Nuprl Lemma : proj-norm-positive
∀n:ℕ. ∀a:ℙ^n. (r0 < ||a||)
Proof
Definitions occuring in Statement :
real-proj: ℙ^n,
real-vec-norm: ||x||,
rless: x < y,
int-to-real: r(n),
nat: ℕ,
all: ∀x:A. B[x],
add: n + m,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
real-proj: ℙ^n,
member: t ∈ T,
uall: ∀[x:A]. B[x],
nat: ℕ,
ge: i ≥ j ,
exists: ∃x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
top: Top,
and: P ∧ Q,
prop: ℙ,
sq_stable: SqStable(P),
squash: ↓T,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
real-vec: ℝ^n
Lemmas referenced :
sq_stable__rless,
int-to-real_wf,
real-vec-norm_wf,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
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_wf,
le_wf,
real-proj_wf,
nat_wf,
real-vec-norm-positive-iff,
rneq_wf,
rneq-symmetry
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
setElimination,
thin,
rename,
cut,
introduction,
extract_by_obid,
dependent_functionElimination,
isectElimination,
natural_numberEquality,
hypothesis,
dependent_set_memberEquality,
addEquality,
hypothesisEquality,
productElimination,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
imageMemberEquality,
baseClosed,
imageElimination,
applyEquality,
because_Cache
Latex:
\mforall{}n:\mBbbN{}. \mforall{}a:\mBbbP{}\^{}n. (r0 < ||a||)
Date html generated:
2017_10_05-AM-00_17_03
Last ObjectModification:
2017_06_18-PM-00_51_42
Theory : inner!product!spaces
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