Nuprl Lemma : max-metric-leq-rn-metric
∀[n:ℕ]. max-metric(n) ≤ rn-metric(n)
Proof
Definitions occuring in Statement :
max-metric: max-metric(n),
rn-metric: rn-metric(n),
real-vec: ℝ^n,
metric-leq: d1 ≤ d2,
nat: ℕ,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
rn-metric: rn-metric(n),
max-metric: max-metric(n),
metric-leq: d1 ≤ d2,
mdist: mdist(d;x;y),
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
all: ∀x:A. B[x],
top: Top,
and: P ∧ Q,
prop: ℙ,
rleq: x ≤ y,
rnonneg: rnonneg(x),
le: A ≤ B,
lt_int: i <z j,
subtract: n - m,
ifthenelse: if b then t else f fi ,
btrue: tt,
less_than': less_than'(a;b),
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
bfalse: ff,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
decidable: Dec(P),
real-vec: ℝ^n,
int_seg: {i..j-},
lelt: i ≤ j < k,
subtype_rel: A ⊆r B,
cand: A c∧ B,
nat_plus: ℕ+,
rev_uimplies: rev_uimplies(P;Q),
rge: x ≥ y
Lemmas referenced :
nat_properties,
full-omega-unsat,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
istype-less_than,
le_witness_for_triv,
primrec-unroll,
real-vec-dist-nonneg,
istype-le,
real-vec_wf,
subtract-1-ge-0,
lt_int_wf,
eqtt_to_assert,
assert_of_lt_int,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert-bnot,
iff_weakening_uiff,
assert_wf,
less_than_wf,
rmax_lb,
primrec_wf,
real_wf,
subtract_wf,
decidable__le,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
int-to-real_wf,
rmax_wf,
rabs_wf,
rsub_wf,
decidable__lt,
int_seg_wf,
real-vec-dist_wf,
rleq-real-vec-dist,
istype-nat,
real-vec-subtype,
real-vec-dist-monotone-in-dim,
rleq_functionality_wrt_implies,
rleq_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
lambdaFormation_alt,
natural_numberEquality,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
dependent_functionElimination,
isect_memberEquality_alt,
voidElimination,
independent_pairFormation,
universeIsType,
productElimination,
equalityTransitivity,
equalitySymmetry,
functionIsTypeImplies,
inhabitedIsType,
because_Cache,
dependent_set_memberEquality_alt,
unionElimination,
equalityElimination,
equalityIstype,
promote_hyp,
instantiate,
cumulativity,
closedConclusion,
applyEquality,
productIsType
Latex:
\mforall{}[n:\mBbbN{}]. max-metric(n) \mleq{} rn-metric(n)
Date html generated:
2019_10_30-AM-08_36_47
Last ObjectModification:
2019_10_02-AM-11_02_37
Theory : reals
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