'(a;b),
squash: ↓T,
less_than: a < b,
prop: ℙ,
false: False,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
lelt: i ≤ j < k,
int_seg: {i..j-},
guard: {T},
implies: P ⇒ Q,
cand: A c∧ B,
and: P ∧ Q,
so_apply: x[s1;s2],
top: Top,
so_lambda: λ2x y.t[x; y],
it: ⋅,
nil: [],
all: ∀x:A. B[x],
select: L[n],
frs-non-dec: frs-non-dec(L),
partitions: partitions(I;p),
partition: partition(I),
trivial-partition: trivial-partition(I),
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
interval_wf,
i-finite_wf,
right-endpoint_wf,
length_of_cons_lemma,
null_cons_lemma,
product_subtype_list,
null_nil_lemma,
list-cases,
last_wf,
false_wf,
left-endpoint_wf,
decidable__lt,
int_formula_prop_not_lemma,
intformnot_wf,
decidable__le,
select_wf,
rleq_wf,
length_wf,
all_wf,
less_than_wf,
int_seg_wf,
le_wf,
int_formula_prop_wf,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_and_lemma,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
intformand_wf,
full-omega-unsat,
int_seg_properties,
base_wf,
stuck-spread,
length_of_nil_lemma,
real_wf,
nil_wf
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesis_subsumption,
promote_hyp,
unionElimination,
functionEquality,
productEquality,
imageElimination,
independent_pairFormation,
dependent_functionElimination,
intEquality,
int_eqEquality,
lambdaEquality,
dependent_pairFormation,
independent_functionElimination,
approximateComputation,
productElimination,
rename,
setElimination,
hypothesisEquality,
because_Cache,
natural_numberEquality,
voidEquality,
voidElimination,
isect_memberEquality,
lambdaFormation,
independent_isectElimination,
baseClosed,
hypothesis,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
dependent_set_memberEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[I:Interval]. trivial-partition(I) \mmember{} partition(I) supposing i-finite(I)
Date html generated:
2018_05_22-PM-02_07_43
Last ObjectModification:
2018_05_21-AM-00_19_14
Theory : reals
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