Nuprl Lemma : cantor_ivl_wf
∀[a,b:ℝ]. ∀[f:ℕ ⟶ 𝔹]. ∀[n:ℕ]. (cantor_ivl(a;b;f;n) ∈ ℝ × ℝ)
Proof
Definitions occuring in Statement :
cantor_ivl: cantor_ivl(a;b;f;n),
real: ℝ,
nat: ℕ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
int_nzero: ℤ-o,
true: True,
nequal: a ≠ b ∈ T ,
not: ¬A,
implies: P ⇒ Q,
uimplies: b supposing a,
sq_type: SQType(T),
all: ∀x:A. B[x],
guard: {T},
false: False,
prop: ℙ,
cantor_ivl: cantor_ivl(a;b;f;n),
has-value: (a)↓
Lemmas referenced :
exp-fastexp,
exp_wf3,
subtype_base_sq,
int_subtype_base,
equal_wf,
true_wf,
nequal_wf,
unit-interval-fan_wf,
value-type-has-value,
int-value-type,
fastexp_wf,
subtract_wf,
int-rdiv_wf,
radd_wf,
int-rmul_wf,
nat_wf,
bool_wf,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalTransitivity,
computationStep,
isectElimination,
thin,
natural_numberEquality,
hypothesisEquality,
hypothesis,
dependent_set_memberEquality,
because_Cache,
addLevel,
lambdaFormation,
instantiate,
cumulativity,
intEquality,
independent_isectElimination,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
voidElimination,
isect_memberFormation,
introduction,
spreadEquality,
callbyvalueReduce,
independent_pairEquality,
axiomEquality,
isect_memberEquality,
functionEquality
Latex:
\mforall{}[a,b:\mBbbR{}]. \mforall{}[f:\mBbbN{} {}\mrightarrow{} \mBbbB{}]. \mforall{}[n:\mBbbN{}]. (cantor\_ivl(a;b;f;n) \mmember{} \mBbbR{} \mtimes{} \mBbbR{})
Date html generated:
2016_05_18-AM-10_55_32
Last ObjectModification:
2015_12_27-PM-10_43_44
Theory : reals
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