Nuprl Lemma : max-metric_wf
∀[n:ℕ]. (max-metric(n) ∈ metric(ℝ^n))
Proof
Definitions occuring in Statement :
max-metric: max-metric(n),
real-vec: ℝ^n,
metric: metric(X),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
max-metric: max-metric(n),
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,
metric: metric(X),
le: A ≤ B,
less_than': less_than'(a;b),
cand: A c∧ B,
uiff: uiff(P;Q),
squash: ↓T,
decidable: Dec(P),
or: P ∨ Q,
real-vec: ℝ^n,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
assert: ↑b,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
int_seg: {i..j-},
lelt: i ≤ j < k,
subtype_rel: A ⊆r B,
true: True,
rev_uimplies: rev_uimplies(P;Q),
absval: |i|,
req_int_terms: t1 ≡ t2,
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,
primrec0_lemma,
int-to-real_wf,
real-vec_wf,
istype-le,
trivial-rleq-radd,
rleq_weakening_equal,
req_weakening,
rleq_wf,
radd_wf,
req_wf,
subtract-1-ge-0,
primrec_wf,
real_wf,
decidable__le,
intformnot_wf,
int_formula_prop_not_lemma,
rmax_wf,
rabs_wf,
rsub_wf,
int_seg_wf,
primrec-unroll,
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,
istype-nat,
subtract_wf,
itermSubtract_wf,
int_term_value_subtract_lemma,
decidable__lt,
real-vec-subtype,
rmax-req2,
rleq-int,
istype-false,
req_functionality,
rmax_functionality,
req_transitivity,
rabs_functionality,
squash_wf,
true_wf,
rabs-int,
req-iff-rsub-is-0,
real_polynomial_null,
real_term_value_sub_lemma,
real_term_value_var_lemma,
real_term_value_const_lemma,
rleq_functionality_wrt_implies,
r-triangle-inequality2,
rleq_functionality,
radd_functionality,
rabs-difference-symmetry,
rmax_lb,
radd_functionality_wrt_rleq,
rleq-rmax
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,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionIsTypeImplies,
inhabitedIsType,
dependent_set_memberEquality_alt,
because_Cache,
productElimination,
productIsType,
functionIsType,
applyEquality,
applyLambdaEquality,
imageMemberEquality,
baseClosed,
imageElimination,
unionElimination,
closedConclusion,
equalityElimination,
equalityIstype,
promote_hyp,
instantiate,
cumulativity,
minusEquality
Latex:
\mforall{}[n:\mBbbN{}]. (max-metric(n) \mmember{} metric(\mBbbR{}\^{}n))
Date html generated:
2019_10_30-AM-08_35_26
Last ObjectModification:
2019_10_02-AM-11_01_41
Theory : reals
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