Nuprl Lemma : simplex-metric_wf
∀[n:ℤ]. (simplex-metric(n) ∈ metric(Δ(n)))
Proof
Definitions occuring in Statement :
simplex-metric: simplex-metric(n),
std-simplex: Δ(n),
metric: metric(X),
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
top: Top,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
simplex-metric: simplex-metric(n),
nat: ℕ,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
and: P ∧ Q,
prop: ℙ,
std-simplex: Δ(n)
Lemmas referenced :
decidable__lt,
istype-void,
metric-on-void,
std-simplex_wf,
std-simplex-void,
rn-metric_wf,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
intformless_wf,
istype-int,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
istype-le,
metric-on-subtype,
real-vec_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
natural_numberEquality,
hypothesis,
unionElimination,
isect_memberEquality_alt,
voidElimination,
applyEquality,
isectElimination,
independent_isectElimination,
because_Cache,
sqequalRule,
dependent_set_memberEquality_alt,
addEquality,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
independent_pairFormation,
universeIsType,
setElimination,
rename
Latex:
\mforall{}[n:\mBbbZ{}]. (simplex-metric(n) \mmember{} metric(\mDelta{}(n)))
Date html generated:
2019_10_30-AM-11_30_38
Last ObjectModification:
2019_08_02-PM-02_20_24
Theory : real!vectors
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