Nuprl Lemma : unit-interval-fan_wf
∀[f:ℕ ⟶ 𝔹]. ∀[n:ℕ]. (unit-interval-fan(f;n) ∈ ℤ × ℤ)
Proof
Definitions occuring in Statement :
unit-interval-fan: unit-interval-fan(f;n),
nat: ℕ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x],
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
unit-interval-fan: unit-interval-fan(f;n),
subtype_rel: A ⊆r B,
nat: ℕ,
uimplies: b supposing a,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
all: ∀x:A. B[x],
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
has-value: (a)↓,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b
Lemmas referenced :
primrec_wf,
nat_wf,
int_seg_subtype_nat,
false_wf,
bool_wf,
eqtt_to_assert,
value-type-has-value,
int-value-type,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
int_seg_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
productEquality,
intEquality,
because_Cache,
hypothesisEquality,
independent_pairEquality,
natural_numberEquality,
lambdaEquality,
productElimination,
applyEquality,
functionExtensionality,
hypothesis,
setElimination,
rename,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
unionElimination,
equalityElimination,
callbyvalueReduce,
addEquality,
multiplyEquality,
equalityTransitivity,
equalitySymmetry,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
voidElimination,
axiomEquality,
isect_memberEquality,
functionEquality
Latex:
\mforall{}[f:\mBbbN{} {}\mrightarrow{} \mBbbB{}]. \mforall{}[n:\mBbbN{}]. (unit-interval-fan(f;n) \mmember{} \mBbbZ{} \mtimes{} \mBbbZ{})
Date html generated:
2017_10_03-AM-09_48_31
Last ObjectModification:
2017_07_28-AM-08_00_34
Theory : reals
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