Nuprl Lemma : constant-mconverges-to
∀[X:Type]. ∀[d:metric(X)]. ∀[y:X]. lim n→∞.y = y
Proof
Definitions occuring in Statement :
mconverges-to: lim n→∞.x[n] = y,
metric: metric(X),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
mconverges-to: lim n→∞.x[n] = y,
all: ∀x:A. B[x],
sq_exists: ∃x:A [B[x]],
member: t ∈ T,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
not: ¬A,
implies: P ⇒ Q,
false: False,
nat_plus: ℕ+,
uimplies: b supposing a,
rneq: x ≠ y,
guard: {T},
or: P ∨ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
ge: i ≥ j ,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
prop: ℙ,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
istype-void,
istype-le,
istype-nat,
rleq_wf,
mdist_wf,
rdiv_wf,
int-to-real_wf,
rless-int,
nat_properties,
nat_plus_properties,
decidable__lt,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformless_wf,
itermConstant_wf,
itermVar_wf,
istype-int,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
rless_wf,
nat_plus_wf,
metric_wf,
istype-universe,
rleq-int-fractions2,
decidable__le,
intformle_wf,
itermMultiply_wf,
int_formula_prop_le_lemma,
int_term_value_mul_lemma,
rleq_functionality,
mdist-same,
req_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
lambdaFormation_alt,
dependent_set_memberFormation_alt,
dependent_set_memberEquality_alt,
natural_numberEquality,
independent_pairFormation,
sqequalRule,
sqequalHypSubstitution,
voidElimination,
cut,
introduction,
extract_by_obid,
hypothesis,
isectElimination,
thin,
hypothesisEquality,
setElimination,
rename,
functionIsType,
because_Cache,
universeIsType,
closedConclusion,
independent_isectElimination,
inrFormation_alt,
dependent_functionElimination,
productElimination,
independent_functionElimination,
unionElimination,
approximateComputation,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
isect_memberEquality_alt,
instantiate,
universeEquality,
multiplyEquality
Latex:
\mforall{}[X:Type]. \mforall{}[d:metric(X)]. \mforall{}[y:X]. lim n\mrightarrow{}\minfty{}.y = y
Date html generated:
2019_10_30-AM-06_38_46
Last ObjectModification:
2019_10_02-AM-10_51_43
Theory : reals
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