Nuprl Lemma : rat-interval-dimension-single
∀[a:ℚ]. (dim([a]) ~ 0)
Proof
Definitions occuring in Statement :
rat-interval-dimension: dim(I),
rat-point-interval: [a],
rationals: ℚ,
uall: ∀[x:A]. B[x],
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
top: Top,
satisfiable_int_formula: satisfiable_int_formula(fmla),
decidable: Dec(P),
lelt: i ≤ j < k,
rev_implies: P ⇐ Q,
not: ¬A,
assert: ↑b,
bnot: ¬bb,
sq_type: SQType(T),
or: P ∨ Q,
exists: ∃x:A. B[x],
bfalse: ff,
false: False,
ifthenelse: if b then t else f fi ,
iff: P ⇐⇒ Q,
guard: {T},
prop: ℙ,
and: P ∧ Q,
uiff: uiff(P;Q),
btrue: tt,
it: ⋅,
unit: Unit,
bool: 𝔹,
implies: P ⇒ Q,
all: ∀x:A. B[x],
rat-point-interval: [a],
rat-interval-dimension: dim(I),
so_apply: x[s],
so_lambda: λ2x.t[x],
int_seg: {i..j-},
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rationals_wf,
istype-less_than,
istype-le,
int_formula_prop_less_lemma,
intformless_wf,
decidable__lt,
int_formula_prop_wf,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
istype-void,
int_formula_prop_not_lemma,
itermConstant_wf,
intformle_wf,
intformnot_wf,
full-omega-unsat,
decidable__le,
qless_wf,
assert-bnot,
bool_subtype_base,
bool_wf,
bool_cases_sqequal,
eqff_to_assert,
qless_irreflexivity,
iff_weakening_equal,
assert-q_less-eq,
eqtt_to_assert,
q_less_wf,
int_subtype_base,
istype-int,
lelt_wf,
set_subtype_base,
int_seg_wf,
subtype_base_sq
Rules used in proof :
axiomSqEquality,
productIsType,
isect_memberEquality_alt,
approximateComputation,
independent_pairFormation,
dependent_set_memberEquality_alt,
universeIsType,
dependent_functionElimination,
promote_hyp,
equalityIstype,
dependent_pairFormation_alt,
voidElimination,
independent_functionElimination,
because_Cache,
productElimination,
equalitySymmetry,
equalityTransitivity,
equalityElimination,
unionElimination,
lambdaFormation_alt,
inhabitedIsType,
hypothesisEquality,
lambdaEquality_alt,
intEquality,
sqequalRule,
independent_isectElimination,
hypothesis,
natural_numberEquality,
cumulativity,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
instantiate,
thin,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[a:\mBbbQ{}]. (dim([a]) \msim{} 0)
Date html generated:
2019_10_29-AM-07_48_01
Last ObjectModification:
2019_10_17-PM-03_27_15
Theory : rationals
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