Nuprl Lemma : rv-norm0
∀[rv:InnerProductSpace]. (||0|| = r0)
Proof
Definitions occuring in Statement :
rv-norm: ||x||,
inner-product-space: InnerProductSpace,
rv-0: 0,
req: x = y,
int-to-real: r(n),
uall: ∀[x:A]. B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
sq_stable: SqStable(P),
squash: ↓T,
and: P ∧ Q,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
not: ¬A,
false: False,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
prop: ℙ,
nat_plus: ℕ+,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
true: True,
guard: {T}
Lemmas referenced :
rv-norm_wf,
rv-0_wf,
req_witness,
inner-product-space_subtype,
int-to-real_wf,
inner-product-space_wf,
sq_stable__req,
req_wf,
rmul_wf,
rv-ip_wf,
square-req-iff,
rleq_weakening_equal,
req_functionality,
rnexp_wf,
istype-void,
istype-le,
exp_wf2,
req_weakening,
rnexp-int,
squash_wf,
true_wf,
real_wf,
istype-int,
exp-zero,
decidable__lt,
full-omega-unsat,
intformnot_wf,
intformless_wf,
itermConstant_wf,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
istype-less_than,
subtype_rel_self,
iff_weakening_equal,
rnexp2,
iff_weakening_uiff,
rv-ip0
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
because_Cache,
hypothesis,
sqequalRule,
inhabitedIsType,
lambdaFormation_alt,
equalityIstype,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
lambdaEquality_alt,
setElimination,
rename,
natural_numberEquality,
universeIsType,
imageMemberEquality,
baseClosed,
imageElimination,
productElimination,
independent_isectElimination,
dependent_set_memberEquality_alt,
independent_pairFormation,
voidElimination,
unionElimination,
approximateComputation,
dependent_pairFormation_alt,
Error :memTop,
instantiate,
universeEquality,
promote_hyp
Latex:
\mforall{}[rv:InnerProductSpace]. (||0|| = r0)
Date html generated:
2020_05_20-PM-01_11_26
Last ObjectModification:
2019_12_09-PM-11_48_31
Theory : inner!product!spaces
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